Radiation and Quantum Electrodynamics

  • Hartmut M. Pilkuhn
Part of the Texts and Monographs in Physics book series (TMP)


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
$$ {A^\mu }(x) = A_{cl}^\mu (x) + A_{op}^\mu (x),A_{op}^0 = 0,div{A_{op}} = 0 $$


Matrix Element Pair Production Differential Cross Section Gauge Invariance Quantum Electrodynamic 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1979

Authors and Affiliations

  • Hartmut M. Pilkuhn
    • 1
  1. 1.Institut für KernphysikUniversität KarlsruheFederal Republic of Germany

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