OUTLINE OF A GENERALLY COVARIANT QUANTUM FIELD THEORY AND A QUANTUM THEORY OF GRAVITY

Abstract

We study a tentative generally covariant quantum field theory, denoted the T-Theory, as a tool to investigate the consistency of quantum general relativity. The theory describes the gravitational field and a minimally coupled scalar field; it is based on the loop representation, and on a certain number of quantization choices. Four-dimensional diffeomorphism-invariant quantum transition probabilities can be computed from the theory. We present the explicit calculation of the transition probability between two volume eigenstates as an example. We discuss the choices on which the T-theory relies, and the possibilities of modifying them.

Latex file, 33 pages

References in corpus (7)

• Discreteness of area and volume in quantum gravity
• Spin Networks and Quantum Gravity
• Weaving a classical geometry with quantum threads
• Von Neumann Algebra Automorphisms and Time-Thermodynamics Relation in General Covariant Quantum Theories
• The physical hamiltonian in nonperturbative quantum gravity
• Fermions in Quantum Gravity
• Spin Networks, Turaev-Viro Theory and the Loop Representation

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