Related papers: Path integrals with discarded degrees of freedom
On the basis of the canonical quantization procedure of a system defined on a cubic lattice, we propose a new method, in which resolutions of unity expressed in terms of eigenvectors are naturally provided, to find eigenvectors of field…
Starting from the Dirac equation in external electromagnetic and torsion fields we derive a path integral representation for the corresponding propagator. An effective action, which appears in the representation, is interpreted as a…
A kink-based path integral method, previously applied to atomic systems, is modified and used to study molecular systems. The method allows the simultaneous evolution of atomic and electronic degrees of freedom. Results for CH$_4 $, NH$_3…
In this paper we construct a path integral formulation of quantum mechanics on noncommutative phase-space. We first map the system to an equivalent system on the noncommutative plane. Then by applying the formalism of representing a quantum…
We present a data-driven optimal control framework that can be viewed as a generalization of the path integral (PI) control approach. We find iterative feedback control laws without parameterization based on probabilistic representation of…
Two subsets of a given set are path-disconnected if they lie in different connected components of the larger set. Verification of path-disconnectedness is essential in proving the infeasibility of motion planning and trajectory optimization…
In this paper I develop a new computational method for pricing path dependent options. Using the path integral representation of the option price, I show that in general it is possible to perform analytically a partial averaging over the…
In the estimation of causal effects, one common method for removing the influence of confounders is to adjust the variables that satisfy the back-door criterion. However, it is not always possible to uniquely determine sets of such…
The Free Energy Principle (FEP) is a leading framework for mathematically modeling self-organization and learning, while Integrated Information Theory (IIT) is a computational ontology of consciousness oriented around irreducible cause and…
In applying the stationary phase approximation to coherent state path integrals a difficulty occurs; there are no classical paths that satisfy the boundary conditions of the path integral. Others have gotten around this problem by…
The book deals with a stochastic formulation of path integration in real time, by rotating the_space_ variables over exp(i pi/4). Preliminary chapters deal with quantum and classical mechanics, probability theory and stochastic calculus,…
The action $A$ of Quadratic Gravity in FLRW metric is invariant under the group of diffeomorphisms of the time coordinate and can be written in terms of the only dynamical variable $g(\tau)\,.$ We construct perturbation theory for…
Through a very careful analysis of Dirac's 1932 paper on the Lagrangian in Quantum Mechanics as well as the second and third editions of his classic book {\it The Principles of Quantum Mechanics}, I show that Dirac's contributions to the…
We construct a path distribution representing the kinetic part of the Feynman path integral at discrete times similar to that defined by Thomas [1], but on a Hilbert space of paths rather than a nuclear sequence space. We also consider…
A new integral identity for functions with continuous second partial derivatives is derived. It is shown that the value of any function f(r,t) at position r and time t is completely determined by its previous values at all other locations…
The theory of interaction at one point is developed for the one-dimensional Schrodinger equation. In analog with the three-dimensional case, the resulting interaction is referred to as the Fermi pseudo-potential. The dominant feature of…
We derive the semiclassical approximation to Feynman's path integral representation of the energy Green function of a massless particle in the shadow region of an ideal obstacle in a medium. The wavelength of the particle is assumed to be…
A set of Green functions ${\cal G}_{\alpha}(x-y), \alpha \in [0, 2 \pi [$, for free scalar field theory is introduced, varying between the Hadamard Green function $\Delta_1(x-y) \equiv \linebreak[2] \lsta{0} \hspace{-0.1cm} \{ \varphi(x),…
We suppose that the ground-state eigenvalue E = F(v) of the Schroedinger Hamiltonian H = -\Delta + vf(x) in one dimension is known for all values of the coupling v > 0. The potential shape f(x) is assumed to be symmetric, bounded below, and…
Interference results when a quantum particle is free to choose among a few indistinguishable paths. A canonical example of Bohr's complementarity principle [1] is a two-path interferometer with an external detector coupled to one of the…