Progress of Theoretical Physics
Vol. 35 No. 5 (1966) pp. 934-959
URL : http://ptp.ipap.jp/link?PTP/35/934/
DOI : 10.1143/PTP.35.934

A Non-Trivial Example of a Relativistic Quantum Theory of Particles without Divergence Difficulties

Hideji Kita

(Received December 20, 1965)

A simple but non-trivial set of generators P_µ and M_µν of the Poincaré group is obtained in terms of creation- and annihilation operators of particles. P₄ contains a cutoff from factor, which is function of the square of the invariant momentum transfer at interaction vertex. The relativistic quantum theory of particles thus obtained has no divergence difficulties. It is shown that the theory differs from the ordinary quantized field theory in the point that the former is not “manifestly” invariant although it still satisfies the symmetry requirements of special relativity. The method used is of rather general character, and the essential points, which have to be taken into consideration for the application to more realistic systems of particles, are discussed.

References:

1. See, for example, P. A. M. Dirac, Rev. Mod. Phys. 21 (1949), 392[APS].
2. C. Hayashi, Prog. Theor. Phys. 10 (1953), 533, [IPAP]where several attempts at constructing non-local interaction theory in those days are cited.
3. D. G. Currie, T. F. Jordan and E. C. G. Sudarshan, Rev. Mod. Phys. 35 (1963), 350, [APS]where further references on related problems can be seen.

Citing Article(s) :

1. Progress of Theoretical Physics Vol. 39 No. 5 (1968) pp. 1333-1360 :

   Another Convergent, Relativistic Model Theory of Interacting Particles

   Hideji Kita

2. Progress of Theoretical Physics Vol. 43 No. 5 (1970) pp. 1364-1385 :

   Structure of the State Space in a Convergent Relativistic Model Theory of Interacting Particles

   Hideji Kita

3. Progress of Theoretical Physics Vol. 47 No. 6 (1972) pp. 2140-2141 :

   Vertex Functions in Convergent Relativistic Model Theories

   Hideji Kita

4. Progress of Theoretical Physics Vol. 48 No. 6 (1972) pp. 2422-2444 :

   A Model of Relativistic Quantum Mechanics of Interacting Particles

   Hideji Kita

5. Progress of Theoretical Physics Vol. 49 No. 5 (1973) pp. 1704-1723 :

   A Realistic Model of Convergent Relativistic Quantum Mechanics of Interacting Particles

   Hideji Kita

6. Progress of Theoretical Physics Supplement No.51 (1972) pp. 1-95 :

   Indefinite-Metric Quantum Field Theory

   Noboru Nakanishi

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