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Dec 2002

Volume 43, Issue 12, pp. 5857-6385

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Wigner functions for curved spaces. I. On hyperboloids

Miguel Angel Alonso, George S. Pogosyan, and Kurt Bernardo Wolf

J. Math. Phys. 43, 5857 (2002); http://dx.doi.org/10.1063/1.1518139 (15 pages) | Cited 12 times

Online Publication Date: 25 November 2002

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We propose a Wigner quasiprobability distribution function for Hamiltonian systems in spaces of constant curvature, in this article on hyperboloids, which returns the correct marginals and has the covariance of the Shapiro functions under SO(D,1) transformations. To the free systems obeying the Laplace–Beltrami equation on the hyperboloid, we add a conic-oscillator potential in the hyperbolic coordinate. As an example, we analyze the one-dimensional case on a hyperbola branch, where this conic-oscillator is the Pöschl–Teller potential. We present the analytical solutions and plot the computed results. The standard theory of quantum oscillators is regained in the contraction limit to the space of zero curvature. © 2002 American Institute of Physics.
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03.65.Db Functional analytical methods
02.20.Uw Quantum groups
02.50.Ng Distribution theory and Monte Carlo studies

Fixed points of quantum operations

A. Arias, A. Gheondea, and S. Gudder

J. Math. Phys. 43, 5872 (2002); http://dx.doi.org/10.1063/1.1519669 (10 pages) | Cited 27 times

Online Publication Date: 25 November 2002

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Quantum operations frequently occur in quantum measurement theory, quantum probability, quantum computation, and quantum information theory. If an operator A is invariant under a quantum operation ϕ, we call A a ϕ-fixed point. Physically, the ϕ-fixed points are the operators that are not disturbed by the action of ϕ. Our main purpose is to answer the following question. If A is a ϕ-fixed point, is A compatible with the operation elements of ϕ? We shall show in general that the answer is no and we shall give some sufficient conditions under which the answer is yes. Our results will follow from some general theorems concerning completely positive maps and injectivity of operator systems and von Neumann algebras. © 2002 American Institute of Physics.
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03.65.Fd Algebraic methods
02.10.-v Logic, set theory, and algebra

Classicality criteria

Nuno Costa Dias

J. Math. Phys. 43, 5882 (2002); http://dx.doi.org/10.1063/1.1516626 (20 pages)

Online Publication Date: 25 November 2002

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We present two possible criteria quantifying the degree of classicality of an arbitrary (finite dimensional) dynamical system. The inputs for these criteria are the classical dynamical structure of the system together with the quantum and the classical data providing the two alternative descriptions of its initial time configuration. It is proved that a general quantum system satisfying the criteria up to some extend displays a time evolution consistent with the classical predictions up to some degree and thus it is argued that the criteria provide a suitable measure of classicality. The features of the formalism are illustrated through two simple examples. © 2002 American Institute of Physics.
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03.65.Sq Semiclassical theories and applications
03.65.Ta Foundations of quantum mechanics; measurement theory

Superintegrability with third-order integrals in quantum and classical mechanics

Simon Gravel and Pavel Winternitz

J. Math. Phys. 43, 5902 (2002); http://dx.doi.org/10.1063/1.1514385 (11 pages) | Cited 52 times

Online Publication Date: 25 November 2002

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We consider here the coexistence of first- and third-order integrals of motion in two-dimensional classical and quantum mechanics. We find explicitly all potentials that admit such integrals, and all their integrals. Quantum superintegrable systems are found that have no classical analog, i.e., the potentials are proportional to ℏ2, so their classical limit is free motion. © 2002 American Institute of Physics.
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03.65.Ca Formalism
45.20.Jj Lagrangian and Hamiltonian mechanics

