Loop Quantum Cosmology: A Window Into the Path Integral Representation of Quantum Gravity
Open Access
Author:
Henderson, Adam Dade
Graduate Program:
Physics
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
August 10, 2011
Committee Members:
Abhay Vasant Ashtekar, Dissertation Advisor/Co-Advisor Abhay Vasant Ashtekar, Committee Chair/Co-Chair Paul Sommers, Committee Member Victor Nistor, Committee Member Dezhe Jin, Committee Member
Keywords:
Quantum Gravity Path Integral
Abstract:
In this dissertation we present sum of histories formulations of loop quantum cosmology.
These are considered for exactly soluble LQC expressed in a Schrodinger
form with time provided by a scalar field where we are interested in transition
amplitudes and as a constrained system where we are interested in the physical
inner product defined by group averaging. As loop quantum cosmology is based on
the new quantum mechanics motivated from the representation of loop quantum
gravity the sum over histories have many distinct features from standard Feynman
path integrals. The sum over histories is given by an discrete sum over histories
which change configuration only finitely many times. The resulting sum over histories
have strong similarities to the current spin foam models while being derived
from a well-controlled canonical quantization. Thus we are able to probe many of
the open questions of spin foam models as well as provide new insights and avenues
of research.
