Prog. Theor. Phys. Vol. 6 No. 3 (1951) pp. 309-321
On the Positron Theory of Vacuum
Department of Physics, Kyoto University
(Received March 15, 1951)
In our previous consideration, the so-called ambiguities of quantum field theory can be removed by the certain general conditions of integrals. These procedures are equivalent with the subtraction theory which subtract the ambiguous terms from the matrix element in equation. In this paper, we again examine these subtractions from the slightly different view point and develop this consideration along the positron theoretical subtraction and indicate the gauge difficulties can be removed by some technical procedure treating with the density matrix of the vacuum. To clarify it, we utilize the solution of density matrix in the constant external electromagnetic field obtained by Fock's propse time method and separate the non gauge terms from it by this procedure and then arrive the throughout gauge invariant result. For the case of the density matrix in the arbitrary external field, we need the slight modifications, but there does not appear the essential changes of the subtraction terms.
DOI : 10.1143/PTP.6.309
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