相关论文: Coherent State Path Integrals in the Weyl Represen…
We present a detailed derivation of the semiclassical propagator in the SU(n) coherent state representation. In order to provide support for immediate physical applications, we restrict this work to the fully symmetric irreducible…
We give background material and some details of calculations for two recent papers [1,2] where we derived a path integral representation of the transition element for supersymmetric and nonsupersymmetric nonlinear sigma models in one…
We introduce a symbolic operator framework for simulating quantum photonic systems that works directly with the canonical commutation relations and the Weyl algebra. Unlike existing Fock-space or Gaussian simulators, our method treats…
We propose a new rigorous time-slicing construction of the phase space Path Integrals for propagators both in Quantum Mechanics and Quantum Field Theory for a fairly general class of quantum observables (e.g. the Schroedinger hamiltonians…
One of the key conceptual challenges in quantum gravity is to understand how quantum theory should modify the very notion of spacetime. One way to investigate this question is to study the alternatives to Schr\"odinger quantum mechanics.…
In this paper, we determine the star product representation of coherent path integrals. By employing the properties of generalized delta functions with complex arguments, the Glauber-Sudarshan P-function corresponding to a non-diagonal…
In quantum statistical mechanics, Moyal's equation governs the time evolution of Wigner functions and of more general Weyl symbols that represent the density matrix of arbitrary mixed states. A formal solution to Moyal's equation is given…
In this note we study the properties of a sequence of approximate propagators for the Schr\"odinger equation, in the spirit of Feynman's path integrals. Precisely, we consider Hamiltonian operators arising as the Weyl quantization of a…
The knowledge of quantum phase flow induced under the Weyl's association rule by the evolution of Heisenberg operators of canonical coordinates and momenta allows to find the evolution of symbols of generic Heisenberg operators. The quantum…
A new set of twisted geometric variables is introduced to parametrize the holonomy-flux phase space in loop quantum gravity. It is verified that these new geometric variables, after symplectic reduction with respect to the Gauss constraint,…
We consider a spin coherent states description of a general quantum spin system. It is shown that it is possible to use the spin-1/2 representation to study the general spin-J case. We identify the 1/2 spinor components as the homogeneous…
Using the generalized coherent states we argue that the path integral formulae for $SU(2)$ and $SU(1,1)$ (in the discrete series) are WKB exact,if the starting point is expressed as the trace of $e^{-iT\hat H}$ with $\hat H$ being given by…
The concern of this article is a semiclassical Weyl calculus on an infinite dimensional Hilbert space $H$. If $(i, H, B)$ is a Wiener triplet associated to $H$, the quantum state space will be the space of $L^2$ functions on $B$ with…
A general semiclassical method in phase space based on the final value representation of the Wigner function is considered that bypasses caustics and the need to root-search for classical trajectories. We demonstrate its potential by…
The coherent-state initial-value representation (IVR) for the semi-classical real-time propagator of a quantum system, developed by Herman and Kluk (HK), is widely used in computational studies of chemical dynamics. On the other hand, the…
We propose a conjugate application of the Bargmann representation of quantum mechanics. Applying the Maslov method to the semiclassical connection formula between the two representations, we derive a uniform semiclassical approximation for…
The semiclassical approximation of coherent state path integrals is employed to study the dynamics of the Jaynes-Cummings model. Decomposing the Hilbert space into subspaces of given excitation quanta above the ground state, the…
We study massive 1/2-spin particles in various external backgrounds keeping in mind applications to neutrino physics. We are mainly interested in massive Majorana (Weyl) fields. However, massive neutral Dirac particles are also considered.…
This paper presents an analytical treatment of the path integral formalism for time-dependent quantum systems within the framework of Wigner-Dunkl mechanics, emphasizing systems with varying masses and time-dependent potentials. By…
The Weyl-Wigner-Moyal formalism is developed for spin by means of a correspondence between spherical harmonics and spherical harmonic tensor operators. The analogue of the Moyal expansion is developed for the Weyl symbol of the product of…