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arXiv 0907.1078hep-th
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零平面上Podolsky广义电动力学的正则结构

The canonical structure of Podolsky's generalized electrodynamics on the Null-Plane

M. C. Bertin, B. M. Pimentel, G. E. R. Zambrano

摘要:

在这项工作中,我们将开发零平面上的波多尔斯基的广义电动力学的正则结构。这个理论在拉格朗日函数中有二阶导数,需要对系统的动量和正则哈密顿量的定义进行更深入的研究。在零平面上,场方程也要求对初边值问题作不同的分析,在零平面上必须选择适当的条件。我们将证明,约束结构,基于狄拉克形式主义,提出了一组第二类约束,这是不包括零平面上的分析,和一个预期的一组第一类约束,是一个U(1)群的规范变换的生成元。通过对场方程的考察,我们得到了零平面上的广义辐射规范,并引入了Dirac括号,考虑到在所选的理论初边值条件下这些括号的唯一性问题。

英文摘要:

In this work we will develop the canonical structure of Podolsky's generalized electrodynamics on the null-plane. This theory has second-order derivatives in the Lagrangian function and requires a closer study for the definition of the momenta and canonical Hamiltonian of the system. On the null-plane the field equations also demand a different analysis of the initial-boundary value problem and proper conditions must be chosen on the null-planes. We will show that the constraint structure, based on Dirac formalism, presents a set of second-class constraints, which are exclusive of the analysis on the null-plane, and an expected set of first-class constraints that are generators of a U(1) group of gauge transformations. An inspection on the field equations will lead us to the generalized radiation gauge on the null-plane, and Dirac Brackets will be introduced considering the problem of uniqueness of these brackets under the chosen initial-boundary condition of the theory.

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