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Dec 2004

Volume 45, Issue 12, pp. 4435-5101

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Extremal covariant positive operator valued measures

Giulio Chiribella and Giacomo Mauro D’Ariano

J. Math. Phys. 45, 4435 (2004); http://dx.doi.org/10.1063/1.1806262 (13 pages) | Cited 14 times

Online Publication Date: 4 November 2004

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We consider the convex set of positive operator valued measures (POVM) which are covariant under a finite dimensional unitary projective representation of a group. We derive a general characterization for the extremal points, and provide bounds for the ranks of the corresponding POVM densities, also relating extremality to uniqueness and stability of optimized measurements. Examples of applications are given.
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03.65.Ta Foundations of quantum mechanics; measurement theory
02.50.Cw Probability theory
03.65.Fd Algebraic methods
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A new geometrical look at gravity coupled with Yang–Mills fields

Stefano Vignolo and Roberto Cianci

J. Math. Phys. 45, 4448 (2004); http://dx.doi.org/10.1063/1.1806536 (16 pages) | Cited 7 times

Online Publication Date: 4 November 2004

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A new geometrical framework for tetrad-affine formulation of gravity, pure or coupled with Yang–Mills fields, is proposed. After analyzing the geometrical properties of the new mathematical setting, field equations are deduced from a variational principle in the Poincaré–Cartan formalism. A generalized Noether Theorem is stated and classical relationship between symmetries and conserved quantities are recovered in the newer scheme. Some explicit examples are given.
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11.10.-z Field theory
04.60.Pp Loop quantum gravity, quantum geometry, spin foams
11.15.-q Gauge field theories
02.40.-k Geometry, differential geometry, and topology
11.30.Na Nonlinear and dynamical symmetries (spectrum-generating symmetries)

Hyperbolic Kac Moody algebras and Einstein billiards

Sophie de Buyl and Christiane Schomblond

J. Math. Phys. 45, 4464 (2004); http://dx.doi.org/10.1063/1.1806537 (29 pages) | Cited 5 times

Online Publication Date: 4 November 2004

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We identify the hyperbolic Kac Moody algebras for which there exists a Lagrangian of gravity, dilatons, and p-forms which produces a billiard that can be identified with their fundamental Weyl chamber. Because of the invariance of the billiard upon toroidal dimensional reduction, the list of admissible algebras is determined by the existence of a Lagrangian in three space–time dimensions, where a systematic analysis can be carried out since only zero-forms are involved. We provide all highest dimensional parent Lagrangians with their full spectrum of p-forms and dilaton couplings. We confirm, in particular, that for the rank 10 hyperbolic algebra, CE10 = A15(2)∧, also known as the dual of B8∧∧, the maximally oxidized Lagrangian is nine-dimensional and involves besides gravity, 2 dilatons, a 2-form, a 1-form, and a 0-form.
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04.60.-m Quantum gravity
02.10.-v Logic, set theory, and algebra
04.20.Fy Canonical formalism, Lagrangians, and variational principles
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Lifshits tails for random smooth magnetic vortices

J. L. Borg and J. V. Pulé

J. Math. Phys. 45, 4493 (2004); http://dx.doi.org/10.1063/1.1807955 (13 pages) | Cited 1 time

Online Publication Date: 4 November 2004

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We study the density of states of the Pauli Hamiltonian with a Poisson random distribution of smooth finite-width vortices and we obtain classical bounds for the Lifshits tails for them. These Hamiltonians are smooth approximations to the self-adjoint extensions of the Aharonov–Bohm Hamiltonian. In this case because pairs of impurities are coupled by the magnetic field we cannot use the Laplace characteristic functional.
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03.65.Ta Foundations of quantum mechanics; measurement theory
02.50.Ng Distribution theory and Monte Carlo studies
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Coherent solutions for relativistic vectorial fields

Attilio Maccari

J. Math. Phys. 45, 4506 (2004); http://dx.doi.org/10.1063/1.1807956 (9 pages)

Online Publication Date: 4 November 2004

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Approximate interacting localized solutions of a vectorial massive nonlinear equation are obtained by using the asymptotic perturbation (AP) method, based on Fourier expansion and spatio-temporal rescaling. The amplitude slow modulation of Fourier modes is described by a system of nonlinear evolution equations solvable via an appropriate change of variables. Various types of localized solutions (dromions, lumps, ring solitons, and breathers) as well as multiple soliton and instanton solutions can be explicitly constructed and their interaction is completely elastic, because they pass through each other and preserve their shape, the only change being a phase shift.
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02.30.Hq Ordinary differential equations
02.10.Ud Linear algebra
05.45.Yv Solitons

