Path integral formulation

A formulation of quantum theory in which an amplitude is computed by summing contributions from possible histories, weighted by their action.

Feynman path integral: A path-integral method that expresses quantum amplitudes as sums over particle trajectories weighted by the action. It gives the formulation’s standard trajectory-based construction.
Quantum amplitude: A complex number whose magnitude and phase encode the probability amplitude for a quantum outcome. The path integral’s output is an amplitude, not a direct probability.
Richard Feynman: An American theoretical physicist who developed the path-integral approach to quantum mechanics and shared the 1965 Nobel Prize in Physics. Feynman established the formulation’s modern quantum-mechanical form.
Hamiltonian formulation: A formulation of quantum dynamics based on a Hamiltonian operator that generates time evolution. It describes evolution through operators rather than sums over histories.
Feynman diagram: A diagrammatic representation of terms in perturbative quantum-field-theory calculations. Expanding field path integrals produces the terms represented by these diagrams.
Action (physics): A quantity defined by integrating a system’s Lagrangian over time, whose stationary values characterize classical motion. Each history’s action sets its phase in the quantum sum.
Superposition principle: The quantum rule that allows states or amplitudes to combine linearly. Contributions from alternative histories combine by superposition.
Paul Dirac: A British theoretical physicist whose work shaped quantum mechanics and quantum field theory. His 1933 work on the Lagrangian in quantum mechanics anticipated Feynman’s construction.
Schrödinger picture: A quantum-mechanical representation in which states evolve in time while operators are generally fixed. It offers a state-evolution description parallel to the path-integral account.
Perturbation theory: A method for approximating solutions by expanding around a simpler, solvable problem. It turns path-integral expressions into systematic approximations for interacting systems.

Linked from 19 pages