Space-Time Approach to Non-Relativistic Quantum Mechanics
1948/04/01 by Richard P. Feynman · 2 voices · 263 citations
Physics and Astronomy · #Quantum Electrodynamics and Casimir Effect #Quantum Mechanics and Applications #Quantum and Classical Electrodynamics
paper · doi:10.1103/revmodphys.20.367
openalex publication_date 1948/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
Abstract
Non-relativistic quantum mechanics is formulated here in a different way. It is, however, mathematically equivalent to the familiar formulation. In quantum mechanics the probability of an event which can happen in several different ways is the absolute square of a sum of complex contributions, one from each alternative way. The probability that a particle will be found to have a path x(t) lying somewhere within a region of space time is the square of a sum of contributions, one from each path in the region. The contribution from a single path is postulated to be an exponential whose (imaginary) phase is the classical action (in units of \ensuremathℏ) for the path in question. The total contribution from all paths reaching x, t from the past is the wave function \ensuremathψ(x, t). This is shown to satisfy Schroedinger's equation. The relation to matrix and operator algebra is discussed. Applications are indicated, in particular to eliminate the coordinates of the field oscillators from the equations of quantum electrodynamics.
Cited by
- Foundations of Modern Probability
- Tangled in entanglements
- An introduction to lattice gauge theory and spin systems
- The symmetrical foundation of Measure, Probability and Quantum theories
- Schrödinger's equation as a consequence of the central limit theorem without prior assumption of physical laws
- Infinite Cycles in Boson Lattice Models
- The Stochastic-Quantum Correspondence
- The quantum theory of time, the block universe and human experience
- Non-Markovian quantum Brownian motion: a non-Hamiltonian approach
- Quantum Mechanics with a non-zero quantum correlation time
- Stochastic failure accumulation as a foundation for exponential mortality and selective disappearance
- Dark Matter Phenomenology: Sterile Neutrino Portal and Gravitational Portal in Extra-Dimensions
- Coherent states: Theory and some applications
- Flat family of QFTs and quantization of d-algebras
- Space-Time Approach to Quantum Electrodynamics
- Linear Canonical Transformations and the Hamilton-Jacobi Theory in Quantum Mechanics
- A note on the short-time quantum propagator
- The real-time Feynman path integral for step potentials
- Quantum aspects of spacetime: A quantum optics view of acceleration radiation and black holes
- Diagonal Born-Oppenheimer Corrections in Condensed-Phase Ring Polymer Surface Hopping
- The Schrödinger equation for a spherically symmetric system, its structure and solutions
- Higher-derivative Lagrangians, nonlocality, problems, and solutions
- Probing the partition function for temperature-dependent potentials with nested sampling
- On Hilbert's sixth problem
- Exercices sur les temps locaux de semi-martingales continues et les excursions browniennes
- Undergraduate Lecture Notes in Topological Quantum Field Theory
- Risk Sensitive Path Integral Control
- Some remarks on history and pre-history of Feynman path integral
- Bell's Theorem and the Causal Arrow of Time
- Topics in Effective Field Theory for Lattice QCD
- Path Integral in Modular Space
- Concerning a natural compatibility condition between the action and the renormalized operator product
- Space-Time Geodesics and the Derivation of Schrödinger's equation
- Mathematical Remarks on the Feynman Path Integral for Nonrelativistic Quantum Electrodynamics
- Dirac and the Path Integral
- Grassmann algebraic field theory, entanglement and fermionic hidden clocks
- More On Grover's Algorithm
- The Time Inversion for Modified Oscillators
- Decoherence and continuous measurements: Phenomenology and models
- The action and the physical scale of field theory
- Brownian intersection local times: Exponential moments and law of large masses
- A particle in equilibrium with a bath realizes worldline supersymmetry
- Introduction to attosecond time-delays in photoionization
- The method of partial wave functions and the structure of time interval between the subsequent quantum transitions
- Path integral approach to one-dimensional discrete-time quantum walk
- Generating Functional in String Field Theory
- Simultaneous occurrence of off-diagonal long-range order and infinite\n permutation cycles in systems of interacting atoms
- Agglomerative clustering and collectiveness measure via exponent generating function
- Quantum Processes and Energy-Momentum Flow
- Operator Methods, Abelian Processes and Dynamic Conditioning
- Statistical mechanics approach to lattice field theory
- A First Principles Derivation of Classical and Quantum Mechanics as the Natural Theories for Smooth Stochastic Paths
- Lectures on Super Analysis -- Why necessary and What's that?
