A New Non-Perturbative Approach to Quantum Theory in Curved Spacetime Using the Wigner Function

Abstract

A new non-perturbative approach to quantum theory in curved spacetime and to quantum gravity, based on a generalisation of the Wigner equation, is proposed. Our definition for a Wigner equation differs from what have otherwise been proposed, and does not imply any approximations. It is a completely exact equation, fully equivalent to the Heisenberg equations of motion. The approach makes different approximation schemes possible, e.g. it is possible to perform a systematic calculation of the quantum effects order by order. An iterative scheme for this is also proposed. The method is illustrated with some simple examples and applications. A calculation of the trace of the renormalised energy-momentum tensor is done, and the conformal anomaly is thereby related to non-conservation of a current in d=2 dimensions and a relationship between a vector and an axial-vector current in d=4 dimensions. The corresponding ``hydrodynamic equations'' governing the evolution of macroscopic quantities are derived by taking appropriate moments. The emphasis is put on the spin-1/2 case, but it is shown how to extend to arbitrary spins. Gravity is treated first in the Palatini formalism, which is not very tractable, and then more successfully in the Ashtekar formalism, where the constraints lead to infinite order differential equations for the Wigner functions.

LaTeX2e (uses amssymb), 36 pages

References in corpus (1)

• Wigner function and quantum kinetic theory in curved space-time and external fields

Cited by in corpus (17)

• Admissible states in quantum phase space
• A Kinetic Theory Approach to Quantum Gravity
• Quantum kinetic theory for spin-1/2 fermions in Wigner function formalism
• Deformation Quantization of Bosonic Strings
• Scalar field dark matter in hybrid approach
• Kinetic theory and classical limit for real scalar quantum field in curved space-time
• The Quantum State Of The Universe From Deformation Quantization and Classical-Quantum Correlation
• Ground-state Wigner functional of linearized gravitational field
• The Wigner formalism on black hole geometries
• Phase Space Quantum Mechanics
• Classical Universe Arising from Quantum Cosmology
• Cosmological Particle Creation Using an Equal-Time Wigner Formalism
• Uncertainty Relations in Deformation Quantization
• Deformation Quantization of Relativistic Particles in Electromagnetic Fields
• Rarita-Schwinger Quantum Free Field Via Deformation Quantization
• Kinetic equation for Lifshitz scalar
• Stargenfunctions, generally parametrized systems and a causal formulation of phase space quantum mechanics