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Quantum Dynamics Of The Polarized Gowdy T3 Model, Charles G. Torre
Quantum Dynamics Of The Polarized Gowdy T3 Model, Charles G. Torre
All Physics Faculty Publications
The polarized Gowdy T3 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 nonlinear 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 …
The Principle Of Symmetric Criticality In General Relativity, Mark E. Fels, Charles G. Torre
The Principle Of Symmetric Criticality In General Relativity, Mark E. Fels, Charles G. Torre
All Physics Faculty Publications
We consider a version of Palais' principle of symmetric criticality (PSC) that is applicable to the Lie symmetry reduction of Lagrangian field theories. Given a group action on a space of fields, PSC asserts that for any group-invariant Lagrangian, the equations obtained by restriction of Euler–Lagrange equations to group-invariant fields are equivalent to the Euler–Lagrange equations of a canonically defined, symmetry-reduced Lagrangian. We investigate the validity of PSC for local gravitational theories built from a metric and show that there are two independent conditions which must be satisfied for PSC to be valid. One of these conditions, obtained previously in …