propagatoren

Propagatoren is a term used primarily in physics and mathematics to denote a function or operator that describes how a physical quantity, field, or state propagates from one spacetime point to another. In its broad sense, a propagator acts as the evolution kernel that maps an initial configuration to its future configuration.

In quantum mechanics and quantum field theory, a propagator is a Green's function of the equations of motion. It encodes the probability amplitude for a particle or excitation to travel from one point to another and to arise at a given time. Several standard variants exist, including the Feynman propagator (time-ordered), the retarded propagator (causal, nonzero only for later times), and the advanced propagator (nonzero only for earlier times). Propagators are central to calculating transition amplitudes, correlation functions, and scattering processes, and they can be derived from the underlying Lagrangian or Hamiltonian. In the path integral formalism, the propagator is expressed as a sum over all possible paths connecting the endpoints.

In mathematics and the theory of partial differential equations, a propagator often refers to the fundamental solution or kernel that solves a PDE with a delta source. Examples include the heat kernel, which propagates heat or probability density in time, and the wave or Schrödinger kernels. These kernels satisfy differential equations with initial or boundary conditions and provide a constructive way to obtain solutions through convolution.

In stochastic processes, the propagator (or transition kernel) describes the evolution of a random state over time: it gives the distribution of the state at a future time conditional on its present value. See also Green's functions and kernels for related concepts.