A PURE DIRAC'S METHOD FOR HUSAIN–KUCHAR THEORY

2013/04/05 by Alberto Escalante, ALBERTO ESCALANTE, J. Berra +1 · 1 citation
Mathematics · Physics and Astronomy · #Algebra over a field #Black Holes and Theoretical Physics #Canonical quantization #Constraint algebra #Gauge theory #Homotopy and Cohomology in Algebraic Topology #Measure (data warehouse) #Noncommutative and Quantum Gravity Theories #Path integral formulation #Phase space #Quantization (signal processing) #Quantum gravity #hep-th

paper · pdf · doi:10.1142/s0219887813500308

published in International Journal of Geometric Methods in Modern Physics 10(07), 1350030 (World Scientific)

openalex publication_date 2013/04/05 · arxiv created 2013/09/27 · arxiv updated 2013/10/15 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

A pure Dirac's canonical analysis, defined in the full phase space for the Husain–Kuchar (HK) model is discussed in detail. This approach allows us to determine the extended action, the extended Hamiltonian, the complete constraint algebra and the gauge transformations for all variables that occur in the action principle. The complete set of constraints defined on the full phase space allow us to calculate the Dirac algebra structure of the theory and a local weighted measure for the path integral quantization method. Finally, we discuss briefly the necessary mathematical structure to perform the canonical quantization program within the framework of the loop quantum gravity approach.

Citations

• Reality Conditions and Ashtekar Variables: a Different Perspective
• Anomaly-free formulation of non-perturbative, four-dimensional Lorentzian quantum gravity
• Canonical Quantization of General Relativity in Discrete Space-Times
• Loop space representation of quantum general relativity
• 2 + 1 dimensional gravity as an exactly soluble system
• New Hamiltonian formulation of general relativity
• Quantization of diffeomorphism invariant theories of connections with local degrees of freedom
• Partial and Complete Observables for Canonical General Relativity
• Automorphism covariant representations of the holonomy-flux lowast-algebra
• Algebra

Cited by

• Discrete canonical analysis of three dimensional gravity with cosmological constant

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• Hamiltonian Constraints and Dirac's Observables: from Relativistic Particles towards Field Theory and General Relativity.