2022-01-23T08:14:07Zhttps://digital.csic.es/dspace-oai/requestoai:digital.csic.es:10261/2482912021-08-19T01:12:50Zcom_10261_135com_10261_4col_10261_388
2021-08-18T09:50:09Z
urn:hdl:10261/248291
Geometric formulation of the covariant phase space methods with boundaries
Margalef-Bentabol, Juan
Villaseñor, Eduardo J. S.
Ministerio de Ciencia, Innovación y Universidades (España)
National Science Foundation (US)
Pittsburgh Foundation
37 pags.
We analyze in full detail the geometric structure of the covariant phase space (CPS) of any local field theory defined over a space-time with boundary. To this end, we introduce a new frame: the "relative bicomplex framework."It is the result of merging an extended version of the "relative framework"(initially developed in the context of algebraic topology by R. Bott and L. W. Tu in the 1980s to deal with boundaries) and the variational bicomplex framework (the differential geometric arena for the variational calculus). The relative bicomplex framework is the natural one to deal with field theories with boundary contributions, including corner contributions. In fact, we prove a formal equivalence between the relative version of a theory with boundary and the nonrelative version of the same theory with no boundary. With these tools at hand, we endow the space of solutions of the theory with a (pre)symplectic structure canonically associated with the action and which, in general, has boundary contributions. We also study the symmetries of the theory and construct, for a large group of them, their Noether currents, and charges. Moreover, we completely characterize the arbitrariness (or lack thereof for fiber bundles with contractible fibers) of these constructions. This clarifies many misconceptions about the role of the boundary terms in the CPS description of a field theory. Finally, we provide what we call the CPS-algorithm to construct the aforementioned (pre)symplectic structure and apply it to some relevant examples.
2021-08-18T09:50:09Z
2021-08-18T09:50:09Z
2021-01-15
2021-08-18T09:50:11Z
artículo
Physical Review D 103: 025011 (2021)
http://hdl.handle.net/10261/248291
http://dx.doi.org/10.13039/100000001
Publisher's version
http://dx.doi.org/10.1103/PhysRevD.103.025011
Sí
MICIU/ICTI2017-2020/FIS2017-84440-C2-2-P
openAccess
American Physical Society