Related papers: Quantum Mechanics on a Poincar\'e Hyperboloid
In this paper we study the problem of Hamiltonization of nonholonomic systems from a geometric point of view. We use gauge transformations by 2-forms (in the sense of Severa and Weinstein [29]) to construct different almost Poisson…
A method for extracting finite-dimensional Hamiltonian systems from a class of 2+1 Hamiltonian mean field theories is presented. These theories possess noncanonical Poisson brackets, which normally resist Hamiltonian truncation, but a…
These are pedagogical notes on the Hamiltonian formulation of constrained dynamical systems. All the examples are finite dimensional, field theories are not covered, and the notes could be used by students for a preliminary study before the…
We present a general classification of Hamiltonian multivector fields and of Poisson forms on the extended multiphase space appearing in the geometric formulation of first order classical field theories. This is a prerequisite for computing…
We investigate the conditions under which the Jacobi identity holds for a class of recently introduced anti-symmetric brackets for the hybrid plasma models with kinetic ions and massless electrons. In particular, we establish the precise…
The Dirac constraint formalism is applied to the d(d>2) dimensional Einstein-Hilbert action when written in first order form, using the metric density and affine connection as independent fields. Field equations not involving time…
The Hamiltonian approach to isomonodromic deformation systems for generic rational covariant derivative operators on the Riemann sphere, having any matrix dimension $r$ and any number of isolated singularities of arbitrary Poincar\'e rank,…
Lie-Poisson gauge formalism provides a semiclassical description of noncommutative $U(1)$ gauge theory with Lie algebra type noncommutativity. Using the Dirac approach to constrained Hamiltonian systems, we focus on a class of Lie-Poisson…
We show that an unambiguous and correct quantization of the second-class constrained system of a free particle on a sphere in $D$ dimensions is possible only by converting the constraints to abelian gauge constraints, which are of first…
Quantum systems with real energies generated by an apparently non-Hermitian Hamiltonian may re-acquire the consistent probabilistic interpretation via an ad hoc metric which specifies the set of observables in the updated Hilbert space of…
The concept of a Dirac algebroid, which is a linear almost Dirac structure on a vector bundle, was designed to generate phase equations for mechanical systems with linear nonholonomic constraints. We apply it to systems with magnetic-like…
Quantum Monte Carlo methods are used to study a quantum phase transition in a 1D Hubbard model with a staggered ionic potential (D). Using recently formulated methods, the electronic polarization and localization are determined directly…
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…
Classical mechanics has a natural mathematical setting in symplectic geometry and it may be asked if the same is true for quantum mechanics. More precisely, is it possible to capture certain quantum idiosyncrasies within the symplectic…
Ionic Bose polarons are quantum entities emerging from the interaction between an ion and a Bose-Einstein condensate (BEC), featuring long-ranged interactions that can compete with the gas healing length. This can result in strong…
Canonical quantization of electromagnetic field inside the time--spatially dispersive inhomogeneous dielectrics is presented. Interacting electromagnetic and matter excitation fields create the closed system, Hamiltonian of which may be…
We propose a (3+1)D linear set of covariant vector equations, which unify the spin 0 ``new Dirac equation'' with its spin 1/2 counterpart, proposed by Staunton. Our equations describe a spin (0,1/2) supermultiplet with different numbers of…
A perfect fluid is quantized by the canonical method. The constraints are found and this allows the Dirac brackets to be calculated. Replacing the Dirac brackets with quantum commutators formally quantizes the system. There is a momentum…
Hamiltonian models based on a localized basis set are widely used in condensed matter physics, as, for example, for the calculation of electronic structures or transport properties. The presence of a weak and homogeneous magnetic field can…
Dirac's identification of the quantum analog of the Poisson bracket with the commutator is reviewed, as is the threat of self-inconsistent overdetermination of the quantization of classical dynamical variables which drove him to restrict…