H. D. Zeh
A historically important but little known debate regarding the necessity and meaning of macroscopic superpositions, in particular those containing different gravitational fields, is discussed from a modern perspective.
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The Feynman parametrization of the Dirac equation is considered in order to obtain an indefinite mass formulation of relativistic quantum mechanics. It is shown that the parameter that labels the evolution is related to the proper time. The Stueckelberg interpretation of antiparticles naturally arises from the formalism.
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.
Effect of Self-Interaction on Feynman's Interpretation of the Lamb Shift
本文扩展费曼对兰姆位移的解释，通过引入自相互作用能量，消除了虚光子吸收导致的非物理贡献，从而推导出贝特公式。
Interpretation of Feynman formalism of quantum mechanics in terms of probabilities of paths
本文重新审视费曼路径积分，提出将跃迁概率视为路径概率之和的重新表述，并由此推导出散射的玻恩近似，从而无需玻恩假设即可实现基于粒子的量子力学诠释。
The Feynman integral is given a stochastic interpretation in the framework of Nelson's stochastic mechanics employing a time-symmetric variant of Nelson's kinematics recently developed by the author.
The broad debate on foundational issues in quantum mechanics, which took place at the famous 1957 Chapel Hill conference on \textit{The Role of Gravitation in Physics}, is here critically analyzed with an emphasis on Richard Feynman's contributions. One of the most debated questions at Chapel Hill was whether the gravitational field had to be quantized and its possible role in wave function collapse. Feynman's arguments in favor of the quantization of the gravitational field, based essentially on a series of gedanken experiments, are here discussed. Then the related problem of the wave functio…
Functional Schrödinger equations for interacting fields are solved via rigorous non-perturbative Feynman type integrals.
New applications of Feynman disentangling method in quantum mechanics are studied and the time-dependent singular oscillator problem is solved in this approach. The important role of representation group theory is discussed in this context.
Starting from the earlier notions of stationary action principles, we show how Schwinger's Quantum Action Principle descended from Dirac's formulation, which independently led Feynman to his path-integral formulation of quantum mechanics. The connection between the two is brought out, and applications are discussed. The Keldysh-Schwinger time-cycle method of extracting matrix elements is described. Part II will discuss the variational formulation of quantum electrodynamics and the development of source theory.
It is shown that the complex phase of the Feynman propagator is a solution of the quantum Hamilton Jacobi equation
A history of Feynman's sum over histories is presented in brief. A focus is placed on the progress of path-integration techniques for exactly path-integrable problems in quantum mechanics.
Recent developments in elementary quantum mechanics have seen a number of extraordinary claims regarding quantum behaviour, and even questioning internal consistency of the theory. These are, we argue, different disguises of what Feynman described as quantum theory's "only mystery".
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.
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.
A proof-of-concept application of a quantum algorithm to multiloop Feynman integrals in the Loop-Tree Duality (LTD) framework is applied to a representative four-loop topology. Bootstrapping causality in the LTD formalism, is a suitable problem to address with quantum computers given the straightforward possibility to encode the two on-shell states of a propagator on the two states of a qubit. A modification of Grover's quantum search algorithm is developed and the quantum algorithm is successfully implemented on IBM Quantum and QUTE simulators.
In this article we present an analytic solution of the famous problem of diffraction and interference of electrons through one and two slits (for simplicity, only the one-dimensional case is considered). In addition to exact formulas, we exhibit various approximations of the electron distribution which facilitate the interpretation of the results. Our derivation is based on the Feynman path integral formula and this work could therefore also serve as an interesting pedagogical introduction to Feynman's formulation of quantum mechanics for university students dealing with the foundations of qua…
In this paper we will demonstrate the use of Feynman Diagrams for one dimensional scattering in quantum mechanics. We will evaluate the S-Matrix explicitly for the Dirac delta and finite wall potentials by summing the full series of Feynman diagrams, illustrating the spirit of perturbation theory. This technique may be useful in introductory quantum mechanics courses, and provides the student with intuition about conservation laws in the context of scattering problems by connecting Feynman diagrams, free propagation, and conservation of the corresponding observable. It also provides a toy mode…
Starting from the earlier notions of stationary action principles, we show how Julian Schwinger's Quantum Action Principle descended from Dirac's formulation, which independently led Feynman to his path-integral formulation of quantum mechanics. The connection between the two is brought out, and applications are discussed. The Keldysh-Schwinger time-cycle method of extracting matrix elements in nonequilibrium situations is described. The variational formulation of quantum field theory and the development of source theory constitute the latter part of this work. In this document, derived from S…
From each of Feynman's and von Neumann's postulates to the restricted Feynman path integrals: a mathematical theory of temporally continuous quantum measurements
本文严格证明了在简单近似下，Mensky 的受限 Feynman 路径积分可由 Feynman 量子化公理和 von Neumann 瞬时测量公理导出，并应用于自旋系统及多种量子效应的表述。
In this paper we study the quantum wave packet and the Feynman_de Broglie_Bohm propagator of the linearized Kostin equation along a classical trajetory.
