Related papers: Classical Mechanics and geometric Quantization on …
We analyze classical and quantum dynamics of a particle in 2d spacetimes with constant curvature which are locally isometric but globally different. We show that global symmetries of spacetime specify the symmetries of physical phase-space…
We consider classical and quantum mechanics for an extended Heisenberg algebra with additional canonical commutation relations for position and momentum coordinates. In our approach this additional noncommutativity is removed from the…
One of the foremost goals of research in physics is to find the most basic and universal theories that describe our universe. Many theories assume the presence of an absolute space and time in which the physical objects are located and…
We study the formulation of statistical mechanics on noncommutative classical phase space, and construct the corresponding canonical ensemble theory. For illustration, some basic and important examples are considered in the framework of…
We study classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a probability distribution to the physical time, which is assumed to be discrete. In this way, a physical clock with discrete…
Two known 2-dim SUSY quantum mechanical constructions - the direct generalization of SUSY with first-order supercharges and Higher order SUSY with second order supercharges - are combined for a class of 2-dim quantum models, which {\it are…
A generalization of classical mechanics is obtained from a complex parametrization of the phase space. The formalism supports complex Hamiltonian functions describing non-conservative classical mechanical systems. A quantization scheme that…
A survey of topics of recent interest in Hamiltonian and Lagrangian dynamical systems, including accessible discussions of regularization of the central force problem; inequivalent Lagrangians and Hamiltonians; constants of central force…
In the paper is presented an invariant quantization procedure of classical mechanics on the phase space over flat configuration space. Then, the passage to an operator representation of quantum mechanics in a Hilbert space over…
We introduce geometric quantization in the setting of shifted symplectic structures. We define Lagrangian fibrations and prequantizations of shifted symplectic stacks and their geometric quantization. In addition, we study many examples…
Classical mechanics, in the operatorial formulation of Koopman and von Neumann, can be written also in a functional form. In this form two Grassmann partners of time make their natural appearance extending in this manner time to a three…
If we admit that quantum mechanics (QM) is universal theory, then QM should contain also some description of classical mechanical systems. The presented text contains description of two different ways how the mathematical description of…
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…
A generalization of the notion of a (pseudo-) Riemannian space is proposed in a framework of noncommutative geometry. In particular, there are parametrized families of generalized Riemannian spaces which are deformations of classical…
The Schr\"odinger equation is shown to be equivalent to a constrained Liouville equation under the assumption that phase space is extended to Grassmann algebra valued variables. For onedimensional systems, the underlying Hamiltonian…
A complete geometric classification of symmetries of autonomous Hamiltonian mechanical systems is established; explaining how to obtain their associated conserved quantities in all cases. In particular, first we review well-known results…
Classical Hamiltonian mechanics, characterized by a single conserved Hamiltonian (energy) and symplectic geometry, `hides' other invariants into symmetries of the Hamiltonian or into the kernel of the Poisson tensor. Nambu mechanics aims to…
We quantise complex, infinite-dimensional projective space CP(H). We apply the result to quantise a complex, finite-dimensional, classical phase space C whose symplectic volume is infinite, by holomorphically embedding it into CP(H). The…
In these lectures we report recent work on the exact quantization of dimensionally reduced gravity, i.e. 2d non-linear (G/H)-coset space sigma-models coupled to gravity and a dilaton. Using methods developed in the context of flat space…
Familiar formulations of classical and quantum mechanics are shown to follow from a general theory of mechanics based on pure states with an intrinsic probability structure. This theory is developed to the stage where theorems from quantum…