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Familiar textbook quantum mechanics assumes a fixed background spacetime to define states on spacelike surfaces and their unitary evolution between them. Quantum theory has changed as our conceptions of space and time have evolved. But…
In this thesis, we investigate the dynamical Casimir effect, the creation of particles from vacuum by dynamical boundary conditions or dynamical background, and its backreaction to the motion of the boundary. The backreaction of particle…
We study the time evolution of a state of a relativistic quantum field theory restricted to a spatial subregion $\Omega$. More precisely, we use the Feynman-Vernon influence functional formalism to describe the dynamics of the field theory…
Wave functions of bounded quantum systems with time-independent potentials, being almost periodic functions, cannot have time asymptotics as in classical chaos. However, bounded quantum systems with time-dependent interactions, as used in…
Location dependence of physical parameters such as the electromagnetic fine structure constant and Newton's G produce body accelerations which violate universality of free fall rates testable with laboratory and space experiments.…
The nature of time in quantum mechanics is closely related to the use of a complex, rather than say real, Hilbert space. This becomes particularly clear when considering quantum field theory in time dependent backgrounds, such as in…
Quantum Gravity by Causal Dynamical Triangulation has over the last few years emerged as a serious contender for a nonperturbative description of the theory. It is a nonperturbative implementation of the sum-over-histories, which relies on…
There should be quantum vacuum fluctuations of spacetime itself, if we accept that the basic quantum principles we are already familiar with apply as well to a quantum theory of gravity. In this paper, we study, in linearized quantum…
We show that generalizations of classical and quantum dynamics with two times lead to fundamentally constrained evolution. At the level of classical physics, Newton's second law is extended and exactly integrated in $1+2$ dimensional space,…
We investigate the implications of decoherence induced by quantum spacetime properties on neutrino oscillation phenomena. We develop a general formalism where the evolution of neutrinos is governed by a Lindblad-type equation and we compute…
Generators of spacetime translations and Lorentz group transformations form the Lie algebra of the Poincar\'e group and give rise to the Casimir invariants for a specification of elementary particle characteristics. Moreover quantum…
The time evolution is studied for the Landau problem with a general time dependent electric field ${\bf E}(t)$ in a plane perpendicular to the magnetic field. A general and explicit factorization of the time evolution operator is derived…
A novel expansion -- which generalizes Magnus expansion -- of the evolution operator associated with a (in general, time-dependent) perturbed Hamiltonian is introduced. It is shown that it has a wide range of possible solutions that can be…
We investigate consequences of allowing the Hilbert space of a quantum system to have a time-dependent metric. For a given possibly nonstationary quantum system, we show that the requirement of having a unitary Schreodinger time-evolution…
It is well known that the expansion of the universe can create particles. However, due to ambiguities when defining particles during the expansion, there are still debates about how to choose vacuum and particle states. To clarify how…
General Theory of Relativity and Quantum theory gives two different description of the same mother nature in the big and small scale respectively. Mathematical languages of these two theories are entirely different, one is geometric while…
Based on the hypothesis that the thermodynamic arrow of time is an emergent phenomenon of quantum state complexity evolution, we further propose that the natural pace of time flow is proportional to the changing rate of quantum state…
The formulation of quantum mechanics within the framework of entropic dynamics is extended to the domain of relativistic quantum fields. The result is a non-dissipative relativistic diffusion in the infinite dimensional space of field…
We study the Schwinger pair creation of scalar charged particles by a homogeneous electric field in an expanding universe in the quantum kinetic approach. We introduce an adiabatic vacuum for the scalar field based on the…
The framework of a theory of gravity from the quantum to the classical regime is presented. The paradigm shift from full spacetime covariance to spatial diffeomorphism invariance, together with clean decomposition of the canonical…