Internal Degrees of Freedom and Elementary Particles. I

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概要

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• 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 x_μ(τ) with substantial internal degrees of freedom concentrated upon x_μ, 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, m^2=-p_<μ^2> (with p_μ as momentum-energy vector) 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 S_<μν> is another basic dynamical quantity of the system and is responsible for spin and Zitterbewegung. Also defined is the instantaneous velocity operator υ_μ, which is not generally colinear with p_μ and must be restricted by certain kinematical conditions. Three different criteria about these conditions on ν_μ make point-like systems classified into various types. For "normal class" of systems, p≡-υ_<μ^2> 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 υ_μ commute with the position x_μ and thus mean internal variables. Such a system generally has, besides rest mass, spin and ρ, three self-adjoint commuting invariant quantities formed out of p_μ, υ_μ and S_<μν> 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 ([υ_μ,υ_ν]≠0), to derive general characteristics for each of them. Dirac and Kemmer particles are special simple examples of the latter,where systems has no substantial internal degrees of freedom apart from υ_μ.

• 理論物理学刊行会の論文
• 1961-06-25

著者

• Takabayasi Takehiko

  Physical Institute Nagoya University

• Takabayasi Takehiko

  Physical Institute University Of Nagoya

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