Classification of constraints and degrees of freedom for quadratic discrete actions
arXiv:1407.6641 · doi:10.1063/1.4900926
Abstract
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 arXiv:1303.4294 [math-ph] (J. Math. Phys. 54, 093505 (2013)) and arXiv:1401.6062 [gr-qc] (J. Math. Phys. 55, 083508 (2014)). 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.
arXiv comment36 pages, 7 figures, 1 table, minor modifications, matches published version
References in corpus (27)
- Quantum Spin Dynamics (QSD)
- Anomaly-free formulation of non-perturbative, four-dimensional Lorentzian quantum gravity
- Trans-Planckian redshifts and the substance of the space-time river
- Improved and Perfect Actions in Discrete Gravity
- Coarse graining methods for spin net and spin foam models
- (Broken) Gauge Symmetries and Constraints in Regge Calculus
- From the discrete to the continuous - towards a cylindrically consistent dynamics
- Perfect discretization of reparametrization invariant path integrals
- Canonical quantization of general relativity in discrete space-times
- From covariant to canonical formulations of discrete gravity
- Canonical simplicial gravity
- Time evolution as refining, coarse graining and entangling
- The Hamiltonian constraint in 3d Riemannian loop quantum gravity
- Coarse graining free theories with gauge symmetries: the linearized case
- Recent Progress in Regge Calculus
- Uniform discretizations: a new approach for the quantization of totally constrained systems
- A regularization of the hamiltonian constraint compatible with the spinfoam dynamics
- Constraint analysis for variational discrete systems
- Principles of Discrete Time Mechanics: I. Particle Systems
- Dirac-like approach for consistent discretizations of classical constrained theories
- Quantization of systems with temporally varying discretization II: Local evolution moves
- Quantization of systems with temporally varying discretization I: Evolving Hilbert spaces
- Consistent and mimetic discretizations in general relativity
- Discretisations, Constraints and Diffeomorphisms in Quantum Gravity
- Consistent discretization and canonical classical and quantum Regge calculus
- Canonical formalism for simplicial gravity
- Multisymplectic effective General Boundary Field Theory
Cited by in corpus (7)
- A change of perspective: switching quantum reference frames via a perspective-neutral framework
- Quantization of systems with temporally varying discretization II: Local evolution moves
- Quantization of systems with temporally varying discretization I: Evolving Hilbert spaces
- A note on the secondary simplicity constraints in loop quantum gravity
- Canonical linearized Regge Calculus: counting lattice gravitons with Pachner moves
- Is the local linearity of space-time inherited from the linearity of probabilities?
- Discrete Linear Canonical Evolution