Covariant quantization of general relativity in four dimensional space time
by
Prof.Yoshimasa Kurihara(KEK)
→
Europe/Amsterdam
H320 (Nikhef)
H320
Nikhef
Description
Our understanding of nature covers a wide range of length scale from the large-scale structure of the universe, using general relativity, to the microscopic behavior of sub-atomic elements, using quantum field theory. However, these two fundamental theories are not yet consistent each other. A construction of a quantum theory of gravity is one of the most fundamental goal of present physics.
In my talk, I would like to explain my recent work related quantization of general relativity: At first, a classical theory of general relativity in the four-dimensional space-time is formulated based on a Chern-Weil theory. An action with a topological invariant in four dimensional space is defined using a novel translation operator, under which an 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 under the completely covariant way using the Nakanishi-Kugo-Ojima formalism. 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.
This talk is based on;
Y. Kurihara, “Characteristic classes in general relativity on a modified Poincaré curvature bundle”, Journal of Mathematical Physics 58 (9) (2017) 092502.
Y. Kurihara, “General relativity as the four dimensional Chern-Weil theory”, arXiv:1703.05574.