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 …
In this paper we study the quantum wave packet and the Feynman-de Broglie-Bohm Propagator of the Schrodinger-Nassar equation for an extended electron.
In this paper we study the quantum wave packet and the Feynman-de Broglie-Bohm propagator of the linearized Schuch-Chung-Hartmann equation along a classical trajetory.
We show that Feynman's Clock construction, in which the time-evolution of a closed quantum system is encoded as a ground state problem, can be extended to open quantum systems. In our formalism, the ground states of an ensemble of non-Hermitian Feynman Clock Hamiltonians yield stochastic trajectories, which unravel the evolution of a Lindblad master equation. In this way, one can use Feynman's Clock not only to simulate the evolution of a quantum system, but also it's interaction with an environment such as a heat bath or measuring apparatus. A simple numerical example of a two-level atom unde…
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
On the basis of a quantum mechanical analogue of the famous Feynman-Kac formula and the Kolmogorov picture, we present a novel method to derive nonequilibrium work equalities for isolated quantum systems, which include the Jarzynski equality and Bochkov-Kuzovlev equality. Compared with previous methods in the literature, our method shows higher similarity in form to that deriving the classical fluctuation relations, which would give important insight when exploring new quantum fluctuation relations.
The Feynman path integral representation of quantum theory is used in a non--parametric Bayesian approach to determine quantum potentials from measurements on a canonical ensemble. This representation allows to study explicitly the classical and semiclassical limits and provides a unified description in terms of functional integrals: the Feynman path integral for the statistical operator, and the integration over the space of potentials for calculating the predictive density. The latter is treated in maximum a posteriori approximation, and various approximation schemes for the former are devel…
We present a novel benchmark application of a quantum algorithm to Feynman loop integrals. The two on-shell states of a Feynman propagator are identified with the two states of a qubit and a quantum algorithm is used to unfold the causal singular configurations of multiloop Feynman diagrams. To identify such configurations, we exploit Grover's algorithm for querying multiple solutions over unstructured datasets, which presents a quadratic speed-up over classical algorithms when the number of solutions is much smaller than the number of possible configurations. A suitable modification is introd…
Interpretation of wave function by coherent ensembles of trajectories
本文基于德布罗意、薛定谔、狄拉克和费曼的思想，引入时空中的相干轨迹系综来修正波函数的系综解释，从而避免测量坍缩悖论，并指出依赖单量子比特代表整个波函数的量子计算或密码学方法将失效。
We present quantum stochastic calculus in terms of diagrams taking weights in the algebra of observables of some quantum system. In particular, we note the absence of non-time-consecutive Goldstien diagrams. We review recent results in Markovian limits in these terms.
Feynman's Relativistic Cut-Off for Quantum Electrodynamics
本文证明费曼1948年提出的相对论性截断方法不仅适用于自旋1/2粒子的自能计算，也适用于自旋0粒子，并指出该方法与波多尔斯基的哈密顿方法等价。
Feynman's sum-over-histories formulation of quantum mechanics has been considered a useful calculational tool in which virtual Feynman histories entering into a coherent quantum superposition cannot be individually measured. Here we show that sequential weak values, inferred by consecutive weak measurements of projectors, allow direct experimental probing of individual virtual Feynman histories thereby revealing the exact nature of quantum interference of coherently superposed histories. Because the total sum of sequential weak values of multi-time projection operators for a complete set of or…
Lorentz-covariant harmonic oscillator wave functions are constructed from the Lorentz-invariant oscillator differential equation of Feynman, Kislinger, and Ravndal for a two-body bound state. The wave functions are not invariant but covariant. As the differential equation contains the time-separation variable, the wave functions contain the same time-separation variable which does not exist in Schrödinger wave functions. This time-separation variable can be shown to belong to Feynman's rest of the universe, and can thus be eliminated from the density matrix. The covariant probability interpret…
Loop Feynman integration on a quantum computer
本文提出新型量子蒙特卡洛积分器 QFIAE，通过引入量子神经网络将多维被积函数分解为傅里叶级数以实现二次加速，首次在量子计算机和模拟器上成功计算单圈费曼积分，验证了方法的有效性及跨领域应用潜力。
The Einstein-Podolsky-Rosen (EPR) paradox that argues for the incompleteness of quantum mechanics as a description of physical reality has been put to rest by John Bell's famous theorem, which inspired numerous experimental tests and brought about further affirmations of quantum reality. Nevertheless, in his writings and public presentations, Richard Feynman never acknowledged the significance of Bell's contribution to the resolution of the EPR paradox. In this paper, we discuss several variants of the Bell inequalities (including one that was specifically espoused by Feynman), and explore the…
This paper discusses several methods for describing the dynamics of open quantum systems, where the environment of the open system is infinite-dimensional. These are purifications, phase space forms, master equation and liouville equation forms. The main contribution is in using Feynman-Kac formalisms to describe the infinite-demsional components.
