The Feynman Propagator from a Single Path

The Quantum Wave Packet and the Feynman De Broglie Bohm Propagator of the Linearized Sussmann Hasse Albrecht Kostin Nassar Equation along a Classical Trajetory

In this paper we study the quantum wave packet and the Feynman-de Broglie_Bohm propagator of the linearized Sussmann_Hasse_Albrecht_Kostin_Nassar equation along a classical trajetory

Feynman Propagator for a System of Interacting Scalar Particles in the Fokker Theory

A generalized canonical formulation of the theory of the electromagnetic Fokker interaction for a system of two particles is proposed. The functional integral on the generalized phase space is defined as the initial one in quantum theory. After integration over the momenta, the measure of integration in the generalized configuration space of world particle lines is determined. The problem of dynamic interpretation of the Feynman propagator for a system of particles with independent proper time parameters is discussed. A modification of the propagator is proposed, in which the role of independe…

A New Method for Calculating Non Relativistic Feynman Propagators in Momentum Space

In this paper, we present a formulation of Schwinger's Method for non relativistic propogators in momentum space. While the aforementioned method has been used heavily in some papers to deduce various non relativistic propogators in position space, we show that a variation of method in momentum space works well. We also show how to extract the Propogator for the concerned case for the harmonic oscillator.

Alternative Method for Determining the Feynman Propagator of a Non-Relativistic Quantum Mechanical Problem

A direct procedure for determining the propagator associated with a quantum mechanical problem was given by the Path Integration Procedure of Feynman. The Green function, which is the Fourier Transform with respect to the time variable of the propagator, can be derived later. In our approach, with the help of a Laplace transform, a direct way to get the energy dependent Green function is presented, and the propagator can be obtained later with an inverse Laplace transform. The method is illustrated through simple one dimensional examples and for time independent potentials, though it can be ge…

Sign of the Feynman Propagator and Irreversibility

For the interacting Feynman propagator $ Δ_{F,int}(x,y) $ of scalar electrodynamics, we show that the sign property, $ \operatorname{Re} iΔ_{F,int} \geq 0 $, hinges on the reversibility of time evolution. In contrast, $ \operatorname{Im} iΔ_{F,int} $ is indeterminate. When we switch to reduced dynamics under the weak coupling approximation, the positive semidefinite sign of $ \operatorname{Re} iΔ_{F,int} $ is generally lost, unless we impose severe restrictions on the Kraus operators that govern time evolution. With another approximation, the rotating wave approximation, we may recover the sig…

通过费曼传播子实现概率分布的高效量子加载

Efficient quantum loading of probability distributions through Feynman propagators

本文利用一维哈密顿量模拟和费曼传播子的解析形式，提出高效加载正态、拉普拉斯等概率分布的量子算法，并给出基于阶梯态和基态投影的变分方法，优于量子机器学习中的通用数据加载方法。

普朗克尺度下Arthurs-Kelly系统的费曼传播子

Feynman Propagator of the Arthurs-Kelly system at the Planck Scale

本文在Arthurs-Kelly系统中引入广义不确定性原理，精确推导出一阶GUP参数下的费曼传播子，并简要探讨其在早期宇宙中的应用。

Three Methods for Computing the Feynman Propagator

We present three methods for calculating the Feynman propagator for the non-relativistic harmonic oscillator. The first method was employed by Schwinger a half a century ago, but has rarely been used in non-relativistic problems since. Also discussed is an algebraic method and a path integral method so that the reader can compare the advantages and disadvantages of each method.

标量场中的变质量与噪声费曼传播子

Variable Mass and the Noisy Feynman Propagator in Scalar Fields

本研究采用参数时间表述中的一阶质量无关克莱因-戈登方程，借助半群演化概念，探究标量电动力学中噪声费曼传播子的符号，为量子场论相关研究提供新视角。

A physical basis for the phase in Feynman path integration

In the path integral formulation of quantum mechanics, the phase factor Exp[iS(x[t])] is associated with every path x[t]. Summing this factor over all paths yields Feynman's propagator as a sum-over-paths. In the original formulation, the complex phase was a mathematical device invoked to extract wave behaviour in a particle framework. In this paper we show that the phase itself can have a physical origin in time reversal, and that the propagator can be drawn by a single deterministic path.

