Classification of constraints and degrees of freedom for quadratic discrete actions
- Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario N2L 2Y5 (Canada)
We provide a comprehensive classification of constraints and degrees of freedom for variational discrete systems governed by quadratic actions. This classification is based on the different types of null vectors of the Lagrangian two-form and employs the canonical formalism developed in Dittrich and Höhn [“Constraint analysis for variational discrete systems,” J. Math. Phys. 54, 093505 (2013); e-print http://arxiv.org/abs/arXiv:1303.4294 [math-ph]] and Höhn [“Quantization of systems with temporally varying discretization I: Evolving Hilbert spaces,” J. Math. Phys. 55, 083508 (2014); e-print http://arxiv.org/abs/arXiv:1401.6062 [gr-qc]]. The analysis is carried out in both the classical and quantum theory and applies to systems with both temporally varying or constant discretization. In particular, it is shown explicitly how changes in the discretization, e.g., resulting from canonical coarse graining or refining operations or an evolving background geometry, change the dynamical content of the system. It is demonstrated how, on a temporally varying discretization, constraints, Dirac observables, symmetries, reduced phase spaces, and physical Hilbert spaces become spacetime region dependent. These results are relevant for free field theory on an evolving lattice and linearized discrete gravity models.
- OSTI ID:
- 22403057
- Journal Information:
- Journal of Mathematical Physics, Vol. 55, Issue 11; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
Similar Records
Quantization of systems with temporally varying discretization. I. Evolving Hilbert spaces
Monotonicity of a relative Rényi entropy