Avoiding superluminal propagation of higher spin waves via projectors onto W2 invariant subspaces

Mauro Napsuciale and Mariana Kirchbach

J. Math. Phys. 45, 4515 (2004); http://dx.doi.org/10.1063/1.1794843 (9 pages) | Cited 1 time

Online Publication Date: 4 November 2004

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We propose to describe higher spins as invariant subspaces of the Casimir operators of the Poincaré Group, P2, and the squared Pauli–Lubanski operator, W2, in a properly chosen representation, ψ(p) (in momentum space), of the Homogeneous Lorentz Group. The resulting equation of motion for any field with s ≠ 0 is then just a specific combination of the respective covariant projectors. We couple minimally electromagnetism to this equation and show that the corresponding wave fronts of the classical solutions propagate causally. Furthermore, for (s,0)⊕(0,s) representations, the formalism predicts the correct gyromagnetic factor, gs = 1/s. The advocated method allows us to describe any higher spin without auxiliary conditions and by one covariant matrix equation alone. This master equation is only quadratic in the momenta and its dimensionality is that of ψ(p). We prove that the suggested master equation avoids the Velo–Zwanziger problem of superluminal propagation of higher spin waves and points toward a consistent description of higher spin quantum fields.
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12.20.Ds Specific calculations
11.10.-z Field theory
02.30.Tb Operator theory
02.10.Yn Matrix theory
02.20.Hj Classical groups

Finite size effects in thermal field theory

N. F. Svaiter

J. Math. Phys. 45, 4524 (2004); http://dx.doi.org/10.1063/1.1808485 (15 pages) | Cited 8 times

Online Publication Date: 5 November 2004

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We consider a neutral self-interacting massive scalar field defined in a d-dimensional Euclidean space. Assuming thermal equilibrium, we discuss the one-loop perturbative renormalization of this theory in the presence of rigid boundary surfaces (two parallel hyperplanes), which break translational symmetry. In order to identify the singular parts of the one-loop two-point and four-point Schwinger functions, we use a combination of dimensional and zeta-function analytic regularization procedures. The infinities which occur in both the regularized one-loop two-point and four-point Schwinger functions fall into two distinct classes: local divergences that could be renormalized with the introduction of the usual bulk counterterms, and surface divergences that demand counterterms concentrated on the boundaries. We present the detailed form of the surface divergences and discuss different strategies that one can assume to solve the problem of the surface divergences. We also briefly mention how to overcome the difficulties generated by infrared divergences in the case of Neumann–Neumann boundary conditions.
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11.30.Qc Spontaneous and radiative symmetry breaking
11.15.Ex Spontaneous breaking of gauge symmetries
11.10.Gh Renormalization
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On a conjecture of Givental

Jun S. Song and Yun S. Song

J. Math. Phys. 45, 4539 (2004); http://dx.doi.org/10.1063/1.1808486 (12 pages) | Cited 1 time

Online Publication Date: 5 November 2004

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These brief notes record our puzzles and findings surrounding Givental’s recent conjecture which expresses higher genus Gromov–Witten invariants in terms of the genus-0 data. We limit our considerations to the case of a complex projective line, whose Gromov–Witten invariants are well-known and easy to compute. We make some simple checks supporting his conjecture.
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02.30.Gp Special functions
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Space–time slices and surfaces of revolution