- A Quantum Field Approach for Advancing Optical Coherence Tomography Part I: First Order Correlations, Single Photon Interference, And Quantum Noise
- Path Integral Formalism for Quantum Open Systems
- Quasi-potential as an implicit regularizer for the loss function in the stochastic gradient descent
- What are temporal correlations
- Thermodynamic Behavior of Statistical Event Counting in Time: Independent and Correlated Measurements
- Star Products that can not be induced by Drinfel'd Twists
- Quantum Computation: A Computer Science Perspective
- The Small Scale Structure of Space-Time: A Bibliographical Review
- Reformulating non-equilibrium steady-states and generalised Hopfield discrimination
- Path integral and the induction law
- Gluing I: Integrals and Symmetries
- On the Interpretation of the Foundations of Quantum Mechanics
- Integral Equation Approach to Stationary Stochastic Counting Process with Independent Increments
- A “general boundary” formulation for quantum mechanics and quantum gravity
- Quantum Operator Design for Lattice Baryon Spectroscopy
- An Introduction into the Feynman Path Integral
- Quantum mechanical path integrals in the first quantised approach to quantum field theory
- Explicit mean-field radius for nearly parallel vortex filaments in statistical equilibrium
- Proof of phase transition in homogeneous systems of interacting bosons
- A free energy principle for a particular physics
- Accelerated Inchworm Method with Tensor-Train Bath Influence Functional
- Photon dispersion in causal sets
- Semi-Classical Holomorphic Transition Amplitudes in Covariant Loop Quantum Gravity
- Self-interacting Brownian motion
- Propagators of isochronous an-harmonic oscillators and Mehler formula for the x-Hermite polynomials
- The Feynman integral path a Henstock integral: a survey and open problems
- A Biophysical Approach to Production Theory
- What is and What should be Time?
- Geometric Properties of Paths in Relativistic Lagrangian Mechanics
- A short derivation of Feynman formula
- Quantum interference interpreted classically through application of Berry's phase
- Effects of Conical Geometry on Approximate Solutions Under Modified Pöschl-Teller Potential and Shannon Entropy
- Quantum light and radiation in Rindler spacetime: from uncertainty relations to the cosmological implications
- Dynamics of wave fronts and filaments in anisotropic cardiac tissue
- Pure Monte Carlo Method: a Third Way for Plasma Simulation
- A Dynamic Histories Interpretation of Quantum Theory
- Statistical Mechanics: Theory and Molecular Simulation
- An Information-Theoretic Approach to Quantum Theory, I: The Abstract Quantum Formalism
- Undergraduate Lecture Notes in De Rham-Hodge Theory
- On the mathematical formulation of the restricted Feynman path integrals through broken line paths
- Numerical Feynman integrals for density operator dynamics using master equation interpolants: faster convergence and significant reduction of computational cost
- Natural number dynamics: reconstructing physics from generalized atomicity
- Generative models for sampling of lattice field theories
- A new look at the Helmholtz equation: Lefschetz thimbles and the einbein action
- On Folding Calabi-Yau Diagrams in M-theory Black Brane Scenarios
- A Pseudo-Differential Operator Construction of Markov Processes Using Feynman Path Integrals
- Fourier formula for quantum partition functions
- Modelling Quantum Theoretical Trajectories within Geometric Relativistic Theories
- Non-Gaussian generalizations of Wick's theorems, related to the Schwinger-Dyson equation
- Unitarily manipulating in time and space a Gaussian wave-packet motional state of a single atom in a quadratic potential field
- Grid porting of Bhabha scattering code through a master-worker scheme
- From the Newton's laws to motions of the fluid and superfluid vacuum: vortex tubes, rings, and others
- Fundamental aspects of quantum Brownian motion
- Approximations to path integrals and spectra of quantum systems
- Non-Commutative Quantum Geometry: A Reappraisal of the Bohm Approach to Quantum Theory
- Interpretation of the Five Dimensional Quantum Propagation of a Spinless\n Massless Particle
- Energy as a measure for the elapse of time
- Imprints of the Quantum World in Classical Mechanics
- A mathematical framework for a standard theory using extended representations of paths and world lines
- Monogamy of quantum entanglement in time
- Path integration on Darboux spaces
- Lissajous curves and semiclassical theory: The two-dimensional harmonic oscillator
- Gap Labelling Theorems for Schrödinger Operators
- Classical and quantum mechanics of the damped harmonic oscillator
- Linear response theory and transient fluctuation relations for diffusion processes: a backward point of view
- AN INTRODUCTION TO QUANTUM GRAVITY
- Path integral in a magnetic field using the Trotter product formula
- The Loschmidt echo in classically chaotic systems: Quantum chaos, irreversibility and decoherence
