In this chapter we introduce an external potential as an operator V of multiplication with a Hermitian 4 × 4 matrix-valued function of the space-time variable x. According to their behavior under Poincaré transformations the fields can be classified as scalar or pseudoscalar, vector potentials or pseudovector potentials, tensor or pseudotensor forces (Sects. 4.1 and 4.2). Vector potentials describe electromagnetic forces, scalar potentials can be used as a model for quark confinement, and tensor forces are needed to describe the behavior of particles with anomalous electric and magnetic moments.
KeywordsExternal Field Dirac Equation Dirac Operator Essential Spectrum Anomalous Magnetic Moment
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