Prog. Theor. Phys. Vol. 41 No. 5 (1969) pp. 1289-1308
A Diagonalization Method of a Hamiltonian in Second-Quantization. II
— Application: Examples of Compatible Second-Degree Programs. Equivalence of Fermi and Yukawa Theories
Centre de Physique Théorique, Laboratoires du C.N.R.S. 31, Chemin Joseph Aiguier, 13-Marseille (9e), France
(Received June 24, 1968)
The method given in paper I is applied and the problem of the equivalence of the Fermi and Yukawa theories is considered under the point of view of physical operators.
Examples of compatible second degree programs are given and explicitely computed. The different behaviour of three models is studied and pointed out. The equivalence of the Yukawa and Fermi theories is investigated by means of the physical operators. The requirement that a first degree program in the Yukawa theory becomes a second degree program in the Fermi theory leads to the well-known result: the renormalization constant Z3 of the composite boson vanishes. Though the formulation is based on the hamiltonian consideration and thus, the relativistic covariance may be destroyed, it is shown that this difficulty may be removed by the covariant variable of Umezawa and Kawabe. The physical meaning of the structure functions will be given in a forthcoming paper.
DOI : 10.1143/PTP.41.1289
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