- On the coordinate (in)dependence of the formal path integral
- Path integration and perturbation theory with complex Euclidean actions
- A New Algorithm for the Inverse of Matrices with Noncommuting Entries
- INSTANTON SOLUTION OF A NONLINEAR POTENTIAL IN FINITE SIZE
- The renormalization group and the ε expansion
- Finite temperature theory of metastable anharmonic potentials
- Word Measures on Unitary Groups
- Nonlocality of the NN interaction in an effective field theory
- On quantum corrections to dislocations mass
- Transient Phenomena in Quantum Bound States Subjected to a Sudden Perturbation
- On the absence of bound-state stabilization through short ultra-intense fields
- Quasinormal modes of D3-brane black holes
- Quantum Gravity: Unification of Principles and Interactions, and Promises of Spectral Geometry
- Time-sliced path integrals with stationary states
- Metastability Driven by Soft Quantum Fluctuation Modes
- Low Energy Continuum and Lattice Effective Field Theories
- Principles of Solid State Electron Optics
- Finsler geometrical path integral
- Quantum mechanics with extended probabilities
- Relating the Lorentzian and exponential: Fermi’s approximation, the Fourier transform, and causality
- Conceptual Developments of 20th Century Field Theories
- Probabilistic Representation of Weak Solutions of Partial Differential Equations with Polynomial Growth Coefficients
- Unitarity and causality in generalized quantum mechanics for nonchronal spacetimes
- Principle of Least Action and Theory of Cyclic Evolution
- Derivation of the postulates of quantum mechanics from the first principles of scale relativity
- Universal Nonlinear Filtering Using Feynman Path Integrals I: The Continuous-Discrete Model with Additive Noise
- Fermat's principle of least time in the presence of uniformly moving boundaries and media
- Algebraic structure of the Feynman propagator and a new correspondence for canonical transformations
- The Universe as an Eigenstate: Spacetime Paths and Decoherence
- Problems with complex actions
- Causality, symmetries and quantum mechanics
- A rigorous path integral for quantum spin using flat-space Wiener regularization
- The mathematical role of (commutative and noncommutative) infinitesimal random walks over (commutative and noncommutative) riemannian manifolds in Quantum Physics
- A discussion on supersymmetric cosmic strings with gauge-field mixing
- Local variational principle
- A Short Lecture on Divergences
- Path Integral Discussion for Smorodinsky-Winternitz Potentials: I. Two- and Three Dimensional Euclidean Space
- Fast convergence of path integrals for many-body systems
- Quantum Electrodynamics at strong Couplings
- Consistency and linearity in quantum theory
- Quantum Field Theory on Curved Backgrounds. I. The Euclidean Functional Integral
- A PEDAGOGICAL INTRODUCTION TO THE SLAVNOV FORMULATION OF QUANTUM YANG–MILLS THEORY
- Using a fermionic ensemble of systems to determine excited states
- Effective theories of coupled classical and quantum variables
- Single-particle path integral for composite fermions and the renormalization of the effective mass
- Feynman's path integrals and Bohm's particle paths
- Dynamics and predictions in the co-event interpretation
- The Kochen–Specker theorem revisited in quantum measure theory
- Real-time Feynman path integral with Picard–Lefschetz theory and its applications to quantum tunneling
- Path integrals for parastatistics
- Glafka 2004: Generalizing Quantum Mechanics for Quantum Gravity
- Introduction to Many-Body Physics
- Heat capacity estimators for random series path-integral methods by finite-difference schemes
- The Theory of Positrons
- Algebraic integration theory
- Consistent histories, the quantum Zeno effect, and time of arrival
- The Radiation Theories of Tomonaga, Schwinger, and Feynman
- Mathematical Formulation of the Quantum Theory of Electromagnetic Interaction
- Quantum information theoretic approach to the mind–brain problem
- Theλ-Transition in Liquid Helium
- Richard Phillips Feynman. 11 May 1918 – 15 February 1988
- Theory of Inelastic Scattering of Cold Neutrons from Liquid Helium
- An Operator Calculus Having Applications in Quantum Electrodynamics
- GENERALIZED SCHRÖDINGER EQUATION IN EUCLIDEAN FIELD THEORY
- Quantum integrals of motion for variable quadratic Hamiltonians
- Fundamental times, lengths and physical constants: Some unknown contributions by Ettore Majorana
- Fundamental length scale of quantum spacetime foam
- Probabilistic solutions of a stretched beam discretized with finite difference scheme and excited by Kanai-Tajimi ground motion
- T Violation and the Unidirectionality of Time
- Foundations of a spacetime path formalism for relativistic quantum mechanics
- Path integral approach to Asian options in the Black–Scholes model
- A sum-over-histories account of an EPR(B) experiment
- The classical limit for quantum mechanical correlation functions
