A real alternative to quantum gravity in loop space

Abstract

We show that the Hamiltonian of four-dimensional Lorentzian gravity, defined on a space of real, SU(2)-valued connections, in spite of its non-polynomiality possesses a natural quantum analogue in a lattice-discretized formulation of the theory. This opens the way for a systematic investigation of its spectrum. The unambiguous and well-defined scalar product is that of the SU(2)-gauge theory. We also comment on various aspects of the continuum theory.

11 pages, plain TeX, Feb 96

References in corpus (7)

• Spin Networks and Quantum Gravity
• Barbero's Hamiltonian derived from a generalized Hilbert-Palatini action
• Geometry Eigenvalues and Scalar Product from Recoupling Theory in Loop Quantum Gravity
• THE VOLUME OPERATOR IN DISCRETIZED QUANTUM GRAVITY
• Reality conditions inducing transforms for quantum gauge field theory and quantum gravity
• Spectrum of the Volume Operator in Quantum Gravity
• Multi-plaquette solutions for discretized Ashtekar gravity

Cited by in corpus (12)

• Quantum Spin Dynamics (QSD) II
• Discrete approaches to quantum gravity in four dimensions
• Geometry Eigenvalues and Scalar Product from Recoupling Theory in Loop Quantum Gravity
• The Immirzi parameter in quantum general relativity
• On the relation between the connection and the loop representation of quantum gravity
• The classical limit and the form of the hamiltonian constraint in nonperturbative quantum gravity
• Simplifying the spectral analysis of the volume operator
• Triad representation of the Chern-Simons state in quantum gravity
• Imposing det E > 0 in discrete quantum gravity
• Bibliography of publications related to Classical and Quantum Gravity in terms of Connection and Loop Variables
• Three Dimensional Strings as Collective Coordinates of Four Dimensional Non-Perturbative Quantum Gravity
• Semiclassical Length Measure from a Quantum-Gravity Wave Function