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Prog. Theor. Phys. Vol. 25 No. 6 (1961) pp. 901-938

[ Full Text PDF : FREE ACCESS (1996K) ]

Internal Degrees of Freedom and Elementary Particles. I

Takehiko Takabayasi

Physical Institute, University of Nagoya, Nagoya

(Received December 12, 1960)

Abstract:

Quantum theory of point-like systems is established by extending the concept of relativistic particle in some respects: A point-like system means a one-parameter series of events xµ(τ) with substantial internal degrees of freedom concentrated upon xµ, and indefinite metric in Hilbert space is generally taken as to the internal degrees. The theory corresponds to an extention of the usual local field equations, suitable to obtaining a unified theory of elementary particles. The rest-mass, m2=-pµ2 (with pµ as momentum-energy vecor) becomes a dynamical quantity of the system with its possible eigenspectrum, leading to uncertainty relations between rest mass value and space-time localization. The internal angular momentum tensor Sµν is another basic dynamical quantity of the system and is responsible for spin and Zitterbewegung. Also defined is the instantaneous velocity operator vµ, which is not generally colinear with pµ and must be restricted by certain kinematical conditions. Three different criteria about these conditions on vµ make point-like systems classified into various types. For “normal class” of systems, ρ≡-vµ2 is an absolute invariant with eigenvalue 1 or 0 and is regarded to represent baryon number. Especially important are point-like systems of the first kind. i.e. the ones in which vµ commute with the position xµ and thus mean internal variables. Such a system generally has, besides rest mass, spin and ρ, three self-adjoint commuting invariant quantities formed our of pµ, vµ and Sµν only, which are to be identified eventually with the intrinsic properties of elementary particles (isospin, hypercharge, etc.). Systems are further divided into “classical models”, where velocity components are commutable (an example being relativistic rotator), and “non-classical models” where they are not ([vµ, vν]≠0), to derive general characteristics for each of them. Dirac and Kemmer particles are special simple examples of the latter, where system has no substantial internal degrees of freedom apart from vµ.


URL : http://ptp.ipap.jp/link?PTP/25/901/
DOI : 10.1143/PTP.25.901

[ Full Text PDF : FREE ACCESS (1996K) ] Citation:

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Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 33 No. 5 (1965) pp. 889-906 :
    On a Classical Spinning Particle Model of Dirac Particle
    Tetsuo Gotō
  2. Progress of Theoretical Physics Vol. 33 No. 5 (1965) pp. 907-931 :
    Rigid Sphere Model of Elementary Particles and the Electromagnetic Field
    Osamu Hara and Tetsuo Goto
  3. Progress of Theoretical Physics Vol. 34 No. 1 (1965) pp. 124-154 :
    Space-Time Model of Elementary Particles and Unitary Symmetry. I
    Takehiko Takabayasi
  4. Progress of Theoretical Physics Vol. 34 No. 6 (1965) pp. 1007-1022 :
    Elastic Sphere Model of Elementary Particles and Its Relation to the Quadri-Local Field Model
    Tetsuo Gotō
  5. Progress of Theoretical Physics Vol. 36 No. 5 (1966) pp. 1074-1076 :
    De Sitter Algebra Associated with the Poincaré Group and Center-of-Inertia
    Takehiko Takabayasi
  6. Progress of Theoretical Physics Vol. 37 No. 4 (1967) pp. 765-766 :
    Internal Movement of Hadrons as Infinite-Dimensional Representation of Inner Lorentz Group
    Takehiko Takabayasi
  7. Progress of Theoretical Physics Vol. 38 No. 3 (1967) pp. 715-732 :
    The Regge Pole Hypothesis and an Extended Particle Model
    Masako Bando, Takeshi Inoue, Yoshio Takada and Sho Tanaka
  8. Progress of Theoretical Physics Vol. 39 No. 3 (1968) pp. 830-846 :
    Limiting Process of Cutoff and Auxiliary Fields in Quantum Field Theory. I
    Kan-ichi Yokoyama
  9. Progress of Theoretical Physics Vol. 59 No. 2 (1978) pp. 633-645 :
    The Interaction of the Bi-Local Field with the External Field
    Tetsuo Gotō and Kiyoshi Kamimura
  10. Progress of Theoretical Physics Vol. 59 No. 6 (1978) pp. 2133-2148 :
    Constraints, Center-of-Masses and Quantization for Relativistically Structured Systems
    Takehiko Takabayasi and Kenji Takeuchi

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