Related papers: Quantum mechanics not on manifold
In this paper, quantum mechanics on a circle with finite number of {\alpha}-uniformly distributed points is discussed. The angle operator and translation operator are defined. Using discrete angle representation, two types of discrete…
The physics of quantum gravity is discussed within the framework of topological quantum field theory. Some of the principles are illustrated with examples taken from theories in which space-time is three dimensional.
We consider the quantum dynamics of a test particle in noncommutative space under the influence of linearized gravitational waves in the long wave-length and low-velocity limit. A prescription for quantizing the classical Hamiltonian for…
A quantum spin-$\frac{1}{2}$ chain with an axial symmetry is normally described by quasiparticles associated with the spins oriented along the axis of rotation. Kinetic constraints can enrich such a description by setting apart different…
This thesis is devoted to studying various aspects of quantum mechanics on non-commutative space-time and to capture some of the surviving aspects of symmetries of quantum field theory on such space-time, illustrated through toy models in…
We derive noncommutative multi-particle quantum mechanics from noncommutative quantum field theory in the nonrelativistic limit. Paricles of opposite charges are found to have opposite noncommutativity. As a result, there is no…
We investigate the incorporation of space noncommutativity into field theory by extending to the spectral continuum the minisuperspace action of the quantum mechanical harmonic oscillator propagator with an enlarged Heisenberg algebra. In…
This thesis is broadly split into two parts. In the first part, simple state sum models for minimally coupled fermion and scalar fields are constructed on a $1$-manifold. The models are independent of the triangulation and give the same…
We provide the quantum mechanics of many particles moving in twisted N-enlarged Newton-Hooke space-time. In particular, we consider the example of such noncommutative system - the set of M particles moving in Coulomb field of external…
A complete model of the universe needs at least three parts: (1) a complete set of physical variables and dynamical laws for them, (2) the correct solution of the dynamical laws, and (3) the connection with conscious experience. In quantum…
We describe a computational investigation of tunneling at finite energy in a weakly coupled quantum mechanical system with two degrees of freedom. We compare a full quantum mechanical analysis to the results obtained by making use of a…
We investigate the transition from second to first order systems. This transforms configuration space into phase space and hence introduces noncommutativity in the former. Quantum mechanically, the transition may be described in terms of…
A quantum system subject to external fields is said to be controllable if these fields can be adjusted to guide the state vector to a desired destination in the state space of the system. Fundamental results on controllability are reviewed…
In this work we report a new result that appears when one investigates the route that starts from a scalar field theory and ends on a supersymmetric quantum mechanics. The subject has been studied before in several distinct ways and here we…
We consider electrodynamics on a noncommutative spacetime using the enveloping algebra approach and perform a non-relativistic expansion of the effective action. We obtain the Hamiltonian for quantum mechanics formulated on a canonical…
Non-relativistic quantum mechanics is shown to emerge from classical mechanics through the requirement of a relativity principle based on special transformations acting on position and momentum uncertainties. These transformations keep the…
In physics, experiments ultimately inform us as to what constitutes a good theoretical model of any physical concept: physical space should be no exception. The best picture of physical space in Newtonian physics is given by the…
The theory of the free Maxwell field in two moving frames on the de Sitter spacetime is investigated pointing out that the conserved momentum and energy operators do not commute to each other. This leads us to consider new plane waves…
We address the problem of sensing the curvature of a manifold by performing measurements on a particle constrained to the manifold itself. In particular, we consider situations where the dynamics of the particle is quantum mechanical and…
We propose a formulation of quantum mechanics in three dimensions with spherical symmetry for a finite level system whose dynamics is not governed by a differential equation of motion. The wavefunction is written as an infinite sum in a…