Discover published sets by community

A mathematical summation over all possible paths a particle can take between two points, weighted by the exponential of the action (in units of the reduced Planck's constant). It's central to the path integral formulation as it replaces the classical single path with a quantum superposition of all possible paths.

An interpretation of quantum mechanics that sums over all conceivable histories of a system, each with a probability amplitude given by the path integral. This provides a visualization of all possible paths, including classically forbidden ones, contributing to the final amplitude.

A differential equation that provides the conditions for which the action is stationary (no change in first-order). These equations are significant in determining the classical path which, in the path integral formulation, is the path of stationary phase around which quantum fluctuations occur.

The regime in which the predictions of quantum mechanics approach those of classical mechanics. In the path integral formulation, the classical limit corresponds to the situation where the path of stationary action (classical path) dominates the path integral due to the phase oscillations averaging out contributions from non-classical paths.

A function that summarizes the dynamics of a system. It is the kinetic energy minus the potential energy for classical systems, and it's used to construct the action by integration over time. The Lagrangian is important in the path integral approach for determining the evolution of quantum systems.

In physics, action is a functional that takes a path (or a history of the system) and returns a scalar, reflecting the dynamics of the system. In the path integral formulation, it's crucial in calculating the probabilities of different paths by being part of the exponent in the path integral.

The propagator in the path integral formulation, also known as the Feynman propagator, is a probability amplitude describing the likelihood of a particle moving from one point to another in a given time. It is described by the path integral over all paths connecting two spacetime points with the action in the exponential.

In the path integral formulation, the phase factor is the exponential of the action (in the imaginary time) divided by the reduced Planck's constant. The phase factor contributes to interference effects as paths with different actions can add constructively or destructively.

A complex number representing the probability amplitude for an event in quantum mechanics. In the context of path integrals, the amplitude for a particular path is derived from the action. The total amplitude is obtained by summing over all paths.