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Hamiltonian constraints and unfree gauge symmetry | | V. A. Abakumova
; S. L. Lyakhovich
; | | Date: |
7 Sep 2020 | | Abstract: | We study Hamiltonian form of unfree gauge symmetry where the gauge parameters
have to obey differential equations. We consider the general case such that the
Dirac-Bergmann algorithm does not necessarily terminate at secondary
constraints, and tertiary and higher order constraints may arise. Given the
involution relations for the first-class constraints of all generations, we
provide explicit formulas for unfree gauge transformations in the Hamiltonian
form, including the differential equations constraining gauge parameters. All
the field theories with unfree gauge symmetry share the common feature: they
admit sort of "global constants of motion" such that do not depend on the local
degrees of freedom. The simplest example is the cosmological constant in the
unimodular gravity. We consider these constants as modular parameters rather
than conserved quantities. We provide a systematic way of identifying all the
modular parameters. We demonstrate that the modular parameters contribute to
the Hamiltonian constraints, while they are not explicitly involved in the
action. The Hamiltonian analysis of the unfree gauge symmetry is precessed by a
brief exposition for the Lagrangian analogue, including explicitly covariant
formula for degrees of freedom number count. We also adjust the BFV-BRST
Hamiltonian quantization method for the case of unfree gauge symmetry. The main
distinction is in the content of the non-minimal sector and gauge fixing
procedure. The general formalism is exemplified by traceless tensor fields of
irreducible spin $s$ with the gauge symmetry parameters obeying transversality
equations. | | Source: | arXiv, 2009.02848 | | Services: | Forum | Review | PDF | Favorites | |
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