Convexity and potential sums for Salpeter-type Hamiltonians

Richard L. Hall, Wolfgang Lucha, and Franz F. Schöberl

J. Math. Phys. 43, 5913 (2002); http://dx.doi.org/10.1063/1.1515381 (13 pages) | Cited 7 times

Online Publication Date: 25 November 2002

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The semirelativistic Hamiltonian H = βmath+V(r), where V(r) is a central potential in math3, is concave in p2 and convex in p ≡ math. This fact enables us to obtain complementary energy bounds for the discrete spectrum of H. By extending the notion of “kinetic potential” we are able to find general energy bounds on the ground-state energy E corresponding to potentials with the form V = ∑iaif(i)(r). In the case of sums of powers and the log potential, where V(r) = ∑q ≠ 0a(q)sgn(q)r q+a(0)ln(r), the bounds can all be expressed in the semiclassical form E ≈ minr{βmath+∑q ≠ 0a(q)sgn(q)(rP(q))q+a(0)ln(rP(0))}. “Upper” and “lower” P numbers are provided for q = −1,1,2, and for the log potential q = 0. Some specific examples are discussed, to show the quality of the bounds. © 2002 American Institute of Physics.
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03.65.Sq Semiclassical theories and applications
03.65.Ge Solutions of wave equations: bound states

Magnetic translation groups in an n-dimensional torus and their representations

Shogo Tanimura

J. Math. Phys. 43, 5926 (2002); http://dx.doi.org/10.1063/1.1513208 (23 pages) | Cited 5 times

Online Publication Date: 25 November 2002

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A charged particle in a uniform magnetic field in a two-dimensional torus has a discrete noncommutative translation symmetry instead of a continuous commutative translation symmetry. We study topology and symmetry of a particle in a magnetic field in a torus of arbitrary dimensions. The magnetic translation group (MTG) is defined as a group of translations that leave the gauge field invariant. We show that the MTG in an n-dimensional torus is isomorphic to a central extension of a cyclic group Zν1×⋯×Zν2l×Tm by U(1) with 2l+m = n. We construct and classify irreducible unitary representations of the MTG in a three-torus and apply the representation theory to three examples. We briefly describe a representation theory for a general n-torus. The MTG in an n-torus can be regarded as a generalization of the so-called noncommutative torus. © 2002 American Institute of Physics.
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12.20.Ds Specific calculations
11.15.Kc Classical and semiclassical techniques
02.40.Gh Noncommutative geometry
11.30.Ly Other internal and higher symmetries

Theory and application of Fermi pseudo-potential in one dimension

Tai Tsun Wu and Ming Lun Yu

J. Math. Phys. 43, 5949 (2002); http://dx.doi.org/10.1063/1.1519940 (28 pages) | Cited 9 times

Online Publication Date: 25 November 2002

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The theory of interaction at one point is developed for the one-dimensional Schrödinger equation. In analog with the three-dimensional case, the resulting interaction is referred to as the Fermi pseudo-potential. The dominant feature of this one-dimensional problem comes from the fact that the real line becomes disconnected when one point is removed. The general interaction at one point is found to be the sum of three terms, the well-known delta-function potential and two Fermi pseudo-potentials, one odd under space reflection and the other even. The odd one gives the proper interpretation for the δ′(x) potential, while the even one is unexpected and more interesting. Among the many applications of these Fermi pseudo-potentials, the simplest one is described. It consists of a superposition of the delta-function potential and the even pseudo-potential applied to two-channel scattering. This simplest application leads to a model of the quantum memory, an essential component of any quantum computer. © 2002 American Institute of Physics.
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03.67.Lx Quantum computation architectures and implementations
03.65.Ge Solutions of wave equations: bound states

Extension of Bethe ansatz to multiple occupancies for one-dimensional SU(4) fermions with δ-function interaction