John T. Giblin and Andrew D. Hwang

J. Math. Phys. 45, 4551 (2004); http://dx.doi.org/10.1063/1.1808487 (9 pages) | Cited 2 times

Online Publication Date: 5 November 2004

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Under certain conditions, a (1+1)-dimensional slice ĝ of a spherically symmetric black hole space–time can be equivariantly embedded in (2+1)-dimensional Minkowski space. The embedding depends on a real parameter that corresponds physically to the surface gravity κ of the black hole horizon. Under conditions that turn out to be closely related, a real surface that possesses rotational symmetry can be equivariantly embedded in three-dimensional Euclidean space. The embedding does not obviously depend on a parameter. However, the Gaussian curvature is given by a simple formula: If the metric is written g = ϕ(r)−1 dr2+ϕ(r)dθ2, then Kg = −½ϕ″(r). This note shows that metrics g and ĝ occur in dual pairs, and that the embeddings described above are orthogonal facets of a single phenomenon. In particular, the metrics and their respective embeddings differ by a Wick rotation that preserves the ambient symmetry. Consequently, the embedding of g depends on a real parameter. The ambient space is not smooth, and κ is inversely proportional to the cone angle at the axis of rotation. Further, the Gaussian curvature of ĝ is given by a simple formula that seems not to be widely known.
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04.20.Gz Spacetime topology, causal structure, spinor structure
04.60.Kz Lower dimensional models; minisuperspace models
97.60.Lf Black holes
04.70.Dy Quantum aspects of black holes, evaporation, thermodynamics
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On the resolvent and spectral functions of a second order differential operator with a regular singularity

H. Falomir, M. A. Muschietti, and P. A. G. Pisani

J. Math. Phys. 45, 4560 (2004); http://dx.doi.org/10.1063/1.1809257 (18 pages) | Cited 16 times

Online Publication Date: 5 November 2004

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We consider the resolvent of a second order differential operator with a regular singularity, admitting a family of self-adjoint extensions. We find that the asymptotic expansion for the resolvent in the general case presents unusual powers of λ which depend on the singularity. The consequences for the pole structure of the ζ function, and for the small-t asymptotic expansion of the heat kernel, are also discussed.
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02.30.Sa Functional analysis
11.10.Gh Renormalization

Deformations of loop algebras and integrable systems: hierarchies of integrable equations

T. Skrypnyk

J. Math. Phys. 45, 4578 (2004); http://dx.doi.org/10.1063/1.1804229 (18 pages) | Cited 7 times

Online Publication Date: 5 November 2004

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Using special quasigraded Lie algebras, that could be viewed as deformations of loop algebras, we obtain new hierarchies of integrable nonlinear equations admitting zero-curvature representations. In particular, we obtain integrable hierarchies that generalize the Heisenberg magnet, Landau–Lifshitz, and anisotropic chiral field hierarchies. We also obtain a new type of so(3) anisotropic chiral field equation along with its higher rank generalization.
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02.30.Hq Ordinary differential equations
02.10.Ud Linear algebra
02.20.Sv Lie algebras of Lie groups

Moduli of quantum Riemannian geometries on ⩽ 4 points

S. Majid and E. Raineri

J. Math. Phys. 45, 4596 (2004); http://dx.doi.org/10.1063/1.1804231 (32 pages) | Cited 1 time

Online Publication Date: 5 November 2004

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We classify parallelizable noncommutative manifold structures on finite sets of small size in the general formalism of framed quantum manifolds and vielbeins introduced previously [S. Majid, Commun. Math. Phys. 225, 131 (2002)]. The full moduli space is found for ⩽ 3 points, and a restricted moduli space for 4 points. Generalized Levi–Cività connections and their curvatures are found for a variety of models including models of a discrete torus. The topological part of the moduli space is found for ⩽ 9 points based on the known atlas of regular graphs. We also remark on aspects of quantum gravity in this approach.
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04.60.Pp Loop quantum gravity, quantum geometry, spin foams
02.40.Pc General topology
02.40.Ky Riemannian geometries
02.10.Ox Combinatorics; graph theory
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Nonintegrability of nonhomogeneous nonlinear lattices

Kazuyuki Yoshimura and Ken Umeno

J. Math. Phys. 45, 4628 (2004); http://dx.doi.org/10.1063/1.1806260 (12 pages) | Cited 2 times

Online Publication Date: 15 November 2004

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We study the integrability of nonlinear lattices with nonhomogeneous polynomial potentials. We prove a nonintegrability theorem for these dynamical systems.
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05.45.-a Nonlinear dynamics and chaos
02.30.Ik Integrable systems
05.50.+q Lattice theory and statistics (Ising, Potts, etc.)
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The invariant charges of the Nambu–Goto string and canonical quantization

Dorothea Bahns

J. Math. Phys. 45, 4640 (2004); http://dx.doi.org/10.1063/1.1776644 (21 pages) | Cited 3 times

Online Publication Date: 15 November 2004

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It is shown that the algebra of diffeomorphism-invariant charges of the Nambu–Goto string cannot be quantized in the framework of canonical quantization. The argument is shown to be independent of the dimension of the underlying Minkowski space.
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11.25.Hf Conformal field theory, algebraic structures
04.60.Ds Canonical quantization
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A technique to identify solvable dynamical systems, and another solvable extension of the goldfish many-body problem

