Boson Wave Equations

Abstract

The dynamical quantum-mechanical wave equations of spin-0 pions, spin-1 vector particles, and massless spin-1 photons are formulated in a consistent one-particle fashion. For the spin-0 Klein—Gordon equation, the interpretation of negative-energy states as describing antiparticles is stressed. The relativistic bound-state Coulomb problem is then solved for π-mesic atoms. The parallel is made between the massive spin-1 and photon wave equations. The notion of currents, current conservation and gauge invariance for photon amplitudes is discussed in detail and linked to the principle of minimal replacement. Minimal coupling of photons to charged particles will be the basis of the general electromagnetic interaction to be considered in later chapters. Second-quantized field theories are briefly described, and an analogy is made between (relativistic) photons and nonrelativistic phonons.