17 The Goldstone Theorem for Relativistic Local Fields

Abstract

Relativistic systems, like elementary particles, are described by an algebra of observables $\mathcal{A}_{obs}$ which satisfies the causality condition, (4.2), and is stable under the automorphisms α(a, Λ) which describe space time translations and Lorentz transformations (with parameters a, Λ respectively). The physically relevant representations of $\mathcal{A}_{obs}$ have to satisfy the relativistic version of conditions I-III (Chap. 5).