In particle physics and quantum field theory (QFT), the propagator is a mathematical object that describes the propagation of particles or fields through space and time. It provides information about the probability amplitude for a particle to propagate between two points in spacetime and is intimately connected to the concept of Feynman diagrams.
The physical meaning of a propagator can be understood by considering the following aspects:
Particle propagation: The propagator represents the probability amplitude for a particle or field to propagate from one spacetime point to another. It encapsulates the idea that particles can exist as virtual entities, temporarily created and annihilated during interactions. The propagator describes the "propagation" of these virtual particles, influencing the probabilities of particle interactions and scattering processes.
Field interactions: In QFT, fields are the fundamental entities, and particles arise as excitations of these fields. The propagator carries information about how these fields interact and exchange energy and momentum. It quantifies the probability amplitude for particles to interact and exchange virtual particles, leading to observable effects.
Feynman diagrams: Propagators play a central role in Feynman diagram calculations, which are graphical representations of particle interactions. In Feynman diagrams, propagators connect the vertices representing interactions and determine the probability amplitudes associated with specific processes. The mathematical expressions for propagators allow physicists to calculate the probabilities of various particle interactions and to make predictions for experimental outcomes.
Green's functions: In the context of QFT, propagators are also related to Green's functions, which describe the response of a field to an external source or disturbance. Green's functions encapsulate the relationship between the field operator and the source term in the field equations. The propagator can be seen as a specific type of Green's function, characterizing the propagation of particles or fields.
Overall, the propagator provides a mathematical framework to understand the behavior of particles and fields in quantum field theory. It enables physicists to calculate probabilities, predict particle interactions, and analyze the effects of quantum fluctuations and virtual particles on observable phenomena.