Canonical aspects of pregeometric vector-based first order gauge theory
arxiv(2024)
摘要
A recently proposed pregeometric auxiliary vector mediated gauge theory is
studied in its canonical domain, by performing the Legendre transform on a
curved background and by considering its covariant phase space. This uncovers
several curious properties and problems, even if the viability of the theory
itself is questionable at best. The constraints become differential equations,
although the Dirac-Bergmann algorithm appears consistent with electromagnetic
degrees of freedom, background permitting. Solving the consistency conditions
provides what appears to be spontaneous Lorentz symmetry breaking to obtain a
secondary constraint. In parallel, the covariant phase space defines the
symplectic structure, immediately relevant for quantization. Conserved currents
naturally follow: some details are collected and elaborated. Properties of
degenerate metric geometry are discussed throughout. The full phenomenology of
the vector theory, classical and quantum, is established to be that of gauge
theory on a classical electromagnetic background. This leads into the
fundamental question of background independence in all physical theories.
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