Exact Propagator of a two dimensional anisotropic Harmonic Oscillator in the presence of a Magnetic Field

In this paper we solve exactly the problem of the spectrum and Feynman propagator of a charged particle submitted to both an anharmonic oscillator in the plane and a constant and homogeneous magnetic field of arbitrary strength aligned with the perpendicular direction to the plane. As we shall see in the beginning of the letter the Hamiltonian, being a quadratic form, is easily diagonalizable and the Classical Action can be used to construct the exact Feynman Propagator using the Stationary Phase Approximation. The result is useful for the treatment of quasi two dimensional samples in the fiel…

Feynman Propagator for Interacting Electrons in the Quantum Fokker Theory

A modification of the Fokker action is proposed, which allows one to formulate the covariant quantum theory of the charge system, in which the proper time of each particle serves as the evolution parameter and the particles themselves receive an additional quantum number - spin. The modification consists in adding to the Fokker action its variation generated by the infinitesimal shifts of the proper time parameters. As a result, the proper time parameters become observable at the quantum level.

A Causal Alternative to Feynman's Propagator

The Feynman propagator used in the conventional in-out formalism in quantum field theory is not a causal propagator as wave packets are propagated virtually instantaneously outside the causal region of the initial state. We formulate a causal in-out formalism in quantum field theory by making use of the Wheeler propagator, the time ordered commutator propagator, which is manifestly causal. Only free scalar field theories and their first quantization are considered. We identify the real Klein Gordon field itself as the wave function of a neutral spinless relativistic particle. Furthermore, we d…

Quantum Walks, Feynman Propagators and Graph Topology on an IBM Quantum Computer

Topological data analysis is a rapidly developing area of data science where one tries to discover topological patterns in data sets to generate insight and knowledge discovery. In this project we use quantum walk algorithms to discover features of a data graph on which the walk takes place. This can be done faster on quantum computers where all paths can be explored using superposition. We begin with simple walks on a polygon and move up to graphs described by higher dimensional meshes. We use insight from the physics description of quantum walks defined in terms of probability amplitudes to …

The Symmetric Stable Lévy Flights and the Feynman Path Integral

We determine the solution of the fractional spatial diffusion equation in n-dimensional Euclidean space for a "free" particle by computing the corresponding propagator. We employ both the Hamiltonian and Lagrangian approaches which produce exact results for the case of jumps governed by symmetric stable Lévy flights.

Estimating the Euclidean quantum propagator with deep generative modeling of Feynman paths

Feynman path integrals provide an elegant, classically inspired representation for the quantum propagator and the quantum dynamics, through summing over a huge manifold of all possible paths. From computational and simulational perspectives, the ergodic tracking of the whole path manifold is a hard problem. Machine learning can help, in an efficient manner, to identify the relevant subspace and the intrinsic structure residing at a small fraction of the vast path manifold. In this work, we propose the Feynman path generator for quantum mechanical systems, which efficiently generates Feynman pa…

Discrete Feynman propagator for the Weyl quantum walk in 2+1 dimensions

Recently quantum walks have been considered as a possible fundamental description of the dynamics of relativistic quantum fields. Within this scenario we derive the analytical solution of the Weyl walk in 2+1 dimensions. We present a discrete path-integral formulation of the Feynman propagator based on the binary encoding of paths on the lattice. The derivation exploits a special feature of the Weyl walk, that occurs also in other dimensions, that is closure under multiplication of the set of the walk transition matrices. This result opens the perspective of a similar solution in the 3+1 case.

Quantum Propagators for Geodesic Congruences

Using the Raychaudhuri equation, we show that a quantum probability amplitude (Feynman propagator) can be univocally associated to any timelike or null affinely parametrized geodesic congruence.

On Eigenvectors, Approximations and the Feynman Propagator

Trying to interpret B. Zilber's project on model theory of quantum mechanics we study a way of building limit models from finite-dimensional approximations. Our point of view is that of metric model theory, and we develop a method of taking ultraproducts of unbounded operators. We first calculate the Feynman propagator for the free particle as defined by physicists as an inner product $\langle x_{0}| K^{t}| x_{1}\rangle $ of the eigenvector $| x_{0}\rangle $ of the position operator with eigenvalue $x_{0}$ and $K^{t}(| x_{1}\rangle )$, where $K^{t}$ is the time evolution operator. However, due…

On Fock-Bargmann space, Dirac delta function, Feynman propagator, angular momentum and SU(3) multiplicity free

The Dirac delta function and the Feynman propagator of the harmonic oscillator are found by a simple calculation using Fock Bargmann space and the generating function of the harmonic oscillator. With help of the Schwinger generating function of Wigner's D-matrix elements we derive the generating function of spherical harmonics, the quadratic transformations and the generating functions of: the characters of SU (2), Legendre and Gegenbauer polynomials. We also deduce the van der Wearden invariant of 3-j symbols of SU (2). Using the Fock Bargmann space and its complex conjugate we find the integ…

