In the context of quantum field theory, a theory is said to be "local" if it satisfies the principle of locality or local causality. The principle of locality is a fundamental concept that ensures the consistency and compatibility of a theory with our understanding of space and causality.
In a local quantum field theory, the interactions between particles are described by local interaction terms in the Lagrangian or Hamiltonian of the theory. This means that the interaction between particles at a given point in spacetime depends only on the values of the fields and their derivatives at that same point. In other words, the theory does not allow for instantaneous action-at-a-distance.
The principle of locality is closely related to the concept of relativistic causality, which states that no influence or information can propagate faster than the speed of light. By imposing locality, the theory respects the causal structure of spacetime, where cause and effect are connected through local interactions that propagate at or below the speed of light.
Local quantum field theories are consistent with special relativity and provide a framework for describing the interactions of particles in a manner that respects the limitations imposed by the speed of light and the structure of spacetime. They form the foundation of the Standard Model of particle physics, which describes the electromagnetic, weak, and strong nuclear interactions.
It's worth noting that the principle of locality is a foundational assumption of most quantum field theories, and it has been supported by a wealth of experimental observations. However, there are certain scenarios, such as quantum entanglement and non-local correlations in quantum mechanics, where the notion of locality may appear to be violated. These situations, however, are consistent with the principles of quantum mechanics and can be understood within the framework of quantum field theory as non-local correlations that do not allow for faster-than-light communication or violate causality.