Zu-Jian Ying, You-Quan Li, Shi-Jian Gu, and Bin Chen

J. Math. Phys. 43, 5977 (2002); http://dx.doi.org/10.1063/1.1515380 (10 pages) | Cited 1 time

Online Publication Date: 25 November 2002

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We consider the problem of consistence between the Bethe ansatz (BA) wave function and the multiparticle (more than two) scattering in one-dimensional δ-function interacting SU(4) fermions, which the approach of BA does not explicitly take into account. We find the scattering conditions of three and four particles located at the same position and show that the conditions can be fulfilled by the two-particle connection conditions of the BA wave function. So the definition of the BA wave function can be exactly extended to those cases with multiple occupancies. The inconsistence between the BA and multiparticle interacting on a same site in the degenerate Hubbard model, which makes the BA fail for the model, is shown to vanish in the limit of small site spacing. A correspondence relation of the BA equation and SU(4) symmetry of the system is also indicated for the fermions. The degeneracy of state with BA eigenenergy is given. Singlet lies in the case when there are equal numbers of particles in each inner component. © 2002 American Institute of Physics.
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75.10.Jm Quantized spin models, including quantum spin frustration
03.65.Nk Scattering theory
05.30.Fk Fermion systems and electron gas
02.20.Sv Lie algebras of Lie groups
11.30.Hv Flavor symmetries
02.10.Ud Linear algebra
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Results on the Wess–Zumino consistency condition for arbitrary Lie algebras

A. Barkallil, G. Barnich, and C. Schomblond

J. Math. Phys. 43, 5987 (2002); http://dx.doi.org/10.1063/1.1513209 (29 pages) | Cited 2 times

Online Publication Date: 25 November 2002

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The so-called covariant Poincaré lemma on the induced cohomology of the space–time exterior derivative in the cohomology of the gauge part of the BRST differential is extended to cover the case of arbitrary, nonreductive Lie algebras. As a consequence, the general solution of the Wess–Zumino consistency condition with a nontrivial descent can, for arbitrary (super) Lie algebras, be computed in the small algebra of the one-form potentials, the ghosts and their exterior derivatives. For particular Lie algebras that are the semidirect sum of a semisimple Lie subalgebra with an ideal, a theorem by Hochschild and Serre is used to characterize more precisely the cohomology of the gauge part of the BRST differential in the small algebra. In the case of an Abelian ideal, this leads to a complete solution of the Wess–Zumino consistency condition in this space. As an application, the consistent deformations of 2+1 dimensional Chern–Simons theory based on iso(2,1) are rediscussed.© 2002 American Institute of Physics.
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11.10.Lm Nonlinear or nonlocal theories and models
11.15.-q Gauge field theories
11.30.Pb Supersymmetry
02.20.Sv Lie algebras of Lie groups
11.10.Jj Asymptotic problems and properties
11.10.Gh Renormalization

Black-brane solution for C2 algebra

M. A. Grebeniuk, V. D. Ivashchuk, and S.-W. Kim

J. Math. Phys. 43, 6016 (2002); http://dx.doi.org/10.1063/1.1513654 (8 pages) | Cited 3 times

Online Publication Date: 25 November 2002

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Black p-brane solutions for a wide class of intersection rules and Ricci-flat “internal” spaces are considered. They are defined up to moduli functions Hs obeying nonlinear differential equations with certain boundary conditions imposed. A new solution with intersections corresponding to the Lie algebra C2 is obtained. The functions H1 and H2 for this solution are polynomials of degree 3 and 4. © 2002 American Institute of Physics.
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11.27.+d Extended classical solutions; cosmic strings, domain walls, texture
02.20.Sv Lie algebras of Lie groups

Cluster properties in relativistic quantum mechanics of N-particle systems

W. N. Polyzou

J. Math. Phys. 43, 6024 (2002); http://dx.doi.org/10.1063/1.1516627 (40 pages) | Cited 7 times

Online Publication Date: 25 November 2002

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A general technique is presented for constructing a quantum theory of a finite number of interacting particles satisfying Poincaré invariance, cluster separability, and the spectral condition. Irreducible representations and Clebsch–Gordan coefficients of the Poincaré group are the central elements of the construction. A different realization of the dynamics is obtained for each basis of an irreducible representation of the Poincaré group. Unitary operators that relate the different realizations of the dynamis are constructed. This technique is distinguished from other solutions [S. N. Sokolov, Dokl. Akad. Nauk USSR 233, 575 (1977); F. Coester and W. N. Polyzou, Phys. Rev. D 26, 1348 (1982)] of this problem because it does not depend on the kinematic subgroups of Dirac’s forms [P. A. M. Dirac, Rev. Mod. Phys. 21, 392 (1949)] of dynamics. Special basis choices lead to kinematic subgroups. © 2002 American Institute of Physics.
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03.65.Fd Algebraic methods
02.20.-a Group theory

