1206.2983 (Liu Zhao et al.)

Hamiltonian description of singular Lagrangian systems with
spontaneously broken time translation symmetry    [PDF]

Liu Zhao, Pengfei Yu, Wei Xu

Shapere and Wilczek recently found some singular Lagrangian systems which spontaneously breaks time translation symmetry. The common feature of their models is that the energy functions is multivalued in terms of the canonical phase space variables and the symmetry breaking ground states are all located at the brunching point singularities. By enlarging the phase space and making use of Dirac's theory on constrained Hamiltonian systems, we present the Hamiltonian description of some of the models discussed by Shapere and Wilczek and found that both the multivaluedness and the brunching point singularities can be avoided, while the spontaneous breaking of time translation and time reversal symmetries becomes more transparent. The only sacrifice to be paid is the use of non Darboux variables on the phase space.

View original: http://arxiv.org/abs/1206.2983