Prog. Theor. Phys. Vol. 9 No. 6 (1953) pp. 685-687
On the Families of Spinor Fields
Institute of Theoretical Physics, Kanazawa University
*Institute of Theoretical Physics, Nagoya University
(Received May 20, 1953)
DOI : 10.1143/PTP.9.685
- From only intuitive considerations, there seems to be no physical distinctions whether we regard two spinor fields as the different particles of Bose statistics or as the different states of particles obeying Fermi statistics. However, this intuitive picture is based on the existence of the assembly of free particles with canonical formalism. On the other hand, it is shown that the possibility of canonical formalism restricts the commutation relations between different spinor particles. For example, if spinor particles belonging to the same family correspond to the various isobar states of one particle, it is necessary to require Fermi statistics among them.
- From the integrability conditions of Tomonaga-Schwinger equations, Nishijima discussed on the possible restrictions upon the commutation relations between different spinor fields.
K. Nishijima, Prog. Theor. Phys. 5 (1950), 187[PTP].
His arguments, however, are based on the promise of the existence of interaction Hamiltonian and, as we shall show, further restriction involving requirement of the existence of interaction Hamiltonian.
- This corresponds to the demand that the description of the state of field as the assembly of free particles is possible.
- In this paper we call fields with “half-odd” integer spin as spinor particles. When ψα has spin 1/2. Rα(∂)Δ(x - x') = -S(x - x').
- The detailed explanations of Eq. (4) are given in
H. Umezawa and Y. Takahashi, Prog. Theor. Phys. 9 (1953), 501[PTP].
and Y. Takahashi and H. Umezawa, Prog. Theor. Phys. 9 (1953), 14[PTP].
Eq. (4) expresses the intimate relations between commutation relations and Green functions of the fields and is the complete condition that unitary transformation S(σ) connects the eq. of motion in the interaction representation with that in the Heisenberg representation.
- We assume that the processes (9) and (10) occur in the four fermion fields.
- S. Oneda, Prog. Theor. Phys. 9 (1953), 327[PTP].
- If the coplanarity is not certain in V0-decay, the possible decay schemes V0 → P + π- + ν will be proposed. In this case neutral boson field V0 must be complex field from the requirement of the of the conservation of heavy particles. See reference (7).
- Besides V0 → P + π-,
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