Exactly solvable models of relativistic δ-sphere interactions in quantum mechanics

J. Shabani and A. Vyabandi

J. Math. Phys. 43, 6064 (2002); http://dx.doi.org/10.1063/1.1518785 (21 pages) | Cited 1 time

Online Publication Date: 25 November 2002

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We discuss the quantum Hamiltonian math describing a δ-sphere interaction introduced in [J. Math. Phys 30, 2275 (1989)] and formally given by math = HD+mathδ(∣x∣−R), where HD is the Dirac Hamiltonian and math is a real 4×4 matrix defined by math = (0A B0). We obtain a series of new results for this model, in particular the resolvent equation, the spectral properties, the nonrelativistic limit and the various quantities related to the scattering theory. These results are generalized to the case of an asymmetric δ-sphere interaction and a δ-sphere plus Coulomb interaction, respectively. © 2002 American Institute of Physics.
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03.65.Fd Algebraic methods
03.30.+p Special relativity

Boundary states, extended symmetry algebra, and module structure for certain rational torus models

Ioannis Smyrnakis

J. Math. Phys. 43, 6085 (2002); http://dx.doi.org/10.1063/1.1517168 (11 pages) | Cited 1 time

Online Publication Date: 25 November 2002

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The massless bosonic field compactified on the circle of rational R2 is reexamined in the presense of boundaries. A particular class of models corresponding to R2 = 1/2k is distinguished by demanding the existence of a consistent set of Neumann boundary states. The boundary states are constructed explicitly for these models and the fusion rules are derived from them. These are the ones prescribed by the Verlinde formula from the S-matrix of the theory. In addition, the extended symmetry algebra of these theories is constructed, which is responsible for the rationality of these theories. Finally, the chiral space of these models is shown to split into a direct sum of irreducible modules of the extended symmetry algebra.© 2002 American Institute of Physics.
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11.25.Hf Conformal field theory, algebraic structures
11.30.Ly Other internal and higher symmetries
11.30.Rd Chiral symmetries
11.10.St Bound and unstable states; Bethe-Salpeter equations
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Scalar-tensor gravity and conformal continuations

K. A. Bronnikov

J. Math. Phys. 43, 6096 (2002); http://dx.doi.org/10.1063/1.1519667 (20 pages) | Cited 6 times

Online Publication Date: 25 November 2002

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Global properties of vacuum static, spherically symmetric configurations are studied in a general class of scalar-tensor theories (STTs) of gravity in various dimensions. The conformal mapping between the Jordan and Einstein frames is used as a tool. Necessary and sufficient conditions are found for the existence of solutions admitting a conformal continuation (CC). The latter means that a singularity in the Einstein-frame manifold maps to a regular surface mathtrans in the Jordan frame, and the solution is then continued beyond this surface. mathtrans can be an ordinary regular sphere or a horizon. In the second case, mathtrans connect two epochs of a Kantowski-Sachs type cosmology. It is shown that the list of possible types of global causal structure of vacuum space–times in any STT, with any potential function U(ϕ), is the same as in general relativity with a cosmological constant. This is even true for conformally continued solutions. A traversable wormhole is shown to be one of the generic structures created as a result of CC. Two explicit examples are presented: the known solution for a conformal field in general relativity, illustrating the emergence of singularities and wormholes due to CC, and a nonsingular three-dimensional model with an infinite sequence of CCs.© 2002 American Institute of Physics.
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04.50.-h Higher-dimensional gravity and other theories of gravity
11.10.-z Field theory
98.80.Jk Mathematical and relativistic aspects of cosmology
98.80.Qc Quantum cosmology
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On the nonlocal equations and nonlocal charges associated with the Harry Dym hierarchy

