In physics, a local quantum field theory (QFT) is a theoretical framework that combines quantum mechanics and special relativity to describe the behavior of elementary particles. It is a mathematical formalism used to study the interactions and dynamics of fields, which are physical quantities defined at every point in space and time.
In a local QFT, each elementary particle is associated with a field, such as the electromagnetic field or the electron field. These fields are quantized, meaning that they are described in terms of discrete units of energy and momentum called quanta or particles.
The term "local" in local quantum field theory refers to the fact that the interactions between particles are described by local interactions at each point in space and time. This means that the equations of the theory involve the values of the fields and their derivatives at each point, allowing for the exchange of energy and momentum between neighboring points.
The dynamics of the fields in a local QFT are governed by a set of equations called the quantum field equations, which are usually derived from a Lagrangian or Hamiltonian formalism. These equations specify how the fields evolve in time and interact with each other.
Local quantum field theories provide a powerful framework for describing the fundamental forces and particles of nature. The standard model of particle physics, for example, is a local quantum field theory that describes the electromagnetic, weak, and strong interactions between elementary particles.
It is worth noting that local quantum field theories are subject to the limitations of our current understanding and may not be complete descriptions of nature at all energy scales. The search for a more fundamental theory that unifies quantum mechanics and general relativity, such as a theory of quantum gravity, is an active area of research in theoretical physics.