Dirac's discrete hypersurface deformation algebras

Understand

The diffeomorphism symmetry of general relativity leads in the canonical formulation to constraints, which encode the dynamics of the theory.

• These constraints satisfy a complicated algebra, known as Dirac's hypersurface deformation algebra.
• This algebra has been a long standing challenge for quantization.
• One reason is that discretizations, on which many quantum gravity approaches rely, generically break diffeomorphism symmetry.