J. C. Brunelli and G. A. T. F. da Costa

J. Math. Phys. 43, 6116 (2002); http://dx.doi.org/10.1063/1.1512974 (13 pages) | Cited 12 times

Online Publication Date: 25 November 2002

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A large class of nonlocal equations and nonlocal charges for the Harry Dym hierarchy is exhibited. They are obtained from nonlocal Casimirs associated with its bi-Hamiltonian structure. The Lax representation for some of these equations is also given. © 2002 American Institute of Physics.
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05.45.Yv Solitons
02.30.Hq Ordinary differential equations
02.30.Jr Partial differential equations

Infinite symmetries and conservation laws

V. Rosenhaus

J. Math. Phys. 43, 6129 (2002); http://dx.doi.org/10.1063/1.1517394 (22 pages) | Cited 7 times

Online Publication Date: 25 November 2002

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We will consider partial differential equations of a variational problem whose symmetry group generators contain arbitrary function(s) of one or more independent variables. Unlike the Second Noether Theorem we will be interested in the case of arbitrary functions of not all base variables. We will study the relations between infinite symmetries and local conservation laws. We will demonstrate that infinite symmetries may lead to a finite number of conservation laws through appropriate boundary conditions, or to a set of additional constraints for the function and its derivatives. © 2002 American Institute of Physics.
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11.15.-q Gauge field theories
11.30.-j Symmetry and conservation laws
02.30.Jr Partial differential equations
02.20.Uw Quantum groups
02.30.Xx Calculus of variations

Soliton-like solutions of higher order wave equations of the Korteweg–de Vries type

E. Tzirtzilakis, V. Marinakis, C. Apokis, and T. Bountis

J. Math. Phys. 43, 6151 (2002); http://dx.doi.org/10.1063/1.1514387 (15 pages) | Cited 12 times

Online Publication Date: 25 November 2002

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In this work we study second and third order approximations of water wave equations of the Korteweg–de Vries (KdV) type. First we derive analytical expressions for solitary wave solutions for some special sets of parameters of the equations. Remarkably enough, in all these approximations, the form of the solitary wave and its amplitude-velocity dependence are identical to the sech2 formula of the one-soliton solution of the KdV. Next we carry out a detailed numerical study of these solutions using a Fourier pseudospectral method combined with a finite-difference scheme, in parameter regions where soliton-like behavior is observed. In these regions, we find solitary waves which are stable and behave like solitons in the sense that they remain virtually unchanged under time evolution and mutual interaction. In general, these solutions sustain small oscillations in the form of radiation waves (trailing the solitary wave) and may still be regarded as stable, provided these radiation waves do not exceed a numerical stability threshold. Instability occurs at high enough wave speeds, when these oscillations exceed the stability threshold already at the outset, and manifests itself as a sudden increase of these oscillations followed by a blowup of the wave after relatively short time intervals. © 2002 American Institute of Physics.
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47.35.-i Hydrodynamic waves
02.60.Lj Ordinary and partial differential equations; boundary value problems
02.70.Bf Finite-difference methods
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Driven Newton equations and separable time-dependent potentials

Hans Lundmark and Stefan Rauch-Wojciechowski

J. Math. Phys. 43, 6166 (2002); http://dx.doi.org/10.1063/1.1514833 (29 pages) | Cited 4 times

Online Publication Date: 25 November 2002

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We present a class of time-dependent potentials in Rn that can be integrated by separation of variables: by embedding them into so-called cofactor pair systems of higher dimension, we are led to a time-dependent change of coordinates that allows the time variable to be separated off, leaving the remaining part in separable Stäckel form. © 2002 American Institute of Physics.
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45.05.+x General theory of classical mechanics of discrete systems
02.30.Jr Partial differential equations
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Uniqueness in MHD in divergence form: Right nullvectors and well-posedness