Francesco Calogero

J. Math. Phys. 45, 4661 (2004); http://dx.doi.org/10.1063/1.1809256 (18 pages) | Cited 9 times

Online Publication Date: 15 November 2004

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We take advantage of the simple approach, recently discussed, which associates to (solvable) matrix equations (solvable) dynamical systems interpretable as (interesting) many-body problems, possibly involving auxiliary dependent variables in addition to those identifying the positions of the moving particles. Starting from a solvable matrix evolution equation, we obtain the corresponding many-body model and note that in one case the auxiliary variables can be altogether eliminated, obtaining thereby an (also Hamiltonian) extension of the “goldfish” model. The solvability of this novel model, and of its isochronous variant, is exhibited. A related, as well solvable, model, is also introduced, as well as its isochronous variant. Finally, the small oscillations of the isochronous models around their equilibrium configurations are investigated, and from their isochronicity certain diophantine relations are evinced.
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02.30.Hq Ordinary differential equations
02.10.Yn Matrix theory
05.30.-d Quantum statistical mechanics
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An algebraic Birkhoff decomposition for the continuous renormalization group

Florian Girelli, Thomas Krajewski, and Pierre Martinetti

J. Math. Phys. 45, 4679 (2004); http://dx.doi.org/10.1063/1.1794366 (19 pages) | Cited 2 times

Online Publication Date: 15 November 2004

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This paper aims at presenting the first steps towards a formulation of the Exact Renormalization Group Equation in the Hopf algebra setting of Connes and Kreimer. It mostly deals with some algebraic preliminaries allowing us to formulate perturbative renormalization within the theory of differential equations. The relation between renormalization, formulated as a change of boundary condition for a differential equation, and an algebraic Birkhoff decomposition for rooted trees is explicited.
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03.65.Fd Algebraic methods
02.20.-a Group theory
02.10.-v Logic, set theory, and algebra
02.30.Hq Ordinary differential equations
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Asymptotic quasinormal frequencies for black holes in nonasymptotically flat space–times

Vitor Cardoso, José Natário, and Ricardo Schiappa

J. Math. Phys. 45, 4698 (2004); http://dx.doi.org/10.1063/1.1812828 (16 pages) | Cited 47 times

Online Publication Date: 15 November 2004

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The exact computation of asymptotic quasinormal frequencies is a technical problem which involves the analytic continuation of a Schrödinger-type equation to the complex plane and then performing a method of monodromy matching at several poles in the plane. While this method was successfully used in asymptotically flat space–time, as applied to both the Schwarzschild and Reissner–Nordstrøm solutions, its extension to nonasymptotically flat space–times has not been achieved yet. In this work it is shown how to extend the method to this case, with the explicit analysis of Schwarzschild–de Sitter and large Schwarzschild–anti–de Sitter black holes, both in four dimensions. We obtain, for the first time, analytic expressions for the asymptotic quasinormal frequencies of these black hole space–times, and our results match previous numerical calculations with great accuracy. We also list some results concerning the general classification of asymptotic quasinormal frequencies in d-dimensional space–times.
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04.70.-s Physics of black holes
97.60.Lf Black holes
04.60.Pp Loop quantum gravity, quantum geometry, spin foams
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Composite systems and the role of the complex numbers in quantum mechanics

