General relativity as the four-dimensional Chern-Weil theory
Year: 2017
Type: preprint
Abstract: A classical theory of general relativity in the four-dimensional space-timeis formulated as a Chern--Simons topological theory. A Chern--Simons
topological theory in four dimensional space is defined using a novel
translation operator, under which a Einstein--Hilbert gravitational action is
invariant up to total derivative and is constructed as a second Chern class. A
canonical quantization of the system is performed in a Heisenberg picture using
the Nakanishi--Kugo--Ojima formalism. A complete set of the quantum Lagrangian
and BRS transformations including auxiliary and ghost fields is given in a self
consistent manner. With a topological insight, an appropriate Hilbert space and
physical states are introduced into the theory. As a consequence, the
positivity of the physical states and the unitarity of the transition matrix
are ensured by the Kugo--Ojima theorem. These results suggests that the quantum
general relativity in this formalism is renormalizable, if a perturbative
expansion is performed with respect to an appropriate expansion constant around
an appropriate grand state in a Heisenberg picture.
Source: arXiv (Cornell University)
Author: Y. Kurihara
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2601879363