Secondary calculus and the covariant phase space

JOURNAL OF GEOMETRY AND PHYSICS

卷:59

Article

Vitagliano, Luca^1,2 

[1] Univ Salerno, DMI, I-84084 Fisciano, SA, Italy

[2] GC Salerno, Ist Nazl Fis Nucl, I-84084 Fisciano, SA, Italy

关键词: Covariant phase space;    Jet spaces;    Geometry of PDEs;    Secondary calculus;    Gauge theory;   

DOI  :  10.1016/j.geomphys.2008.12.001

来源: Elsevier

【 摘 要 】

The covariant phase space of a lagrangian field theory is the solution space of the associated Euler-Lagrange equations. It is, in principle, a nice environment for covariant quantization of a lagrangian field theory. Indeed, it is manifestly covariant and possesses a canonical (functional) presymplectic structure omega (as first noticed by Zuckerman in 1986) whose degeneracy (functional) distribution is naturally interpreted as the Lie algebra of gauge transformations. We propose a fully rigorous approach to the covariant phase space in the framework of jet spaces and (A. M. Vinogradov's) secondary calculus. In particular, we describe the degeneracy distribution of omega. As a by product we rederive the existence of a Lie bracket among gauge invariant functions on the covariant phase space. (C) 2008 Elsevier B.V. All rights reserved.

【 授权许可】

Free