Coarse graining free theories with gauge symmetries: the linearized case

Details Coarse graining free theories with gauge symmetries: the linearized case Coarse graining free theories with gauge symmetries: the linearized case

2010-11-16

arxiv.org/abs/1011.3667v2

New J.Phys.13:045009,2011

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

31 pages, 3 pictures, title changed, reference updated

Scientific paper

10.1088/1367-2630/13/4/045009

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.

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