"The path integral formulation is a description in quantum mechanics that generalizes the action principle of classical mechanics. It replaces the classical notion of a single, unique classical trajectory for a system with a sum, or functional integral, over an infinity of quantum-mechanically possible trajectories to compute a quantum amplitude."
Introduces the powerful technique of the path integral, which allows us to compute quantum amplitudes and probabilities over all possible paths.
Classical mechanics: A study of the motion of macroscopic objects using Newton's laws of motion, with a focus on Lagrangian and Hamiltonian mechanics.
Quantum mechanics: A study of the behavior of microscopic particles, with a focus on wavefunctions, operators, and observables.
Feynman diagrams: A graphical representation of the terms in a perturbative expansion of a quantum mechanical field theory.
Functional integrals: The path integral formulation of quantum mechanics, which involves integrating over all possible paths that a particle could take between two points in space and time.
Gauge theories: A class of quantum field theories that describe the interactions between particles and forces, including electromagnetism and the strong and weak nuclear forces.
Renormalization: A technique used to deal with the divergences that arise in field theories due to the infinite number of virtual particles that can be involved in an interaction.
Quantum electrodynamics: The quantum mechanical theory of the electromagnetic force, which describes the interactions between photons, electrons, and other charged particles.
Quantum chromodynamics: The quantum mechanical theory of the strong nuclear force, which describes the interactions between quarks and gluons.
Spontaneous symmetry breaking: A phenomenon in quantum field theory where a physical system appears to lose its symmetry under certain conditions.
Topological field theory: A type of quantum field theory that is characterized by topological invariants, which are unaffected by continuous deformation of the system.
Feynman Path Integrals: A commonly used form of path integral that describes the evolution of a particle in quantum mechanics.
Euclidean Path Integrals: A type of path integral used in statistical mechanics and quantum field theory.
Schrödinger path integral: A path integral that describes the probabilities of various outcomes in quantum mechanics.
Martin-Siggia-Rose path integral: A path integral that describes the dynamics of a stochastic process.
Wiener path integral: A path integral that describes the behavior of a Brownian particle.
Wilsonian path integral: A path integral that describes the dynamics of fields in renormalization group theory.
Imaginary time path integral: Another type of path integral used in statistical mechanics and quantum field theory that involves the use of imaginary time.
Matrix model path integral: A path integral that describes the behavior of matrices in quantum mechanics.
Group path integral: A path integral that describes the behavior of groups in quantum mechanics.
Supersymmetric path integral: A path integral that describes the dynamics of supersymmetric systems.
Topological path integral: A path integral that describes the behavior of topological features in quantum field theory.
"Manifest Lorentz covariance is easier to achieve than in the operator formalism of canonical quantization."
"The path integral allows one to easily change coordinates between very different canonical descriptions of the same quantum system."
"It is in practice easier to guess the correct form of the Lagrangian of a theory, which naturally enters the path integrals."
"Unitarity of the S-matrix is obscure in the formulation."
"The path integral also relates quantum and stochastic processes."
"The basic idea of the path integral formulation can be traced back to Norbert Wiener, who introduced the Wiener integral for solving problems in diffusion and Brownian motion."
"This idea was extended to the use of the Lagrangian in quantum mechanics by Paul Dirac in his 1933 article."
"The complete method was developed in 1948 by Richard Feynman."
"The original motivation stemmed from the desire to obtain a quantum-mechanical formulation for the Wheeler–Feynman absorber theory using a Lagrangian as a starting point."
"It replaces the classical notion of a single, unique classical trajectory for a system with a sum, or functional integral, over an infinity of quantum-mechanically possible trajectories."
"Manifest Lorentz covariance is easier to achieve than in the operator formalism of canonical quantization."
"The path integral allows one to easily change coordinates between very different canonical descriptions of the same quantum system."
"It is in practice easier to guess the correct form of the Lagrangian of a theory, which naturally enters the path integrals."
"Unitarity of the S-matrix is obscure in the formulation."
"The path integral also relates quantum and stochastic processes."
"The basic idea of the path integral formulation can be traced back to Norbert Wiener, who introduced the Wiener integral for solving problems in diffusion and Brownian motion."
"This idea was extended to the use of the Lagrangian in quantum mechanics by Paul Dirac in his 1933 article."
"The complete method was developed in 1948 by Richard Feynman."
"The original motivation stemmed from the desire to obtain a quantum-mechanical formulation for the Wheeler–Feynman absorber theory using a Lagrangian as a starting point."