Constrained projective quantum states for the degenerate Plebański gravity

2017/03/21 by Andrzej Okolow, Andrzej Okołów
Mathematics · Physics and Astronomy · #Degenerate energy levels #Kinematics #Loop quantum gravity #Noncommutative and Quantum Gravity Theories #Projective test #Quantum #Quantum Electrodynamics and Casimir Effect #Quantum Mechanics and Applications #Quantum field theory #Quantum gravity #Quantum state #gr-qc #hep-th #math-ph #math.MP

paper · pdf · doi:10.1063/1.4990792

published as J. Math. Phys. 58, 102302 (2017) · 36 pages, LaTeX2e

arxiv created 2017/03/21 · openalex created_date 2017/05/05 · openalex publication_date 2017/10/01 · arxiv updated 2017/11/16 · openalex updated_date 2026/08/05

Abstract

So far, projective quantum states have been constructed for a number of field theories including loop quantum gravity. However, these states are kinematic in the sense that their construction does not take into account the dynamics of the theories. In particular, the construction neglects constraints on phase spaces. Here we present projective quantum states which satisfy a constraint—the states are built for a “toy-theory” called degenerate Plebański gravity.

Citations

• Introduction to Modern Canonical Quantum General Relativity
• Uniqueness of Diffeomorphism Invariant States on Holonomy–Flux Algebras
• Hilbert space built over connections with a non-compact structure group
• Projective techniques and functional integration for gauge theories
• Quantization of diffeomorphism invariant theories of connections with local degrees of freedom

Cited by

• A modification of the projective construction of quantum states for field theories