Non-Relativistic Propagators via Schwinger's Method

In order to popularize the so called Schwinger's method we reconsider the Feynman propagator of two non-relativistic systems: a charged particle in a uniform magnetic field and a charged harmonic oscillator in a uniform magnetic field. Instead of solving the Heisenberg equations for the position and the canonical momentum operators, ${\bf R}$ and ${\bf P}$, we apply this method by solving the Heisenberg equations for the gauge invariant operators ${\bf R}$ and $\mathversion{bold}$π$ = {\bf P}-e{\bf A}$, the latter being the mechanical momentum operator. In our procedure we avoid fixing the gau…

A note on the short-time quantum propagator

In the Feynman formalism of quantum mechanics one encounters a postulate, namely, that the propagator in an infinitesimal time-interval is the classical wave function. This postulate, which was later studied thoroughly by Holland, was recently highlighted by using the improved Makri-Miller propagator. The present note, whose conclusion is in agreement with that recent achievement, demonstrates that the Heisenberg picture of quantum mechanics invariably includes the Feynman postulate and is able to yield a proof for it. In other words, by starting out from the Heisenberg picture, it is proved t…

Wigner distribution functions for complex dynamical systems: a path integral approach

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 phase space trajectory is found to contribute to the propagator. Inspired by Feynman's and Vernon's influence functional theory we extend the method to calculate the propagator for the reduced Wigner function of a system of interest coupled to an external system. Explicit expressions are obtained when the external system consists of a set of independent harmo…

费曼路径积分中的边界条件与辅助相位

Boundary Condition and the Auxiliary Phase in Feynman Path Integral

本文探讨了狄利克雷、诺伊曼、罗宾及其混合边界条件下费曼路径积分中辅助相位因子的性质，并验证了线段上自由粒子的传播子公式与薛定谔方程结果一致（仅含平凡归一化因子）。

束缚态阿哈罗诺夫-玻姆效应的动量空间费曼积分

Momentum Space Feynman Integral for the Bound State Aharonov-Bohm Effect

本文在极坐标动量空间中构造了描述束缚态阿哈罗诺夫-玻姆效应的薛定谔传播子费曼积分，并将其定义为白噪声泛函。

Antimatter in the Direct-Action Theory of Fields

One of Feynman's greatest contributions to physics was the interpretation of negative energies as antimatter in quantum field theory. A key component of this interpretation is the Feynman propagator, which seeks to describe the behavior of antimatter at the virtual particle level. Ironically, it turns out that one can dispense with the Feynman propagator in a direct-action theory of fields, while still retaining the interpretation of negative energy solutions as antiparticles.

Fourier-Flow model generating Feynman paths

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 into a weighted sum over all possible paths. The underlying difficulty is to tackle the whole path manifold from finite samples that can effectively represent the Feynman propagator dictated probability distribution. Modern generative models in machine learning can handle learning and representing probability distribution with high computational efficiency.…

球坐标系中自由狄拉克传播子的路径积分形式

Path integral formalism for the free Dirac propagator in spherical coordinates

本文在球坐标系中用费曼路径积分方法推导自由自旋1/2费米子的相对论格林函数，并通过坐标变换将其化为可精确求解的形式，结果用球贝塞尔函数和球旋量表示。

传播子的Feynman-Dyson图微扰展开的不收敛性

Nonconvergence of the Feynman-Dyson diagrammatic perturbation expansion of propagators

本研究通过数值计算揭示Feynman-Dyson图微扰展开的多种病态行为及不收敛根源，指出Padé近似可修正问题，同时质疑该理论与相关假设结合的有效性。

由传播子和路径积分得到的星指数

Star exponentials from propagators and path integrals

本文建立了形变量子化中星指数与费曼路径积分的关系，通过将传播子表示为星指数的积分变换，构造了不依赖形式级数收敛性的星指数，并给出了有限维系统的星积分类似量子场论表示。

Dirac's formalism for time-dependent Hamiltonian systems in the extended phase space

The Dirac's formalism for constrained systems is applied to the analysis of time-dependent Hamiltonians in the extended phase space. We show that the Lewis invariant is a reparametrization invariant and we calculate the Feynman propagator using the extended phase description. We show that the quantum phase of the Feynman propagator is given by the boundary term of the canonical transformation of the extended phase space.

Simple Quantum Mechanical Phenomena and the Feynman Real Time Path Integral

The path integral formalism gives a very illustrative and intuitive understanding of quantum mechanics but due to its difficult sum over phases one usually prefers Schrödinger's approach. We will show that it is possible to calculate simple quantum phenomena by performing Feynman's sum over all paths staying entirely in real time. Once the propagator is obtained it is particularly easy to get the energy spectrum or the evolution of any wavefunction.

星指数与费米系统及费曼-凯克公式

Star-exponential for Fermi systems and the Feynman-Kac formula

本文提出费米系统星指数的计算方法，并推导出费米版本的费曼-凯克公式，为费米系统研究提供新的计算工具。