Related papers: Quantum Mechanics on a Ring: Continuity versus Gau…
It is shown that quantum mechanics on noncommutative spaces (NQM) can be obtained by the canonical quantization of some underlying second class constrained system formulated in extended configuration space. It leads, in particular, to an…
In this thesis noncommutative gauge theory is extended beyond the canonical case, i.e. to structures where the commutator no longer is a constant. In the first part noncommutative spaces created by star-products are studied. We are able to…
It is known that the momentum operator canonically conjugated to the position operator for a particle moving in some bounded interval of the line {(with Dirichlet boundary conditions) is not essentially self-adjoint}: it has a continuous…
We consider non-relativistic systems in quantum mechanics interacting through the Coulomb potential, and discuss the existence of bound states which are stable against spontaneous dissociation into smaller atoms or ions. We review the…
We propose that the mechanism responsible for the ``collapse of the wave function" (or "decoherence" in its broadest meaning) in quantum mechanics is the nonlinearities already present in the theory via nonabelian gauge interactions. Unlike…
We define for quantum many-body systems a quasi-adiabatic continuation of quantum states. The continuation is valid when the Hamiltonian has a gap, or else has a sufficiently small low-energy density of states, and thus is away from a…
We study quantum field theories with boundary by utilizing non-invertible symmetries. We consider three kinds of boundary conditions of the four dimensional $\mathbb{Z}_2$ lattice gauge theory at the critical point as examples. The weights…
The equivalence postulate approach to quantum mechanics entails a derivation of quantum mechanics from a fundamental geometrical principle. Underlying the formalism there exists a basic cocycle condition, which is invariant under…
Quantum field theory is assumed to be gauge invariant. It is shown that for a Dirac field the assumption of gauge invariance impacts on the way the vacuum state is defined. It is shown that the conventional definition of the vacuum state…
Aspects of quantum mechanics on a ring are studied. Either one or two impenetrable barriers are inserted at nodal and non-nodal points to turn the ring into either one or two infinite square wells. In the process, the wave function of a…
It is shown that quantum mechanics on noncommutative (NC) spaces can be obtained by canonical quantization of some underlying constrained systems. Noncommutative geometry arises after taking into account the second class constraints…
It is claimed in another paper that the collapse of a quantum mechanical wave function is more than invariant, it is trans-representational. It must occur along a fully invariant surface. The obvious surface available for this purpose is…
Quantum mechanics of a particle in an infinite square well under the influence of a time-dependent electric field is reconsidered. In some gauge, the Hamiltonian depends linearly on the momentum operator which is symmetric but not…
The purpose of the paper is to study the foundations of the main axioms of Quantum Mechanics. From a general study of the mathematical properties of the models used in Physics to represent systems, we prove that the states of a system can…
Classically general covariance is found from the idea that a vector is a physical quantity which exists independently of choice of coordinate system and is unchanged by a change of coordinate system. It is often assumed that there exists…
It is demonstrated that, making minimal changes in ordinary quantum mechanics, a reasonable irreversible quantum mechanics can be obtained. This theory has a more general spectral decompositions, with eigenvectors corresponding to unstable…
It is shown that in semi-classical electrodynamics, which describes how electrically charged particles move according to the laws of quantum mechanics under the influence of a prescribed classical electromagnetic field, only a restricted…
Standard quantum mechanics unquestionably violates the separability principle that classical physics (be it point-like analytic, statistical, or field-theoretic) accustomed us to consider as valid. In this paper, quantum nonseparability is…
In this work some issues in the context of Noncommutative Quantum Mechanics (NCQM) are addressed. The main focus is on finding whether symmetries present in Quantum Mechanics still hold in the phase-space noncommutative version. In…
Quantum mechanical boundary conditions along a timelike line, corresponding to the origin in radial coordinates, in two-dimensional dilaton gravity coupled to $N$ matter fields, are considered. Conformal invariance and vacuum stability…