Related papers: Generating Functionals for Harmonic Expectation Va…
Graphical functions have emerged as a powerful framework for evaluating multi-loop Feynman integrals in perturbative quantum field theory. Defined as massless three-point position-space integrals, they reveal rich analytic structures and…
In earlier work, we have developed a Kinetic Field Theory (KFT) for cosmological structure formation and showed that the non-linear density-fluctuation power spectrum known from numerical simulations can be reproduced quite well even if…
We construct harmonic functions in the quarter plane for discrete Laplace operators. In particular, the functions are conditioned to vanish on the boundary and the Laplacians admit coefficients associated with transition probabilities of…
We propose Functional Flow Matching (FFM), a function-space generative model that generalizes the recently-introduced Flow Matching model to operate in infinite-dimensional spaces. Our approach works by first defining a path of probability…
In this work we study the spatial-momentum dependence of mesonic spectral functions obtained from the quark-meson model using a recently proposed method to calculate real-time observables at finite temperature and density from the…
As an alternative but unified and more fundamental description for quantum physics, Feynman path integrals generalize the classical action principle to a probabilistic perspective, under which the physical observables' estimation translates…
In phase space, we analytically obtain the characteristic functions (CFs) of a forced harmonic oscillator [Talkner et al., Phys. Rev. E, 75, 050102 (2007)], a time-dependent mass and frequency harmonic oscillator [Deffner and Lutz, Phys.…
Using functional derivatives with respect to free propagators and interactions we derive a closed set of Schwinger-Dyson equations in quantum electrodynamics. Its conversion to graphical recursion relations allows us to systematically…
The generating functional is derived for the fluctuation-dissipation relations which result from the unitarity and reversibility of microscopic dynamics and connect various statistical characteristics of many consecutive (continuous)…
We introduce a novel, systematic method for the complete symbolic reduction of multi-loop Feynman integrals, leveraging the power of generating functions. The differential equations governing these generating functions naturally yield…
The cumulant generating function of time-averaged current is studied from an operational viewpoint. Specifically, for interacting Brownian particles under non-equilibrium conditions, we show that the first derivative of the cumulant…
The Feynman path integral for the generalized harmonic oscillator is reviewed, and it is shown that the path integral can be used to find a complete set of wave functions for the oscillator. Harmonic oscillators with different…
In this paper, we first describe how to find the generating function for the sum of the areas under generalized Dyck paths (with an arbitrary set of steps) using Motzkin paths as a motivating example. We then focus on Motzkin and Dyck…
Graphical functions are single-valued complex functions which arise from Feynman amplitudes. We study their properties and use their connection to multiple polylogarithms to calculate Feynman periods. For the zig-zag and two more families…
We present a general formalism based on scattering theory to calculate quantum correlation functions involving several time-dependent current operators. A key ingredient is the causality of the scattering matrix, which allows one to deal…
The equations of time-dependent density functional theory are derived, via the expression for the quantum weak value, from ring polymer quantum theory using a symmetry between time and imaginary time. The imaginary time path integral…
Functional equations (FE) arise quite naturally in the analysis of stochastic systems of different kinds : queueing and telecommunication networks, random walks, enumeration of planar lattice walks, etc. Frequently, the object is to…
We elaborate on the functional integral describing the stochastic dynamics of a spectator field during inflation, comparing its diagrammatic expansion to that obtained directly from a perturbative solution of the corresponding Langevin…
We consider a number of combinatorial problems in which rational generating functions may be obtained, whose denominators have factors with certain singularities. Specifically, there exist points near which one of the factors is asymptotic…
We point out that in the context of quantum fields in time dependent classical backgrounds, the number of created particles with a given momentum largely deviates about its mean value. Since the corresponding Fourier modes are nonlocal,…