What Is a Local Physical Theory?

Abstract

In this Chapter we introduce the mathematical formalism of a local physical theory (LPT). Briefly, a LPT is an association of local operator algebras to spacetime regions subjected to the requirements of isotony, microcausality and covariance, all borrowed from algebraic quantum field theory. Depending on whether the local algebras are commutative or noncommutative, we call a LPT a local classical theory (LCT) or a local quantum theory (LQT). At the end of the chapter we motivate the application of von Neumann algebras in the LPT framework.