Quantization of diffeomorphism invariant theories of connections with a non-compact structure group - an example

Abstract

A simple diffeomorphism invariant theory of connections with the non-compact structure group R of real numbers is quantized. The theory is defined on a four-dimensional 'space-time' by an action resembling closely the self-dual Plebanski action for general relativity. The space of quantum states is constructed by means of projective techniques by Kijowski. Except this point the applied quantization procedure is based on Loop Quantum Gravity methods.

59 pages, no figures, LaTeX2e, this is a shortened version published in Comm. Math. Phys

References in corpus (1)

• Uniqueness of diffeomorphism invariant states on holonomy-flux algebras

Cited by in corpus (15)

• Fundamental Structure of Loop Quantum Gravity
• Flux formulation of loop quantum gravity: Classical framework
• Construction of spaces of kinematic quantum states for field theories via projective techniques
• ADM-like Hamiltonian formulation of gravity in the teleparallel geometry
• Kinematic quantum states for the Teleparallel Equivalent of General Relativity
• Projective Limits of State Spaces II. Quantum Formalism
• Projective Limits of State Spaces I. Classical Formalism
• Projective Loop Quantum Gravity I. State Space
• Topspin Networks in Loop Quantum Gravity
• Variables suitable for constructing quantum states for the Teleparallel Equivalent of General Relativity II
• A modification of the projective construction of quantum states for field theories
• A new realization of quantum geometry
• Projective Loop Quantum Gravity II. Searching for Semi-Classical States
• Space of quantum states built over metrics of fixed signature
• Constrained projective quantum states for the degenerate Plebanski gravity