Related papers: Remarks on low-energy approximations for Feynman p…
This paper reviews the linearized path integral approach for computing time dependent properties of systems that can be approximated using a mixed quantum-classical description. This approach is applied to studying vibrational pure…
This paper reviews the formulation of the Feynman-Vernon model of linear dissipative systems for a standard Brownian particle moving in an external potential $V(x,t)$ and introduces the formulation of a generalized oscillator model of a…
These lectures are intended as an introduction to the technique of path integrals and their applications in physics. The audience is mainly first-year graduate students, and it is assumed that the reader has a good foundation in quantum…
Path integrals developed by Richard Feynman have been an important tool in Physics in studying quantum field theory. In mathematics, it has also been widely used in providing formal proofs in the study of Index theorem and asymptotic…
In this paper, we have constructed the Feynman path integral method for non-paraxial optics. This is done by using the mathematical analogy between a non-paraxial optical system and the generalized Schr\"odinger equation deformed by the…
In this contribution I discuss a path integral approach for the quantum motion on two-dimensional spaces according to Koenigs, for short ``Koenigs-Spaces''. Their construction is simple: One takes a Hamiltonian from two-dimensional flat…
Much like the action, diffeomorphism invariance can be used to fix the form of the path integral measure in quantum gravity. Moreover, since there is a redundancy between what constitutes "the action" and what constitutes "the measure" one…
We consider how vectorial aspects (polarization) of light propagation can be implemented, and its origin, within a Feynman path integral approach. A key part of this scheme is in generalising the standard optical path length integral from a…
The precise description of quantum nuclear fluctuations in atomistic modelling is possible by employing path integral techniques, which involve a considerable computational overhead due to the need of simulating multiple replicas of the…
In the Feynman-Kac[1] path integral approach the eigenvalues of a quantum system can be computed using Wiener measure which uses Brownian particle motion. In our previous work[2-3] on such systems we have observed that the Wiener process…
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…
The $\varepsilon$-form of a system of differential equations for Feynman integrals has led to tremendeous progress in our abilities to compute Feynman integrals, as long as they fall into the class of multiple polylogarithms. It is…
Both null and timelike rays experience trajectory bending in a gravitational field. In this work, we systematically develop a perturbative method to compute the deflection angle of rays with general velocity $v$ in arbitrary static and…
We apply path integrals to study nonequilibrium work theorems in the context of Brownian dynamics, deriving in particular the equations of motion governing the most typical and most dominant trajectories. For the analytically soluble cases…
This paper focuses on characterizing the energy profile along pathways connecting different regions of configuration space in the context of a prototypical glass model, the pure spherical $p$-spin model with $p=3$. The study investigates…
New physical insight into the correspondence between path integral concepts and the Schr\"odinger formulation is gained by the analysis of the effective classical potential, that is defined within the Feynman path integral formulation of…
The logical consistency of a description of Quantum Theory in the context of General Relativity, which includes Minimal Coupling Principle, is analyzed from the point of view of Feynman's formulation in terms of path integrals. We will…
Gravitational scattering of the electromagnetic field from a heavy scalar field provides a fundamental testbed for understanding the deflection of light by massive bodies. In many approaches based on effective field theory, the calculation…
The notion of fractional dynamics is related to equations of motion with one or a few terms with derivatives of a fractional order. This type of equation appears in the description of chaotic dynamics, wave propagation in fractal media, and…
Fractional Brownian motion (fBm) is an experimentally-relevant, non-Markovian Gaussian stochastic process with long-ranged correlations between the increments, parametrised by the so-called Hurst exponent $H$; depending on its value the…