Related papers: Semiclassical Quantization for the Motion of Guidi…
The SU(1,1) coherent states for a relativistic model of the linear singular oscillator are considered. The corresponding partition function is evaluated. The path integral for the transition amplitude between SU(1,1) coherent states is…
We study the canonical and the coherent state quantization of a particle moving in a magnetic field on a non-commutative plane. Starting from the so called \theta-modified action, we perform the canonical quantization and analyze the gauge…
The path integral formulation can reproduce the right energy spectrum of the harmonic oscillator potential, but it cannot resolve the Coulomb potential problem. This is because the path integral cannot properly take into account the…
We present a new method for the consistent construction of time-continuous coherent-state path integrals using the theory of half-form quantization. Through the inversion of the quantization procedure we construct a de-quantization map…
The method of integrals of motion is used to construct families of generalized coherent states of a nonrelativistic spinless charged particle in a constant electric field. Families of states, differing in the values of their standard…
A procedure based on the semiclassical approximation for high energy levels is developed to yield solutions to the classical equation of charge motion and to the Bargmann-Michel-Telegdi spin equation. To this end, exact solutions to the…
The spin coherent state path integral describing the dynamics of a spin-1/2-system in a magnetic field of arbitrary time-dependence is considered. Defining the path integral as the limit of a Wiener regularized expression, the semiclassical…
A detailed derivation of the semiclassical propagator in the generalized coherent-state representation is performed by applying the saddle-point method to a path integral over the classical phase space. With the purpose of providing greater…
A semiclassical quantization condition is derived for Landau levels in general spin-orbit coupled systems. This generalizes the Onsager quantization condition via a matrix-valued phase which describes spin dynamics along the classical…
We define the Bohr-Sommerfeld quantization via $T$-modules for a $b$-symplectic toric manifold and show that it coincides with the formal geometric quantization of [GMW18b]. In particular, we prove that its dimension is given by a signed…
A semiclassical Bohr-Sommerfeld approximation is derived for an N-particle, two-mode Bose-Hubbard system modeling a Bose-Einstein condensate in a double-well potential. This semiclassical description is based on the `classical' dynamics of…
The Bohr-Sommerfeld quantization rule lies at the heart of the modern semiclassical theory of a Bloch electron in a magnetic field. This rule is predictive of Landau levels and quantum oscillations for conventional metals, as well as for a…
The motion of neutral particles with magnetic moments in an inhomogeneous magnetic field is described in a semi-classical framework. The concept of Coherent Internal States is used in the formulation of the semiclassical approximation from…
We develop a mathematically well-defined path integral formalism for general symplectic manifolds. We argue that in order to make a path integral quantization covariant under general coordinate transformations on the phase space and involve…
We have discovered a class of dynamically stable coherent states for motion on the half-line. The regularization of the half-line boundary and the consequent quantum motion are expounded within the framework of covariant affine…
A generalized Peierls substitution which takes into account a Berry phase term must be considered for the semiclassical treatment of electrons in a magnetic field. This substitution turns out to be an essential element for the correct…
We consider the semiclassical theory in a joint phase space of spin and orbital degrees of freedom. The method is developed from the path integrals using the spin-coherent-state representation, and yields the trace formula for the density…
The semiclassical propagation of spin coherent states is considered in complex phase space. For two time-independent systems we find the appropriate classical trajectories and show that their combined contributions are able to describe…
In the framework of geometric quantization we extend the Bohr-Sommerfeld rules to a full quantization theory which resembles Heisenberg's matrix theory. This extension is possible because Bohr-Sommerfeld rules not only provide an orthogonal…
We formulate a semiclassical theory for systems with spin-orbit interactions. Using spin coherent states, we start from the path integral in an extended phase space, formulate the classical dynamics of the coupled orbital and spin degrees…