Gerd Niestegge

J. Math. Phys. 45, 4714 (2004); http://dx.doi.org/10.1063/1.1811371 (12 pages) | Cited 5 times

Online Publication Date: 15 November 2004

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See Also: Erratum

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An axiomatic approach to the mathematical formalism of quantum mechanics, based upon a certain concept of conditional probability, has been proposed in two recent papers by the author. It leads to Jordan operator algebras and thus comes rather close to the standard Hilbert space model of quantum mechanics, but still includes the so-called exceptional Jordan algebras, for which a Hilbert space representation does not exist. This approach is now extended by defining a mathematical model of composite systems. Such a model is required for the study of the joint distribution of two quantum observables. A very general type of observables (not only the real-valued observables corresponding to the self-adjoint operators) is considered. The joint distribution is defined, using the concept of conditional probability, and exhibits a certain dependence on the succession of the observations which is different from the classical case and unknown so far in quantum mechanics. Finally, it turns out that, at least in the finite-dimensional case, a really satisfying model of the composite system exists only if each single system is modeled by a complex Jordan matrix algebra (or a direct sum), and the model then becomes the tensor product. This provides some reasoning why the exceptional Jordan algebras can be ruled out, why quantum mechanics needs the complex numbers and the complex Hilbert space, and why the tensor product is the right choice for the model of a composite system.
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03.65.Fd Algebraic methods
02.10.Yn Matrix theory
02.10.De Algebraic structures and number theory
02.10.Ud Linear algebra
02.50.Cw Probability theory
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On spherically symmetric solutions with horizon in model with multicomponent anisotropic fluid

H. Dehnen and V. D. Ivashchuk

J. Math. Phys. 45, 4726 (2004); http://dx.doi.org/10.1063/1.1812357 (11 pages) | Cited 2 times

Online Publication Date: 15 November 2004

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A family of spherically symmetric solutions in the model with m-component multicomponent anisotropic fluid is considered. The metric of the solution depends on parameters qs>0, s = 1,…,m, relating radial pressures and the densities and contains (n−1)m parameters corresponding to Ricci-flat “internal space” metrics and obeying certain m(m−1)/2 (“orthogonality”) relations. For qs = 1 (for all s) and certain equations of state (pis = ±ρs) the metric coincides with the metric of intersecting black brane solution in the model with antisymmetric forms. A family of solutions with (regular) horizon corresponding to natural numbers qs = 1,2,… is singled out. Certain examples of “generalized simulation” of intersecting M-branes in D = 11 supergravity are considered. The post-Newtonian parameters β and γ corresponding to the four-dimensional section of the metric are calculated.
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04.70.-s Physics of black holes
97.60.Lf Black holes
11.27.+d Extended classical solutions; cosmic strings, domain walls, texture
04.65.+e Supergravity
98.80.-k Cosmology
04.20.Jb Exact solutions
04.40.Nr Einstein-Maxwell spacetimes, spacetimes with fluids, radiation or classical fields
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On the Treves theorem for the Ablowitz–Kaup–Newell–Segur equation

Carlo Morosi and Livio Pizzocchero

J. Math. Phys. 45, 4737 (2004); http://dx.doi.org/10.1063/1.1805730 (17 pages)

Online Publication Date: 22 November 2004

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According to a theorem of Treves, the conserved functionals of the Ablowitz, Kaup, Newell, and Segur (AKNS) equation vanish on all pairs of formal Laurent series (math,math) of a specified form, both of them with a pole of the first order. We propose a new and very simple proof for this statement, based on the theory of Bäcklund transformations; using the same method, we prove that the AKNS conserved functionals vanish on other pairs of Laurent series. The spirit is the same as in our previous paper on the Treves theorem for the Korteweg–de Vries hierarchy, with some nontrivial technical differences.
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02.30.Sa Functional analysis
03.65.Ge Solutions of wave equations: bound states
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Angular intricacies in hot gauge field theories

T. Grandou

J. Math. Phys. 45, 4754 (2004); http://dx.doi.org/10.1063/1.1814418 (10 pages)

Online Publication Date: 22 November 2004

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It is argued that in hot quantum field theories, “hard thermal loops” leading order calculations call for a definite sequence of angular averages and discontinuity (or imaginary part prescription) operations, and run otherwise into incorrect results. The 10 years old collinear singularity problem of hot QCD provides a dramatic illustration of that fate.
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11.15.-q Gauge field theories
12.38.Cy Summation of perturbation theory
02.30.Cj Measure and integration
02.60.Jh Numerical differentiation and integration
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Conformal Killing horizons

