By J. M. Jauch, F. Rohrlich (auth.)
Since the invention of the corpuscular nature of radiation via Planck greater than fifty years in the past the quantum thought of radiation has undergone many phases of improvement which looked as if it would trade among stunning good fortune and hopeless frustration. the latest section begun in 1947 with the invention of the electromagnetic point shifts and the conclusion that the exist ing thought, while appropriately interpreted, was once completely enough to give an explanation for those results to an it sounds as if limitless measure of accuracy. This part has now reached a undeniable end: for the 1st time within the checkered heritage of this box of analysis it has develop into attainable to offer a unified and constant presen tation of radiation concept in complete conformity with the rules of relativity and quantum mechanics. To this activity the current publication is dedicated. The plan for a booklet of this sort used to be conceived in the course of the 12 months 1951 whereas the first-named writer (J. M. J. ) held a Fulbright study scholarship at Cambridge college. in this yr of freedom from educating and different tasks he had the potential for conferring with physicists in lots of varied international locations at the fresh advancements in radiation thought. The reviews appeared to be virtually unanimous publication on quantum electrodynamics today will be of inestimable price to physicists in lots of elements of the realm. despite the fact that, it used to be now not till the spring of 1952 that paintings at the publication all started in earnest.
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Additional resources for The Theory of Photons and Electrons: The Relativistic Quantum Field Theory of Charged Particles with Spin One-half
The transformation (1-62) of the state vectors associated with such a commuting operator merely multiplies each state vector with a purely imaginary number which may be a function of t. Thus (1-62) for this case may be written (1-62a) with g(n a real-valued function of tion is then given by t. The finite form of this type of transforma(1-62b) and it is seen to be simply a transformation of the phases of the state vectors. Such phase transformations in the definition of the eigenvectors have no physical consequences and the ambiguity in the F which is associated with a given ~r may be ignored.
1-11 Conservation laws. The definitions of the momentum operators (1-82) and (1-83) seem to depend on the surface u over which the integrals are to be taken. These integrals are, in fact, independent of this surface and this is the content of the conservation laws. We prove these conservation laws by establishing first that the transformation matrix Cto'ir') is invariant under Lorentz transformations. Indeed, since the trans- 1-11) formed eigenvectors formation matrix 21 CONSERVATION LAWS n' are given by (1-33), we obtain for the new trans- (ro'lr')' == (Un(ro'),Un(r'» = (n(ro'),n(t')) = (ro'ln, (1-88) where we have made use of the fact that U is unitary.
T The quantum theory of the radiation field was developed by P. A. M. Dirac, Proc. Roy. Soc. 112, 661 (1926); 114, 243, 710 (1927). P. Jordan and W. Pauli, Z. Physik 47, 151 (1928). W. Heisenberg and W. Pauli, Z. Physik 56, 1 (1929); 59, 169 (1930). 2-4] QUAN'l'IZA'fION OF THE RADIATION FIELD 29 Hermitian operators which represent the localized observables of the system. It follows that the field variables must commute at two different points which are separated by a space-like interval. Consequently, the radiation field must be quantized according to Eq.