Discretisations, Constraints and Diffeomorphisms in Quantum Gravity
نویسندگان
چکیده
In this review we discuss the interplay between discretization, constraint implementation, and diffeomorphism symmetry in Loop Quantum Gravity and Spin Foam models. To this end we review the Consistent Discretizations approach, which is an application of the master constraint program to construct the physical Hilbert space of the canonical theory, as well as the Perfect Actions approach, which aims at finding a path integral measure with the correct symmetry behavior under diffeomorphisms.
منابع مشابه
Physical Diffeomorphisms in Loop Quantum Gravity
We investigate the action of diffeomorphisms in the context of Hamiltonian Gravity. By considering how the diffeomorphism-invariant Hilbert space of Loop Quantum Gravity should be constructed, we formulate a physical principle by demanding, that the gauge-invariant Hilbert space is a completion of gauge(i.e. diffeomorphism-)orbits of the classical (configuration) variables, explaining which ext...
متن کاملThe diffeomorphism algebra approach to quantum gravity
The representation theory of non-centrally extended Lie algebras of Noether symmetries, including spacetime diffeomorphisms and reparametrizations of the observer’s trajectory, has recently been developped. It naturally solves some long-standing problems in quantum gravity, e.g. the role of diffeomorphisms and the causal structure, but some new questions also arise.
متن کاملCTP-TAMU-13/92 Area-Preserving Diffeomorphisms, w ∞ Algebras and w ∞ Gravity †
The w ∞ algebra is a particular generalization of the Virasoro algebra with generators of higher spin 2, 3, ..., ∞. It can be viewed as the algebra of a class of functions, relative to a Poisson bracket, on a suitably chosen surface. Thus, w ∞ is a special case of area-preserving diffeomorphisms of an arbitrary surface. We review various aspects of area-preserving diffeomorphisms, w ∞ algebras ...
متن کاملO ct 2 00 5 SU ( 2 ) Loop Quantum Gravity seen from Covariant Theory
Covariant loop gravity comes out of the canonical analysis of the Palatini action and the use of the Dirac brackets arising from dealing with the second class constraints (“simplicity” constraints). Within this framework, we underline a quantization ambiguity due to the existence of a family of possible Lorentz connections. We show the existence of a Lorentz connection generalizing the Ashtekar...
متن کاملSe p 20 02 SU ( 2 ) Loop Quantum Gravity seen from Covariant Theory
Covariant loop gravity comes out of the canonical analysis of the Palatini action and the use of the Dirac brackets arising from dealing with the second class constraints (“simplicity” constraints). Within this framework, we underline a quantization ambiguity due to the existence of a family of possible Lorentz connections. We show the existence of a Lorentz connection generalizing the Ashtekar...
متن کامل