Introduction

The concept of associating particles with fields originated during the studyof various physical phenomena involving electromagnetic radiation. Forexample, the observations and theoretical explanations of the black bodyradiation by Planck, the photoelectric effect by Einstein, and thescattering of a photon off an electron by Compton established thatelectromagnetic radiation can be described in terms of “discretequanta of energy” called photon, identified as a massless particle ofspin 1. Consequently, Maxwell's equations of classicalelectrodynamics, describing the time evolution of the electric and magneticfields are interpreted to be the equations of motion of the photon, writtenin terms of the massless spin 1 electromagnetic field. Later, thequantization of the electromagnetic field was formulated to explain theemission and absorption of radiation in terms of the creation andannihilation of photons during the interaction of the electromagnetic fieldwith the physical systems. The concept of treating photons as quanta of theelectromagnetic fields was successful in explaining the physical phenomenainduced by the electromagnetic interactions; methods of field quantizationwere used leading to quantum electrodynamics (QED), the quantum field theoryof electromagnetic interactions. The concept was later generalized by Fermi[23, 207] and Yukawa [208, 209] to formulate, respectively, the theory ofweak and strong interactions in analogy with the theory of QED.

In order to describe QED, the quantum field theory of electromagnetic fieldsand their interaction with matter, in terms of the massless spin 1 fieldscorresponding to photons, the equations of motion of should be fullyrelativistic. This requires the reformulation of classical equations ofmotion for the fields to obtain the quantum equations of motion for thefields and find their solutions, in case of free fields as well as fieldsinteracting with matter. This is generally done using perturbation theoryfor which a relativistically covariant perturbation theory is required.

The path of transition from a classical description of fields to a quantumdescription of fields, requiring the quantization of fields, their equationsof motion, propagation, and interaction with matter involves understandingmany new concepts and mathematical methods. For this purpose, the Lagrangianformulation for describing the dynamics of particles and their interactionwith the fields is found to be suitable.