Related papers: Noncommutative spaces as quantized constrained Ham…
Using the multisymplectic Hamiltonian formalism, we propose a Poisson bracket for the electromagnetic field that, in addition to satisfying the restricted principle of relativity, reproduces well-established results from the standard…
We study covariant models for vacuum spherical gravity within a canonical setting. Starting from a general ansatz, we derive the most general family of Hamiltonian constraints that are quadratic in first-order and linear in second-order…
We study the {\it quasi-classical limit} of a quantum system composed of finitely many non-relativistic particles coupled to a quantized field in Nelson-type models. We prove that, as the field becomes classical and the corresponding…
A Hamiltonian formulation of generic many-particle systems with space-dependent balanced loss and gain coefficients is presented. It is shown that the balancing of loss and gain necessarily occurs in a pair-wise fashion. Further, using a…
We propose a mathematical structure, based on a noncommutative geometry, which combines essential aspects of general relativity and quantum mechanics, and leads to correct "limiting cases" of both these theories. We quantize a groupoid…
In this paper a new formulation of quantum dynamics of totally constrained systems is developed, in which physical quantities representing time are included as observables. In this formulation the hamiltonian constraints are imposed on a…
Non-commutative structures were introduced, independently and around the same time, in mathematical and in condensed matter physics (see Table~1). Souriau's construction applied to the two-parameter central extension of the planar Galilei…
We discuss the quantum mechanics of a particle in a magnetic field when its position x^{\mu} is restricted to a periodic lattice, while its momentum p^{\mu} is restricted to a periodic dual lattice. Through these considerations we define…
We consider the quantum dynamics of a single particle in the plane under the influence of a constant perpendicular magnetic and a crossed electric potential field. For a class of smooth and small potentials we construct a non-trivial…
We consider the semiclassical equations of motion of a particle when both an external electromagnetic field and the Berry gauge field in the momentum space are present. It is shown that these equations are Hamiltonian and relations between…
We study influence of noncommutativity of coordinates and noncommutativity of momenta on the motion of a particle (macroscopic body) in uniform and non-uniform gravitational fields in noncommutative phase space of canonical type with…
We consider the phase space of the Maxwell field as a simplified framework to study the quantisation of holonomies (Wilson line operators) on lightlike (null) surfaces. Our results are markedly different from the spacelike case. On a…
The eigenvalue problem of the Hamiltonian of an electron confined to a plane and subjected to a perpendicular time-independent magnetic field which is the sum of a homogeneous field and an additional field contributed by a singular flux…
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…
A constant homogeneous magnetic field is applied to a composite system made of two scalar particles with opposite charges. Motion is described by a pair of coupled Klein-Gordon equations that are written in closed form with help of a…
In this paper, we investigated the Pauli equation in a two-dimensional noncommutative phase-space by considering a constant magnetic field perpendicular to the plane. We mapped the noncommutative problem to the equivalent commutative one…
The Maxwell-covariant particle model is formulated in tensorial extended D=4 space-time (x_mu, z_{mu nu}) parametrized by ten-dimensional coset of D=4 Maxwell group, with added auxiliary Weyl spinors lambda_alpha, y^alpha. We provide the…
The relativistic spinning particle model, proposed in [3,4], is analyzed in a Hamiltonian framework. The spin is simulated by extending the configuration space by introducing a light-like four vector degree of freedom. The model is heavily…
We implement the so-called Weyl-Heisenberg covariant integral quantization in the case of a classical system constrained by a bounded or semi-bounded geometry. The procedure, which is free of the ordering problem of operators, is…
In an external constant magnetic field, so strong that the electron Larmour length is much shorter than its Compton length, we consider the modification of the Coulomb potential of a point charge owing to the vacuum polarization. We…