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Properties of the wave function equivalent potentials introduced by HAL QCD collaboration are studied in a non-relativistic coupled-channel model. The derivative expansion is generalized, and then applied to the energy-independent and…
We present a new method of calculating scalar propagator and vertex functions in the two-loop approximation, for arbitrary masses of particles. It is based on a double integral representation, suitable for numerical evaluation. Real and…
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…
Introducing a perturbative definition, phase space path integrals can be calculated without slicing. This leads to a short-time expansion of the quantum-mechanical path amplitude, or a high-temperature expansion of the unnormalized density…
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 path integral representation of the evolution operator for the four-dimensional Dirac equation is proposed. A quadratic form of the canonical momenta regularizes the original representation of the path integral in the electron phase…
We have recently studied a simplified version of the path integral for a particle on a sphere, and more generally on maximally symmetric spaces, and proved that Riemann normal coordinates allow the use of a quadratic kinetic term in the…
Recently, it was found that a new set of simple techniques allow one to conveniently express ordinary integrals through differentiation. These techniques add to the general toolbox for integration and integral transforms such as the Fourier…
Recent experimental studies have demonstrated that cellular motion can be directed by topographical gradients, such as those resulting from spatial variations in the features of a micropatterned substrate. This phenomenon, known as…
This note aims to provide a complete and comprehensible derivation of the contributions to amplitude detuning in first order from multipoles up to dodecapolar order. In addition, the principle of feed-down is explored and example terms are…
In this work we develop and apply a path integral formulation for the microscopic degrees of freedom obeying stochastic differential equations to an active Brownian particle (ABP) trapped in a harmonic potential. The formalism allows to…
The technique of functional integration over velocities is applied to the calculation of the propagator of a spinning particle with and without anomalous magnetic moment. A representation for the spin factor is obtained in this context for…
The in-in path integral of a scalar field propagating in a fixed background is formulated in a suitable function space. The free kinetic operator, whose inverse gives the propagators of the in-in perturbation theory, becomes essentially…
In this paper we consider a model of particles jumping on a row of cells, called in physics the one dimensional totally asymmetric exclusion process (TASEP). More precisely we deal with the TASEP with open or periodic boundary conditions…
We study the behavior of a tracer particle driven by a one-dimensional fluctuating potential, defined initially as a Brownian motion, and evolving in time according to the heat equation. We obtain two main results. First, in the short time…
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…
We propose a new approach based on the path integral formalism to the calculation of the probability distribution functions of quadratic quantities of the Gaussian polymer chain in d-dimensional space, such as the radius of gyration and…
We will derive a rigorous real time propagator for the Non-relativistic Quantum Mechanic $L^2$ transition probability amplitude and for the Non-relativistic wave function. The propagator will be explicitly given in terms of the time…
Fractional Levy motion (fLm) is the natural generalization of fractional Brownian motion in the context of self-similar stochastic processes and stable probability distributions. In this paper we give an explicit derivation of the…
By recursively solving the underlying Schr\" odinger equation, we set up an efficient systematic approach for deriving analytic expressions for discretized effective actions. With this we obtain discrete short-time propagators for both one…