J. Sultana and C. C. Dyer

J. Math. Phys. 45, 4764 (2004); http://dx.doi.org/10.1063/1.1814417 (13 pages) | Cited 4 times

Online Publication Date: 22 November 2004

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For time dependent black hole space–times the event horizon cannot be described by a Killing horizon. In the case when the space–time admits a timelike conformal Killing field, which becomes null on a boundary called the conformal stationary limit surface, one can locally describe the expanding event horizon by using this boundary, provided that it is a null geodesic hypersurface. In this case the boundary is called a conformal Killing horizon and is shown to be null and geodesic if and only if the twist of the conformal Killing trajectories on the hypersurface vanishes. Moreover if the space–time is conformally related to a stationary asymptotically flat black hole space–time, it is shown that this hypersurface is globally equivalent to the event horizon, provided that the conformal factor goes to a constant at null infinity. When the conformal stationary limit surface does not coincide with the conformal Killing horizon, a generalization of the weak rigidity theorem which establishes the conformal Killing property of the event horizon and the rigidity of its rotation is obtained. A physical definition of surface gravity for conformal Killing horizons is given, which is then used to formulate a generalized zeroth law of black hole physics.
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04.70.-s Physics of black holes
97.60.Lf Black holes
04.20.Gz Spacetime topology, causal structure, spinor structure
11.25.Hf Conformal field theory, algebraic structures
02.10.Ud Linear algebra
02.40.Hw Classical differential geometry
04.60.-m Quantum gravity
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The Poincaré equation: A new polynomial and its unusual properties

Keke Zhang, Xinhao Liao, and Paul Earnshaw

J. Math. Phys. 45, 4777 (2004); http://dx.doi.org/10.1063/1.1811786 (14 pages) | Cited 4 times

Online Publication Date: 22 November 2004

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The Poincaré equation, a second-order partial differential equation describing wave motions in a rotating spheroid of arbitrary eccentricity satisfying a certain set of the boundary condition, is studied. A new polynomial as the general solution of the Poincaré equation in spheroidal geometry is found for the first time. The paper focuses on some unusual and intriguing mathematical properties of the new Poincaré polynomial. The possible completeness of the set of eigenfunctions of the Poincaré equation in the form of the new polynomial is also discussed. The new Poincaré polynomial would provide a powerful basis for the mathematical analysis in many important geophysical and astrophysical problems.
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95.30.Lz Hydrodynamics
02.30.Jr Partial differential equations
02.40.-k Geometry, differential geometry, and topology
02.10.De Algebraic structures and number theory
02.10.Ud Linear algebra
97.10.Kc Stellar rotation
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An approach to nonstandard quantum mechanics

A. Raab

J. Math. Phys. 45, 4791 (2004); http://dx.doi.org/10.1063/1.1812358 (19 pages)

Online Publication Date: 22 November 2004

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We use nonstandard analysis to formulate quantum mechanics in hyperfinite-dimensional spaces. Self-adjoint operators on hyperfinite-dimensional spaces have complete eigensets, and bound states and continuum states of a Hamiltonian can thus be treated on an equal footing. We show that the formalism extends the standard formulation of quantum mechanics. To this end we develop the Loeb-function calculus in nonstandard hulls. The idea is to perform calculations in a hyperfinite-dimensional space, but to interpret expectation values in the corresponding nonstandard hull. We further apply the framework to nonrelativistic quantum scattering theory. For time-dependent scattering theory, we identify the starting time and the finishing time of a scattering experiment, and we obtain a natural separation of time scales on which the preparation process, the interaction process, and the detection process take place. For time-independent scattering theory, we derive rigorously explicit formulas for the Møller wave operators and the S-matrix.
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03.65.Nk Scattering theory
03.65.Fd Algebraic methods
02.10.Ud Linear algebra
03.65.Ge Solutions of wave equations: bound states
02.30.Sa Functional analysis
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Stable quantum systems in anti–de Sitter space: Causality, independence, and spectral properties

Detlev Buchholz and Stephen J. Summers

J. Math. Phys. 45, 4810 (2004); http://dx.doi.org/10.1063/1.1804230 (22 pages) | Cited 7 times

Online Publication Date: 24 November 2004

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If a state is passive for uniformly accelerated observers in n-dimensional (n ≥ 2) anti–de Sitter (Ads) space–time (i.e., cannot be used by them to operate a perpetuum mobile), they will (a) register a universal value of the Unruh temperature, (b) discover a PCT symmetry, and (c) find that observables in complementary wedge-shaped regions necessarily commute with each other in this state. The stability properties of such a passive state induce a “geodesic causal structure” on AdS and concommitant locality relations. It is shown that observables in these complementary wedge-shaped regions fulfill strong additional independence conditions. In two-dimensional AdS these even suffice to enable the derivation of a nontrivial, local, covariant net indexed by bounded space–time regions. All these results are model-independent and hold in any theory which is compatible with a weak notion of space–time localization. Examples are provided of models satisfying the hypotheses of these theorems.
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03.65.-w Quantum mechanics
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