A generalized Feynman-Kac formula based on the Wiener measure is presented. Within the setting of a quantum particle in an electromagnetic field it yields the standard Feynman-Kac formula for the corresponding Schrödinger semigroup. In this case rigorous criteria for its validity are compiled. Finally, phase-space path-integral representations for more general quantum Hamiltonians are derived. These representations rely on a generalized Lie-Trotter formula which takes care of the operator-ordering multiplicity, but in general is not related to a path measure.
We show the equivalence of the functions $G_{\rm p}(t)$ and $|Ψ(d,t)|^2$ for the ``passage time'' in tunneling. The former, obtained within the framework of the real time Feynman histories approach to the tunneling time problem, using the Gell-Mann and Hartle's decoherence functional, and the latter involving an exact analytical solution to the time-dependent Schrödinger equation for cutoff initial waves.
Feynman's formulation of quantum theory is remarkable in its combination of formal simplicity and computational power. However, as a formulation of the abstract structure of quantum theory, it is incomplete as it does not account for most of the fundamental mathematical structure of the standard von Neumann-Dirac formalism such as the unitary evolution of quantum states. In this paper, we show how to reconstruct the entirety of the finite-dimensional quantum formalism starting from Feynman's rules with the aid of a single new physical postulate, the no-disturbance postulate. This postulate sta…
The five laws of relativistic quantum mechanics, according to Feynman's path integral formulation, are concisely stated and applied to experiments. Reflection diffraction grating experiments for both photons and electrons are analysed, in particular the Davisson-Germer experiment in which the wave-like property of electrons was first established. It is shown how classical, purely spatial, effective wave theories for both photons and electrons are predicted by the path integral formulation of quantum mechanics. The standard Copenhagen interpretation of wave mechanics is critically discussed in …
Geometrical causality: casting Feynman integrals into quantum algorithms
本文利用圈-树对偶性的几何因果选择规则构造哈密顿量，将费曼积分计算转化为最小化问题，并部署于量子计算机以寻求加速，旨在克服多圈多腿振幅计算中的资源瓶颈。
We describe the "Feynman diagram" approach to nonrelativistic quantum mechanics on R^n, with magnetic and potential terms. In particular, for each classical path γconnecting points q_0 and q_1 in time t, we define a formal power series V_γ(t,q_0,q_1) in \hbar, given combinatorially by a sum of diagrams that each represent finite-dimensional convergent integrals. We prove that exp(V_γ) satisfies Schrödinger's equation, and explain in what sense the t\to 0 limit approaches the δdistribution. As such, our construction gives explicitly the full \hbar\to 0 asymptotics of the fundamental solution to…
Starting from the microscopic theory of Bardeen-Cooper-Schrieffer (BCS) for the fermionic superfluids, we show that the vortex dynamics can be followed naturally by extending Feynman's influence functional approach to incorporate the transverse force. There is a striking mutual independence of the transverse and longitudinal influences: The former has the topological origin and is insensitive to details, while the latter corresponds to the well-known damping kernel depending on details.
We study the effects of dissipation and decoherence induced on a harmonic oscillator by the coupling to a chaotic system with two degrees of freedom. Using the Feynman-Vernon approach and treating the chaotic system semiclassically we show that the effects of the low dimensional chaotic environment are in many ways similar to those produced by thermal baths. The classical correlation and response functions play important roles in both classical and quantum formulations. Our results are qualitatively similar to the high temperature regime of the Caldeira-Leggett model.