Maurice H. P. M. van Putten

J. Math. Phys. 43, 6195 (2002); http://dx.doi.org/10.1063/1.1510174 (14 pages) | Cited 2 times

Online Publication Date: 25 November 2002

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Magnetohydrodynamics in divergence form describes a hyperbolic system of covariant and constraint-free equations. It comprises a linear combination of an algebraic constraint and Faraday’s equations. Here, we study the problem of well-posedness, and identify a preferred linear combination in this divergence formulation. The limit of weak magnetic fields shows the slow magnetosonic and Alfvén waves to bifurcate from the contact discontinuity (entropy waves), while the fast magnetosonic wave is a regular perturbation of the hydrodynamical sound speed. These results are further reported as a starting point for characteristic based shock capturing schemes for simulations with ultra-relativistic shocks in magnetized relativistic fluids.© 2002 American Institute of Physics.
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52.30.Cv Magnetohydrodynamics (including electron magnetohydrodynamics)
52.35.Bj Magnetohydrodynamic waves (e.g., Alfven waves)
52.35.Fp Electrostatic waves and oscillations (e.g., ion-acoustic waves)
52.25.Kn Thermodynamics of plasmas
05.45.-a Nonlinear dynamics and chaos
52.35.Tc Shock waves and discontinuities
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Four-particle decay of the Bethe–Salpeter kernel in the high-temperature Ising model

F. Auil

J. Math. Phys. 43, 6209 (2002); http://dx.doi.org/10.1063/1.1510176 (15 pages)

Online Publication Date: 25 November 2002

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In this article we study the four-particle decay of the Bethe–Salpeter (B-S) kernel for the high-temperature Ising model. We use the hyperplane decoupling method [T. Spencer, Commun. Math. Phys. 44, 143 (1975); R. S. Schor, Nucl. Phys. B 222, 71 (1983)] to prove exponential decay in a set of variables particularly adapted to the methods of Spencer and Zirilli [Commun. Math. Phys. 49, 1 (1976)] for the analysis of scattering and bound states in QFT, transcribed to lattice theories by Auil and Barata [Ann. Henri Poincare 2, 1065 (2001)]. We study arbitrary derivatives of the general n-point correlation functions with respect to the interpolating variables, and we are able to obtain, in some cases, information about the third derivatives of the B-S kernel. As a later consequence, we have two-body asymptotic completeness for the (massive) Euclidean lattice field theory implemented by this model. This allows us to analyze the Ornstein–Zernike behavior of four-point functions, related to the specific heat of the model.© 2002 American Institute of Physics.
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75.10.Hk Classical spin models
05.50.+q Lattice theory and statistics (Ising, Potts, etc.)
75.40.Cx Static properties (order parameter, static susceptibility, heat capacities, critical exponents, etc.)

Central limit theorem for fluctuations in the high temperature region of the Sherrington–Kirkpatrick spin glass model

Francesco Guerra and Fabio Lucio Toninelli

J. Math. Phys. 43, 6224 (2002); http://dx.doi.org/10.1063/1.1515109 (14 pages) | Cited 5 times

Online Publication Date: 25 November 2002

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In a region above the Almeida–Thouless line, where we are able to control the thermodynamic limit of the Sherrington–Kirkpatrick model and to prove replica symmetry, we show that the fluctuations of the overlaps and of the free energy are Gaussian, on the scale 1/math, for large N. The method we employ is based on the idea we recently developed of introducing quadratic coupling between two replicas. The proof makes use of the cavity equations and of concentration of measure inequalities for the free energy. © 2002 American Institute of Physics.
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75.10.Nr Spin-glass and other random models
75.30.Ds Spin waves
75.40.Gb Dynamic properties (dynamic susceptibility, spin waves, spin diffusion, dynamic scaling, etc.)
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Duality and representations for new exotic bialgebras

