Quantum Dynamics of the Polarized Gowdy T 3 Model
نویسنده
چکیده
The polarized Gowdy T 3 vacuum spacetimes are characterized, modulo gauge, by a " point particle " degree of freedom and a function ϕ that satisfies a linear field equation and a non-linear constraint. The quantum Gowdy model has been defined by using a representation for ϕ on a Fock space F. Using this quantum model, it has recently been shown that the dynamical evolution determined by the linear field equation for ϕ is not unitarily implemented on F. In this paper: (1) We derive the classical and quantum model using the " covariant phase space " formalism. (2) We show that time evolution is not unitarily implemented even on the physical Hilbert space of states H ⊂ F defined by the quantum constraint. (3) We show that the spatially smeared canonical coordinates and momenta as well as the time-dependent Hamiltonian for ϕ are well-defined, self-adjoint operators for all time, admitting the usual probability interpretation despite the lack of unitary dynamics.
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