Classical fields in curved spacetime

Abstract

This chapter discusses classical fields in an arbitrary Riemann spacetime. General considerations are followed by the formulation of scalar fields with non-minimal coupling. Spontaneous symmetry breaking in curved space is shown to provide the induced gravity action with a cosmological constant. The construction of spinor fields in curved spacetime is based on the notions of group theory from Part I and on the local Lorentz invariance. Massless vector fields (massless vector gauge fields) are described and the interactions between scalar, fermion and gauge fields formulated. A detailed discussion of classical conformal transformations and conformal symmetry for both matter fields and vacuum action is also provided.