Year: 2025
Type: dissertation
Abstract: The trace anomaly represents a significant outcome of quantum field theory in curved spacetime.This thesis investigates the trace anomaly within a general metric-affine geometry that encompasses both torsion and nonmetricity.We first review the foundations of quantum field theory on curved spacetime and the framework of Metric-Affine gravity (MAG).The trace anomaly is typically computed using the heat kernel method which is typically utilized for the assessment of a one-loop effective action.The fundamental of this approach is the asymptotic expansion of the trace of the heat operator, which is known as the Seeley-DeWitt (SD) expansion.In this context, the expansion coefficients are occasionally referred to as Minakshisundaram coefficients, particularly within the field of differential geometry.In this thesis, we introduce Seeley's algorithm, which provides a systematic approach to computing these coefficients for any spacetime.Moreover, we compute the SD expansion for arbitrary spacetimes within the framework of Metric-Affine gravity, incorporating the effects of the nonmetricity and torsion tensors for the first time.Subsequently, we compute the trace anomaly at the one-loop level in scaling-invariant theories subjected to conformal, rescaling, and projective transformations.To illustrate, we examine the spin-0 and spin-1/2 cases, considering various interactions between matter and the gravitational sector.It is demonstrated that the invariance under the frame rescaling transformation results in an anomaly in the relationship between the hypermomentum and the stress-energy tensor, which arises from the dilation part mediated by the Weyl component of nonmetricity.In contrast, under the projective transformation, no anomaly is present; specifically, there is no non-zero trace of the hypermomentum tensor in any of the concrete examples considered.i
Authors: 宮下, 優一, Miyashita, Yuichi
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Award: 宇宙論における量子重力と非局所場理論
OpenAlex ID: W6987634457