We propose an algorithm based on variational quantum imaginary time evolution for solving the Feynman-Kac partial differential equation resulting from a multidimensional system of stochastic differential equations. We utilize the correspondence between the Feynman-Kac partial differential equation (PDE) and the Wick-rotated Schrödinger equation for this purpose. The results for a $(2+1)$ dimensional Feynman-Kac system obtained through the variational quantum algorithm are then compared against classical ODE solvers and Monte Carlo simulation. We see a remarkable agreement between the classical…
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…
Regarding the Pauli principle in quantum field theory and in many-body quantum mechanics, Feynman advocated that Pauli's exclusion principle can be completely ignored in intermediate states of perturbation theory. He observed that all virtual processes (of the same order) that violate the Pauli principle cancel out. Feynman accordingly introduced a prescription, which is to disregard the Pauli principle in all intermediate processes. This ingeneous trick is of crucial importance in the Feynman diagram technique. We show, however, an example in which Feynman's prescription fails. This casts dou…
Quantum optical coherence theory based on Feynman's path integral
该研究介绍并综述了基于费曼路径积分的量子光学相干理论，指出其能更好关联数学计算与物理解释，预测热光电场经典模型或不准确，统一解释了双光子聚束与Hong-Ou-Mandel凹陷的物理本质，助力理解光的相干性及光子本质问题。
Feynman's clock and hierarchy-informed sampling for quantum error mitigation
针对近期量子算法物理实现中降低量子噪声的需求，提出将BBGKY - ISM方案从自旋链量子模拟扩展到任意量子电路的新方法，利用费曼时钟哈密顿量映射，经数值模拟验证其能有效降低量子误差。
Our previous work on quantum mechanics in Hilbert spaces of finite dimensions N is applied to elucidate the deep meaning of Feynman's path integral pointed out by G. Svetlichny. He speculated that the secret of the Feynman path integral may lie in the property of mutual unbiasedness of temporally proximal bases. We confirm the corresponding property of the short-time propagator by using a specially devised N x N -approximation of quantum mechanics in L^2(R) applied to our finite-dimensional analogue of a free quantum particle.
The equivalence of two formulations of Fokker's quantum theory is proved - based on the Feynman functional integral representation of the propagator for a system of charges with direct electromagnetic interaction and the quantum principle of least action as an analogue of the Schrödinger wave equation. The common basis for the two approaches is the generalized canonical form of Fokker's action.
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.…
Feynman's path to Schrödinger (and various other things)
本文梳理费曼如何受狄拉克类比启发，将拉格朗日框架引入量子力学并建立路径积分表述，进而从路径积分推导出薛定谔方程并证明概率守恒，为本科生连接这一方法与标准课程内容。
The Landau-Feynman transiently open quantum system: entanglement and density operators
针对学界对Landau-Feynman两体瞬态耦合量子系统情形长期存在的概念混淆，本文指出该场景下应使用纠缠而非混合态的概念，澄清了相关争议的核心认知误区。
Feynman's laws of quantum dynamics are concisely stated, discussed in comparison with other formulations of quantum mechanics and applied to selected problems in the physical optics of photons and massive particles as well as flavour oscillations. The classical wave theory of light is derived from these laws for the case in which temporal variation of path amplitudes may be neglected, whereas specific experiments, sensitive to the temporal properties of path amplitudes, are suggested. The reflection coefficient of light from the surface of a transparent medium is found to be markedly different…
The USRA Feynman Quantum Academy: If You Give a Student a Quantum Internship
本文回顾了 USRA 费曼量子学院实习项目 8 年来的发展，说明研究生实习如何连接早期科研人才与量子计算机构，并展示其培养未来量子劳动力的成果。
Gaussian Reformulation of the Feynman Path Integral for Quantum Statistical Mechanics with Results for the Second Virial Coefficient of $^4$He
研究针对量子统计力学的费曼路径积分进行高斯重整化，通过晶格上环聚合物统计和维格纳 - 柯克伍德函数高温展开获方差均值，避免传统问题，给出氦第二维里系数的解析与模拟结果并与实验比较。
Similarities between the non-deterministic nature of quantum theory and the unpredictable patterns of human cognition and decision making have been observed and commented on many times since the invention of Quantum Mechanics in the first part of the 20th century. Niels Bohr himself took note of the parallels.[3] In fact, an entire field of study, Quantum Cognition, has been borne from the study of this analogy. [3] However, many of the attempts to model human behavior with quantum mechanics conflate the identity of a particle with its own wavefunction, which is incorrect and invalidates the a…
On Weak Values and Feynman's Blind Alley
本文讨论基于弱值的推理是否能让人陈述未观测量子系统的过去，并结合不确定性原理论证费曼的观点大概率仍未被推翻。
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.
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