- Classical and quantum probability
- CHIRAL ANOMALIES VIA CLASSICAL AND QUANTUM FUNCTIONAL METHODS
- Semiclassical approach to the quantum Loschmidt echo in deep quantum regions: From validity to breakdown
- Unwinding of circular helicoidal molecules vs. size
- Interferometry with Atoms
- Recursive Schrödinger equation approach to faster converging path integrals
- Context, spacetime loops and the interpretation of quantum mechanics
- Information transport in classical statistical systems
- Complex energies and beginnings of time suggest a theory of scattering and decay
- Boosting QED and QCD bound states in the path integral formalism
- Quantum corrections to ϕ 4 model solutions and applications to Heisenberg chain dynamics
- Algebraic Topology Foundations of Supersymmetry and Symmetry Breaking in Quantum Field Theory and Quantum Gravity: A Review
- Path-sum solution of the Weyl quantum walk in 3 + 1 dimensions
- Negative specific heat for quasi-2D vortex structures in electron plasmas: an explicit, closed-form derivation
- On Hamiltonian Formulations of the Schrödinger System
- Spin factor in the path integral representation for the Dirac propagator in external fields
- Progress in classical and quantum variational principles
- Quantization of Generalized Abelian Gauge Field Theory under Rotor Model
- Approximation to Wiener measure on a general noncompact Riemannian manifold
- Dirac, Bohm and the Algebraic Approach
- Time asymmetric quantum theory – I. Modifying an axiom of quantum physics
- Quantum Field Theory and Dense Measurement
- CONTINUOUS TIME-DEPENDENT MEASUREMENTS: QUANTUM ANTI-ZENO PARADOX WITH APPLICATIONS
- Pressure statistics from the path integral for Darcy flow through random porous media
- Gravity analog model of non-equilibrium thermodynamics
- A Philosophical Approach to Quantum Field Theory
- Path integrals in polar field variables in QFT
- Ranking to Learn and Learning to Rank: On the Role of Ranking in Pattern Recognition Applications
- A Noether Theorem for discrete Covariant Mechanics
- The Feynman Path Integral: An Historical Slice
- Rigorous real-time Feynman path integral for vector potentials
- On quantum-geometric connections and propagators in curved spacetime
- Potential theory, path integrals and the Laplacian of the indicator
- The state is not abolished, it withers away: how quantum field theory\n became a theory of scattering
- Lévy-Ciesielski random series as a useful platform for Monte Carlo path integral sampling
- Exceptional points and quantum correlations in precise measurements
- Origin of complex quantum amplitudes and Feynman’s rules
- Quantum identities for the action
- General boundary quantum field theory: Timelike hypersurfaces in the Klein-Gordon theory
- Probabilistic approach to time-dependent load-transfer models of fracture
- A signed particle formulation of non-relativistic quantum mechanics
- Quantum mechanical path integrals in curved spaces and the type-A trace anomaly
- Efficient Simulation of Finite-Temperature Open Quantum Systems
- Regularizing Feynman path integrals using the generalized Kontsevich-Vishik trace
- Macroscopic quantum tunneling and quantum–classical phase transitions of the escape rate in large spin systems
- Electron diffraction analysis of individual single-walled carbon nanotubes
- Quantum mechanics as classical statistical mechanics with an ontic extension and an epistemic restriction
- Quantum Wave Equation of Non-conservative System
- Spacetime alternatives in the quantum mechanics of a relativistic particle
- Nonclassical phase-space trajectories for the damped harmonic quantum oscillator
- Path Integration and Separation of Variables in Spaces of Constant Curvature in Two and Three Dimensions
- Domain shape dependence of semiclassical corrections to energy
- Existence of short-time approximations of any polynomial order for the computation of density matrices by path integral methods
- Feynman formulae and phase space Feynman path integrals for tau-quantization of some Lévy-Khintchine type Hamilton functions
- An Ahistorical Approach to Elementary Physics
- The Dirac-Bohm Picture
- Dynamical invariants for variable quadratic Hamiltonians
- Ramsey-type phase control of free-electron beams
- Quantum effective potential from discarded degrees of freedom
- An Analytic Expression for the Distribution of the Generalized Shiryaev–Roberts Diffusion
- Hamiltonian path integrals in momentum space representation via white noise techniques
- On peculiarities and pit falls in path integrals
- The Poincaré-Shannon Machine: Statistical Physics and Machine Learning Aspects of Information Cohomology
- Entropic penalties in circular DNA assembly
- Continuous fuzzy measurement of energy for a two-level system
- History of quantum field theory [wikipedia]
- Path-integral formulation [wikipedia]
- Richard Feynman [wikipedia]
- Huygens–Fresnel principle [wikipedia]
- Antiparticle [wikipedia]
Discussions
Related