Related papers: ``Classical'' Propagator and Path Integral in the …
We demonstrate the relevance of complex Gaussian stochastic processes to the stochastic state vector description of non-Markovian open quantum systems. These processes express the general Feynman-Vernon path integral propagator for open…
We emphasize the fact the evolution of quantum states in the inverted oscillator (IO) is reduced to classical equations of motion, stressing that the corresponding tunnelling and reflexion coefficients addressed in the literature are…
The phenomenology of quantum systems in curved space-times is among the most fascinating fields of physics, allowing --often at the gedankenexperiment level-- constraints on tentative theories of quantum gravity. Determining the dynamics of…
The (Feynman) propagator $G(x_2,x_1)$ encodes the entire dynamics of a massive, free scalar field propagating in an arbitrary curved spacetime. The usual procedures for computing the propagator -- either as a time ordered correlator or from…
Many quantization schemes rely on analogs of classical mechanics where the connections with classical mechanics are indirect. In this work I propose a new and direct connection between classical mechanics and quantum mechanics where the…
Starting from Feynman's Lagrangian description of quantum mechanics, we propose a method to construct explicitly the propagator for the Wigner distribution function of a single system. For general quadratic Lagrangians, only the classical…
By using path integrals, the stochastic process associated to the time evolution of the quantum probability density is formally rewritten in terms of a stochastic differential equation, given by Newton's equation of motion with an…
In this paper we develop the alternative path-integral approach to quantum mechanics. We present a resolvent of a Hamiltonian (which is Laplace transform of a evolution operator) in a form which has a sense of ``the sum over paths'' but it…
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 essence of the path integral method in quantum physics can be expressed in terms of two relations between unitary propagators, describing perturbations of the underlying system. They inherit the causal structure of the theory and its…
We introduce two new integral transforms of the quantum mechanical transition kernel that represent physical information about the path integral. These transforms can be interpreted as probability distributions on particle trajectories…
Path integrals play a crucial role in describing the dynamics of physical systems subject to classical or quantum noise. In fact, when correctly normalized, they express the probability of transition between two states of the system. In…
We construct a representation of the coherent state path integral using the Weyl symbol of the Hamiltonian operator. This representation is very different from the usual path integral forms suggested by Klauder and Skagerstan in…
The Gaussian Wave-Packet phase-space representation is used to show that the expansion in powers of $\hbar$ of the quantum Liouville propagator leads, in the zeroth order term, to results close to those obtained in the statistical…
The Weyl-Wigner representation of quantum mechanics allows one to map the density operator in a function in phase space - the Wigner function - which acts like a probability distribution. In the context of statistical mechanics, this…
By using the overcompleteness of coherent states we find an alternative form of the unit operator for which the ket and the bra appearing under the integration sign do not refer to the same phase-space point. This defines a new quantum…
We construct the action-angle variables of a classical integrable model defined on complex projective phase space and calculate the quantum mechanical propagator in the coherent state path integral representation using the stationary phase…
We investigate the transition from quantum to classical mechanics using a one-dimensional free particle model. In the classical analysis, we consider the initial positions and velocities of the particle drawn from Gaussian distributions.…
We present a comprehensive study of semiclassical phase-space propagation in the Wigner representation, emphasizing numerical applications, in particular as an initial-value representation. Two semiclassical approximation schemes are…
We develop a path integral representation for the dynamics of quantum systems with a finite-dimensional Hilbert space, formulated entirely within a discrete phase space. Starting from the discrete Wigner function defined on $\mathbb{Z}_d…