重力與非交換場論的研究

Abstract

Historically, general relativity originates from a geometrical viewpoint, i.e., gravity is regarded as the curvature of the spacetime. However, thanks to the invention of quantum field theory, there exists another viewpoint which treats gravity effect as an exchange of massless spin 2 gravitons between particles. Formulating the theory of general relativity makes it possible that the ultimate laws of nature can be formulated in a united, universal framework and that gravity should be promoted to a quantized theory.

In the first part of this thesis, we develop the theory of a free graviton and will find an inconsistency in our theory should be solved. We focus on Feynman’s and Deser’s approaches to the problem, clarifying the meaning of their methods and explicitly working out the calculations to see if their results are correct.

Field theory formulated in a noncommutative space is expected to possess a property called UV/IR mixing originated from the nonlocal property of product of functions on noncommutative space. Hence, due to this nontrivial mixture between UV and IR phenomena in noncommutative quantum field theory, we expect that when considering NC-QFT at finite temperature, the chiral anomaly will have temperature dependence. In the second part of this thesis, we explicitly carry out the one-loop calculation of chiral anomaly in (1+1)-dim NC-QED at finite temperature in this thesis to see whether that expectation is true.