D. Arnaudon, A. Chakrabarti, V. K. Dobrev, and S. G. Mihov

J. Math. Phys. 43, 6238 (2002); http://dx.doi.org/10.1063/1.1516845 (27 pages) | Cited 5 times

Online Publication Date: 25 November 2002

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We find the exotic matrix bialgebras which correspond to the two nontriangular nonsingular 4×4 R-matrices in the classification of Hietarinta, namely, RS0,3 and RS1,4. We find two new exotic bialgebras S03 and S14 which are not deformations of the classical algebras of functions on GL(2) or GL(1∣1). With this we finalize the classification of the matrix bialgebras which unital associative algebras generated by four elements. We also find the corresponding dual bialgebras of these new exotic bialgebras and study their representation theory in detail. We also discuss in detail a special case of RS1,4 in which the corresponding algebra turns out to be a special case of the two-parameter quantum group deformation GLp,q(2). © 2002 American Institute of Physics.
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03.65.Fd Algebraic methods
02.20.Uw Quantum groups
02.10.Yn Matrix theory
02.60.Dc Numerical linear algebra

Geometric coupling thresholds in a two-dimensional strip

D. Borisov, P. Exner, and R. Gadyl’shin

J. Math. Phys. 43, 6265 (2002); http://dx.doi.org/10.1063/1.1519941 (14 pages) | Cited 18 times

Online Publication Date: 25 November 2002

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We consider the Laplacian in a strip math×(0,d) with the boundary condition which is Dirichlet except at the segment of a length 2a of one of the boundaries where it is switched to Neumann. This operator is known to have a non-empty and simple discrete spectrum for any a>0. There is a sequence 0<a1<a2<⋯ of critical values at which new eigenvalues emerge from the continuum when the Neumann window expands. We find the asymptotic behavior of these eigenvalues around the thresholds showing that the gap is in the leading order proportional to (a−an)2 with an explicit coefficient expressed in terms of the corresponding threshold-energy resonance eigenfunction. © 2002 American Institute of Physics.
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03.65.-w Quantum mechanics
02.40.-k Geometry, differential geometry, and topology

Continuous spin representations of the Poincaré and super-Poincaré groups

Lars Brink, Abu M. Khan, Pierre Ramond, and Xiaozhen Xiong

J. Math. Phys. 43, 6279 (2002); http://dx.doi.org/10.1063/1.1518138 (17 pages) | Cited 6 times

Online Publication Date: 25 November 2002

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We construct Wigner’s continuous spin representations of the Poincaré algebra for massless particles in higher dimensions. The states are labeled both by the length of a spacelike translation vector and the Dynkin indices of the short little group SO(d−3), where d is the space–time dimension. Continuous spin representations are in one-to-one correspondence with representations of the short little group. We also demonstrate how combinations of the bosonic and fermionic representations form supermultiplets of the super-Poincaré algebra. If the light-cone translations are nilpotent, these representations become finite dimensional, but contain zero or negative norm states, and their supersymmetry algebra contains a central charge in four and ten dimensions. © 2002 American Institute of Physics.
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11.10.-z Field theory
03.65.Pm Relativistic wave equations
11.30.Pb Supersymmetry
11.30.Ly Other internal and higher symmetries

Analytical expressions for some multiplicity-free isoscalar factors of Sf⊃Sf−1

Lianrong Dai, Feng Pan, and J. P. Draayer

J. Math. Phys. 43, 6296 (2002); http://dx.doi.org/10.1063/1.1517169 (11 pages) | Cited 1 time

Online Publication Date: 25 November 2002

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An algebraic routine for the evaluation of analytical expressions for isoscalar factors (ISFs) of Sf⊃Sf−1 is formulated based on the linear equation method (LEM) and the analytical continuation of the rank f. As examples, ISFs of Sf⊃Sf−1 for the coupling [f−1,1]⋅[f−1,1], [f−1,1]⋅[f−2,2], [f−2,1,1]⋅[f−2,1,1] are tabulated. The results demonstrate that the number of ISF tables can be greatly reduced compared with corresponding numerical results produced using other methods. © 2002 American Institute of Physics.
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03.65.Fd Algebraic methods
02.20.Uw Quantum groups
02.30.Uu Integral transforms
02.10.-v Logic, set theory, and algebra
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