It's the objective of this booklet to debate an easy approach through Feynman direction indispensable formulation within which the transformation to collective fields quantities to merechanges of integration variables in practical integrals. After the transformation, the trail formula will back be discarded. The ensuing box thought is quantizedin the traditional style and the basic quanta without delay describe the collective excitations
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103) ψ¯ ≡ ψ † γ 0 . 104) and ¯ The symbol ψ(x) is short for As a historical note we mention that Dirac found his by considering the naive relativistic time independent Schr¨odinger equation of an electron ˆ Hψ(x) = ˆ 2 + M 2 ψ(x) = Eψ(x). 105) He asked the question whether the square root could be found explicitly if the equation were considered as a matrix equation acting on several components of ψ(x, t) to represent the spin degrees of freedom of the electron. 106) ˆ D twice with αi , β being unknown matrices.
R. Fredkin, S. K. Ma, Phys. Rev. 174, 227 (1968); Y. Kuroda, A. D. S. Nagi, J. Low. Temp. 23, 751 (1976).  D. Rainer, J. W. Serene, Phys. Rev. B13, 4745 (1976); Y. Kuroda, A. D. S. Nagi, J. Low Temp. Phys. 25, 569 (1976). 38 2 Relativistic Fields  For a review see: D. R. Bes, R. A. Broglia, Lectures delivered at “E. Fermi” Varenna Summer School, Varenna, Como. Italy, 1976. For recent studies: D. R. Bes, R. A. Broglia, R. Liotta, B. R. Mottelson, Phys. Letters 52B, 253 (1974); 56B, 109 (1975), Nuclear Phys.
The fact that ηC = −1 means that the electromagnetic field is odd under charge conjugation. H. 4 Relativistic Free Fermi Fields For Fermi fields, the situation is technically more involved. Experimentally, fermions always have an even number of spin degrees of freedom. In order to describe these we give the field ψ a spin index α running through (2s+1) components. Under rotations, these spin components are mixed with each other as observed experimentally in the Stern-Gerlach experiment. Lorentz transformations lead to certain well defined mixtures of different spin components.
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