Pseudoclassical system with gauge and time-reparametrization invariance

Abstract

We present a pseudoclassical mechanics model which exhibits gauge symmetry and time-reparametrization invariance. As such, first- and second-class constraints restrict the phase space, and the Hamiltonian weakly vanishes. We show that the Dirac conjecture does not hold -- the secondary first-class constraint is not a symmetry generator -- and only the gauge fixing condition associated with the primary first-class constraint is needed to remove the gauge ambiguities. The gauge fixed theory is equivalent to the Fermi harmonic oscillator extended by a boundary term. We quantize in the deformation quantization and in the Schrodinger representation approaches and observe that the boundary term prepares the system in the state of positive energy.

18 pages

References in corpus (4)

• Symmetries in Physics: Philosophical Reflections
• Unconventional SUSY and Conventional Physics: A Pedagogical Review
• Chiral gauge theory and gravity from unconventional supersymmetry
• $\mathcal{N}=2$ Extended MacDowell-Mansouri Supergravity

Cited by in corpus (2)

• Massless Rarita-Schwinger equations: Half and three halves spin solution
• Gauge and time-reparametrization invariant spin-half fields