Dr. Yong-Shi Wu
University of Utah
Project Title
Stochastic Approach to Quantum Gravity and Cosmology
Co-Investigators
Fuwen Shu, Asia Pacific Center for Theoretical Physics
Project Summary
Einstein's General Theory of Relativity is the fundamental theory of space-time and gravitation of our time. Quantum theory is the dynamical theory of atomic and subatomic particles and fields that mediate fundamental interactions (except gravity). Both are well-tested and universally accepted, but they are known to be incompatible with each other. How to unify the two fundamental theories of our physical world remains a challenge since the thirties of last century. In unifying gravity with quantum theory, many school of thoughts hold that general relativity should be modified, but whether or how quantum theory should be modified has been not thought of as thoroughly. We suggest to apply a stochastic (random) approach, that directly starts with studying the effects of quantum fluctuations, which are known at the root of many phenomena peculiar to quantum theory. We will apply such an approach to quantum dynamics of black holes and to inflationary cosmology of early universe. Either (partial) success or failure of this approach to gravity or cosmology will shed light, from a more physical (rather than formal) point of view, on the problem of whether or how quantum theory should be modified for a successful unifying theory of quantum gravity.
Technical Abstract
We propose a research project on the stochastic approach to quantum gravity and cosmology. To achieve a theory that incorporates consistently gravity into a quantum theory framework, we suggest to apply the framework of stochastic quantization to phenomena involving gravity. Instead of formal developments, we prefer to study problems of physics interests, such as 1) quantum dynamics of the BTZ black hole in three dimensions and 2) quantum effects (in the models of inflation) on the interplay between gravity and scalar fields with noncanonical kinetic terms. The stochastic evolution equation is just the geometric Ricci flow with an extra random fluctuation (say, white noise) term. Recently there is a breakthrough on understanding the classical Ricci flow in three dimensions due to Perelman's work. Our study will concentrate on the effects of the extra fluctuation term. The stochastic approach is a constructive one to studying quantum dynamics, and can easily go beyond the semi-classical regime at least numerically. These features make the stochastic approach more suitable than usual canonical or path integral approach to deal with quantum dynamics of gravitational systems, such as black holes or the early universe which are known to be intrinsically unstable.
Hide Technical Abstract
We propose a research project on the stochastic approach to quantum gravity and cosmology. To achieve a theory that incorporates consistently gravity into a quantum theory framework, we suggest to apply the framework of stochastic quantization to phenomena involving gravity. Instead of formal developments, we prefer to study problems of physics interests, such as 1) quantum dynamics of the BTZ black hole in three dimensions and 2) quantum effects (in the models of inflation) on the interplay between gravity and scalar fields with noncanonical kinetic terms. The stochastic evolution equation is just the geometric Ricci flow with an extra random fluctuation (say, white noise) term. Recently there is a breakthrough on understanding the classical Ricci flow in three dimensions due to Perelman's work. Our study will concentrate on the effects of the extra fluctuation term. The stochastic approach is a constructive one to studying quantum dynamics, and can easily go beyond the semi-classical regime at least numerically. These features make the stochastic approach more suitable than usual canonical or path integral approach to deal with quantum dynamics of gravitational systems, such as black holes or the early universe which are known to be intrinsically unstable.
Hide Technical Abstract
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