Evaluation of the Collision Matrix for Dirac Particles in an External Potential
1954; American Institute of Physics; Volume: 96; Issue: 1 Linguagem: Inglês
10.1103/physrev.96.202
ISSN1536-6065
Autores Tópico(s)Quantum Electrodynamics and Casimir Effect
ResumoThe collision matrix for a quantized Dirac field in an external electromagnetic potential is evaluated by a method which utilizes the close relation between the theory of positrons and the formal one-particle Dirac theory. The main mathematical tool employed is a theorem by Baker and Hausdorff on exponentials of noncommuting quantities. One obtains the collision matrix expressed as a product of exponentials, involving creation and destruction operators in a way suitable for the calculation of matrix elements in the occupation number representation. In the Appendix the evaluation of the collision matrix for a real scalar field in interaction with a given source distribution is carried out by means of a similar technique.
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