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arXiv 0807.2508hep-thmath-phmath.MP
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非对易规范理论中的空时同态

Space-Time Diffeomorphisms in Noncommutative Gauge Theories

Marcos Rosenbaum, J. David Vergara, L. Roman Juarez

备注：
This is a contribution to the Special Issue on Deformation Quantization, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/
发表信息：
SIGMA 4 (2008), 055, 21 pages
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摘要：

在以前的工作[Rosenbaum M.例如，J.物理. A：数学.理论. 40（2007），10367-10382，hep-th/0611160]我们已经示出了对于正则参数化场论，其中时空与理论中的其他场被置于相同的基础上，时空同态的表示如何提供了用于分析作为时空非对易性的结果的这些同态的诱导扭曲变形的非常方便的方案。然而，对于规范场（当然也对于正则几何动力学），其中约束的泊松括号显式地取决于嵌入变量，该泊松代数不能直接与时空同态的完备李代数的表示相连接，因为并非所有的场变量都具有动力学特征[Isham C. J.，Kuchar K.V.，Ann. Physics 164（1985），288-315，316-333]。尽管如此，这样的同态映射可以通过首先修改原始作用量然后在形式中添加附加约束来恢复，以便恢复原始理论，如Kuchar和Stone在[Kuchar K. V.，Stone S.L.，Classical量子引力4（1987），319-328].利用所有这些想法的组合，我们因此能够应用我们的正则重参数化方法，以获得非交换时空的变形李代数的同态，以及考虑如何规范变换的规范和粒子场的扭曲代数的作用。因此，希望能澄清文献中关于非对易时空中规范理论对称性的一些悬而未决的问题。

英文摘要：

In previous work [Rosenbaum M. et al., J. Phys. A: Math. Theor. 40 (2007), 10367-10382, hep-th/0611160] we have shown how for canonical parametrized field theories, where space-time is placed on the same footing as the other fields in the theory, the representation of space-time diffeomorphisms provides a very convenient scheme for analyzing the induced twisted deformation of these diffeomorphisms, as a result of the space-time noncommutativity. However, for gauge field theories (and of course also for canonical geometrodynamics) where the Poisson brackets of the constraints explicitely depend on the embedding variables, this Poisson algebra cannot be connected directly with a representation of the complete Lie algebra of space-time diffeomorphisms, because not all the field variables turn out to have a dynamical character [Isham C.J., Kuchar K.V., Ann. Physics 164 (1985), 288-315, 316-333]. Nonetheless, such an homomorphic mapping can be recuperated by first modifying the original action and then adding additional constraints in the formalism in order to retrieve the original theory, as shown by Kuchar and Stone for the case of the parametrized Maxwell field in [Kuchar K.V., Stone S.L., Classical Quantum Gravity 4 (1987), 319-328]. Making use of a combination of all of these ideas, we are therefore able to apply our canonical reparametrization approach in order to derive the deformed Lie algebra of the noncommutative space-time diffeomorphisms as well as to consider how gauge transformations act on the twisted algebras of gauge and particle fields. Thus, hopefully, adding clarification on some outstanding issues in the literature concerning the symmetries for gauge theories in noncommutative space-times.

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