Evaluation of the Collision Matrix for Dirac Particles in an External Potential
- 1 October 1954
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review B
- Vol. 96 (1) , 202-207
- https://doi.org/10.1103/physrev.96.202
Abstract
The 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.Keywords
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