相关论文: Particle on the sphere: group-theoretic quantizati…
A fundamental problem regarding the Dirac quantization of a free particle on an $N-1$ curved hypersurface embedded in $N$($\geq 2$) flat space is the impossibility to give the same form of the curvature-induced quantum potential, the…
Quantization of $R^2$ and $S^1 \times S^1$ phase spaces are explicitly carried out tweaking the techniques of geometric quantization. Crucial is a combined use of left and right invariant vector fields. Canonical bases, operators and their…
We compare classical and quantum dynamics of a particle in the de Sitter spacetimes with different topologies to show that the result of quantization strongly depends on global properties of a classical system. We present essentially…
We consider the motion of a particle on a surface which is a small perturbation of the standard sphere. One may qualitatively describe the motion by means of a precessing great circle of the sphere. The observation is employed to derive a…
We show how to obtain all covariant field equations for massless particles of arbitrary integer, or half-integer, helicity in four dimensions from the quantization of the rigid particle, whose action is given by the integrated extrinsic…
Recent ideas on modular localization in local quantum physics are used to clarify the relation between on- and off-shell quantities in particle physics; in particular the relation between on-shell crossing symmetry and off-shell Einstein…
We present a new procedure which allows a coherent state (CS) quantization of any set with a measure. It is manifest through the replacement of classical observables by CS quantum observables, which acts on a Hilbert space of prescribed…
A modification of the canonical quantization procedure for systems with time-dependent second-class constraints is discussed and applied to the quantization of the relativistic particle in a plane wave. The time dependence of constraints…
Transition to a nonrelativistic Pauli equation in Riemann space of constant positive curvature for a Dirac particle in presence of the Coulomb field is performed in the system of radial equations, exact solutions are constructed in terms of…
We present the N=2 supersymmetric formulation for the classical and quantum dynamics of a nonrelativistic charged particle on a curved surface in the presence of a perpendicular magnetic field. For a particle moving on a constant-curvature…
We introduce N=1 supersymmetric generalization of the mechanical system describing a particle with fractional spin in D=1+2 dimensions and being classically equivalent to the formulation based on the Dirac monopole two-form. The model…
The paper is continuation of [6] where we have discussed some classical and quantization problems of rigid bodies of infinitesimal size moving in Riemannian spaces. Strictly speaking, we have considered oscillatory dynamical models on…
We prove that the group of area-preserving diffeomorphisms of the 2-sphere admits a non-trivial homogeneous quasimorphism to the real numbers with the following property. Its value on any diffeomorphism supported in a sufficiently small…
In the framework of Dirac quantization with second class constraints, a free particle moving on the surface of a $(d-1)-$dimensional sphere has an ambiguity in the energy spectrum due to the arbitrary shift of canonical momenta. We…
We describe a global approach to the study of duality transformations between antisymmetric fields with transitions and argue that the natural geometrical setting for the approach is that of gerbes, these objects are mathematical…
The non-perturbative solution to the strong CP problem with magnetic monopoles as originally proposed by the author is described. It is shown that the gauge orbit space with gauge potentials and gauge tranformations restricted on the space…
We analyze some relevant semiclassical and quantum features of the implementation of Polymer Quantum Mechanics to the phenomenology of the flat isotropic Universe. We firstly investigate a parallelism between the semiclassical polymer…
In our previous publications we introduced differential calculus on the enveloping algebras U(gl(m)) similar to the usual calculus on the commutative algebra Sym(gl(m)). The main ingredient of our calculus are quantum partial derivatives…
The monopole systems with hidden symmetry of the two-dimensional Coulomb problem are considered. One of them, the "charge-charged magnetic vortex" with a half-spin, is constructed by reducing the quantum circular oscillator with respect to…
This paper resolves a long-standing open problem by providing a classification of Willmore $2$-spheres in $S^n$. We show that any such $2$-sphere is either totally isotropic--originating from the projection of a special twistor curve in the…