Coarse graining free theories with gauge symmetries: the linearized case
arXiv:1011.3667 · doi:10.1088/1367-2630/13/4/045009
Abstract
Discretizations of continuum theories often do not preserve the gauge symmetry content. This occurs in particular for diffeomorphism symmetry in general relativity, which leads to severe difficulties both in canonical and covariant quantization approaches. We discuss here the method of perfect actions, which attempts to restore gauge symmetries by mirroring exactly continuum physics on a lattice via a coarse graining process. Analytical results can only be obtained via a perturbative approach, for which we consider the first steps, namely the coarse graining of the linearized theory. The linearized gauge symmetries are exact also in the discretized theory, hence we develop a formalism to deal with gauge systems. Finally we provide a discretization of linearized gravity as well as a coarse graining map and show that with this choice the 3D linearized gravity action is invariant under coarse graining.
arXiv comment31 pages, 3 pictures, title changed, reference updated
References in corpus (23)
- Spin Foam Models for Quantum Gravity
- Twisted geometries: A geometric parametrisation of SU(2) phase space
- The Phoenix Project: Master Constraint Programme for Loop Quantum Gravity
- Discrete approaches to quantum gravity in four dimensions
- Perfect Lattice Actions for Quarks and Gluons
- Algebraic Quantum Gravity (AQG) I. Conceptual Setup
- Phase space descriptions for simplicial 4d geometries
- Improved and Perfect Actions in Discrete Gravity
- Testing the Master Constraint Programme for Loop Quantum Gravity I. General Framework
- Perfect discretization of reparametrization invariant path integrals
- Regge calculus from a new angle
- Simplicity in simplicial phase space
- Linearized dynamics from the 4-simplex Regge action
- From covariant to canonical formulations of discrete gravity
- Quantum gravity asymptotics from the SU(2) 15j symbol
- Breaking and restoring of diffeomorphism symmetry in discrete gravity
- Uniform discretizations: a new approach for the quantization of totally constrained systems
- Gauge Invariance in Simplicial Gravity
- Non-Perturbative Gravity and the Spin of the Lattice Graviton
- Area Regge Calculus and Discontinuous Metrics
- Diffeomorphism invariant measure for finite dimensional geometries
- Diffeomorphism symmetry in quantum gravity models
- Perfect Scalars on the Lattice
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- Discrete Gravity Models and Loop Quantum Gravity: a Short Review
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