Relativistic Particle Physics pp 78-135 | Cite as

# Radiation and Quantum Electrodynamics

Chapter

## Abstract

So far in this book the 4-potential .

*A*^{ μ }(*t*, x) was either classical or due to a nucleus. An essential extension of the formalism is necessary for processes in which photons are emitted or absorbed. For example, if an excited atom |*e*_{ i }> has been formed by a rapid collision at a certain time, the probability amplitude of finding the atom in the state |*e*_{ i }> decreases afterwards, and new states |*e*_{ f }> |*γ*_{λ}**(k)**> appear, in which the atom is in states of lower energy, the missing energy being carried away by a photon |*γ*_{ λ }of momentum*ħ***k**. The Hamilton operator (1–4.2) is capable of inducing such transitions, but only if*A*^{ μ }is interpreted as an operator which can create and annihilate photons. As explained in section 2–8, gauge invariance permits us to impose the condition div**A**= 0 on this operator. Since we wish to keep classical electric and magnetic fields as well, we put$$ {A^\mu }(x) = A_{cl}^\mu (x) + A_{op}^\mu (x),A_{op}^0 = 0,div{A_{op}} = 0 $$

### Keywords

Covariance Pepe Helici## Preview

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## Copyright information

© Springer-Verlag Berlin Heidelberg 1979