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Mar 2013

Volume 54, Issue 3, Articles (03xxxx)

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J. Math. Phys. 54, 033512 (2013); http://dx.doi.org/10.1063/1.4794514 (20 pages)

Andrew Neate and Aubrey Truman
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back to top Relativistic Quantum Mechanics, Quantum Field Theory, Quantum Gravity, and String Theory

Representing the vacuum polarization on de Sitter

Katie E. Leonard, Tomislav Prokopec, and Richard P. Woodard

J. Math. Phys. 54, 032301 (2013); http://dx.doi.org/10.1063/1.4793987 (9 pages)

Online Publication Date: 6 March 2013

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Previous studies of the vacuum polarization on de Sitter have demonstrated that there is a simple, noncovariant representation of it in which the physics is transparent. There is also a cumbersome, covariant representation in which the physics is obscure. Despite being unwieldy, the latter form has a powerful appeal for those who are concerned about de Sitter invariance. We show that nothing is lost by employing the simple, noncovariant representation because there is a closed form procedure for converting its structure functions to those of the covariant representation. We also present a vastly improved technique for reading off the noncovariant structure functions from the primitive diagrams. And we discuss the issue of representing the vacuum polarization for a general metric background.
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12.20.Ds Specific calculations
98.80.Cq Particle-theory and field-theory models of the early Universe (including cosmic pancakes, cosmic strings, chaotic phenomena, inflationary universe, etc.)

Representations of some quantum tori Lie subalgebras

Jingjing Jiang and Song Wang

J. Math. Phys. 54, 032302 (2013); http://dx.doi.org/10.1063/1.4795350 (15 pages)

Online Publication Date: 20 March 2013

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In this paper, we define the q-analog Virasoro-like Lie subalgebras in x∞ = a∞(b∞, c∞, d∞). The embedding formulas into x∞ are introduced. Irreducible highest weight representations of mathq, mathq, and mathq-series of the q-analog Virasoro-like Lie algebras in terms of vertex operators are constructed. We also construct the polynomial representations of the mathq, mathq, mathq, and mathq-series of the q-analog Virasoro-like Lie algebras.
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02.20.Sv Lie algebras of Lie groups
03.65.Fd Algebraic methods

Towards an invariant geometry of double field theory

Olaf Hohm and Barton Zwiebach

J. Math. Phys. 54, 032303 (2013); http://dx.doi.org/10.1063/1.4795513 (35 pages)

Online Publication Date: 26 March 2013

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We introduce a geometrical framework for double field theory in which generalized Riemann and torsion tensors are defined without reference to a particular basis. This invariant geometry provides a unifying framework for the frame-like and metric-like formulations developed before. We discuss the relation to generalized geometry and give an “index-free” proof of the algebraic Bianchi identity. Finally, we analyze to what extent the generalized Riemann tensor encodes the curvatures of Riemannian geometry. We show that it contains the conventional Ricci tensor and scalar curvature but not the full Riemann tensor, suggesting the possibility of a further extension of this framework.
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02.40.-k Geometry, differential geometry, and topology
45.10.Na Geometrical and tensorial methods
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