Hall 123

The Role of Spacetime Curvature in Quantum Phenomena at Various Length Scales

Raghvendra Singh

IMSc

This thesis delves into how the structure of spacetime
affects quantum phenomena at both microscopic and macroscopic scales.
It examines the possibility of Euclidean characteristics at small
scales and analyzes the corresponding action within a covariant
framework. The study's significant contributions include exploring
entropy computation through Euclidean methods, revealing deviations
from traditional entropy in field theories, and Lanczos-Lovelock
actions. Incorporating a minimal length scale into the modified
dispersion relation leads to a covariant formulation of the
generalized uncertainty principle (GUP), which connects the Heisenberg
algebra, momentum space geometry, and a modified dispersion relation
within a unified framework. Furthermore, the thesis examines wave
function localization for macroscopic objects, emphasizing the role of
gravitational effects in the emergence of classical behavior. Overall,
this work provides insights into the relationship between spacetime
structure and quantum phenomena and offers contributions to entropy
computation, GUP, and classical behavior emergence.