Related papers: Quantum mechanics not on manifold
Quantum systems with constraints are often considered in modern theoretical physcics. All realistic field models based on the idea of gauge symmetry are of this type. A partial case of constraints being linear in coordinate and momenta…
We consider a scalar quantum field theory, in which the interaction takes the form of a field cutoff; the energy diverges to infinity whenever the value of the field at some point falls outside a finite interval. In a simple…
The full spectrum and eigenfunctions of the quantum version of a nonlinear oscillator defined on an N-dimensional space with nonconstant curvature are rigorously found. Since the underlying curved space generates a position-dependent…
It is commonly assumed that quantum field theory arises by applying ordinary quantum mechanics to the low energy effective degrees of freedom of a more fundamental theory defined at ultra-high-energy/short-wavelength scales. We shall argue…
Duality transformations within the quantum mechanics of a finite number of degrees of freedom can be regarded as the dependence of the notion of a quantum, i.e., an elementary excitation of the vacuum, on the observer on classical phase…
We discuss various descriptions of a quantum particle on noncommutative space in a (possibly non-constant) magnetic field. We have tried to present the basic facts in a unified and synthetic manner, and to clarify the relationship between…
We study some aspects of the quantum theory of a charged particle moving in a time-independent, uni-directional magnetic field. When the field is uniform, we make a few clarifying remarks on the use of angular momentum eigenstates and…
Noncommutative quantum mechanics can be considered as a first step in the construction of quantum field theory on noncommutative spaces of generic form, when the commutator between coordinates is a function of these coordinates. In this…
A new approach is suggested which allows to describe phenomenologically arbitrary topologies of the Universe. It consists in a generalizaton of third quantization. This quantization is carried out for the case of asymptotic closeness to a…
A quantum shuttle is an archetypical nanoelectromechanical device, where the mechanical degree of freedom is quantized. Using a full-scale numerical solution of the generalized master equation describing the shuttle, we have recently shown…
We introduce a new model of background independent physics in which the degrees of freedom live on a complete graph and the physics is invariant under the permutations of all the points. We argue that the model has a low energy phase in…
Classical limits of quantum systems are shown to lead to different conceptions of spaces different from the classical one underlying the process of quantization of such systems. The accent is put in situations where traces of…
We discuss the dynamics of a classical spinless quantum particle carrying electric charge and constrained to move on a non singular static surface in ordinary three dimensional space in the presence of arbitrary configurations of time…
Starting with the first-order singular Lagrangian containing the redundant variables, the noncommutative quantum mechanics on a curved space is investigated by the constraint star-product quantization formalism of the projection operator…
An otherwise free classical particle moving through an extended spatially homogeneous medium with which it may exchange energy and momentum will undergo a frictional drag force in the direction opposite to its velocity with a magnitude…
The quantum system of a massless charged scalar field with a self-interaction is investigated. By introducing a spacial cut-off function, the Hamiltonian of the system is realized as a linear operator on a boson Fock space. It is proven…
A recently introduced class of quantum spherical spin models is considered in detail. Since the spherical constraint already contains a kinetic part, the Hamiltonian need not have kinetic term. As a consequence, situations with or without…
We analyze constrained quantum systems where the dynamics do not preserve the constraints. This is done in particular for the restriction of a quantum particle in Euclidean n-space to a curved submanifold, and we propose a method of…
Free quantum field theories on curved backgrounds are discussed via three explicit examples: the real scalar field, the Dirac field and the Proca field. The first step consists of outlining the main properties of globally hyperbolic…
Supersymmetric quantum mechanics is formulated on a two dimensional noncommutative plane and applied to the supersymmetric harmonic oscillator. We find that the ordinary commutative supersymmetry is partially broken and only half of the…