著者

Takabayasi Takehiko

出版者

一般社団法人日本物理学会

雑誌

理論物理学の進歩 (ISSN:0033068X)

巻号頁・発行日

vol.49, no.5, pp.1724-1745, 1973-05-25

被引用文献数

1

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Classical theory of a relativistic string is formulated based on the parameter representation x_μ=x_μ(σ,τ) for the world strip swept by its motion. The necessity of the physically unam-biguous interpretation of this many-time formalism requires certain conditions. Invariance under the scale transformation of parameters is stressed. The physical meaning of τ is clarified. Besides the equation of motion and boundary condition which follow from the variational principle additional constrain t equations are needed to ensure a well-defined model without tachyonic solutions. The quantization of this classical theory is made in the usual way in the Heisenberg picture with respect to τ. Then by going over to the Schrodinger picture the parameter τ is automatically eliminated and we are left with a wave equation alone. Moreover this equation and the constraint equation are incorporated into a single "detailed wave equation", which was given previously as the fundamental equation of the quantum mechanics of a relativistic string. Case of external interaction is briefly treated.

著者

Takabayasi Takehiko

出版者

一般社団法人日本物理学会

雑誌

理論物理学の進歩 (ISSN:0033068X)

巻号頁・発行日

vol.47, no.3, pp.1026-1046, 1972-03-25

被引用文献数

2

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The theory of detailed wave equation (DWE), which represents relativistic quantum dynamics of an extended system with external interaction for a specific value of Regge intercept, avoiding ghost states and leading to dual amplitude, is further developed in several respects. The original formulation (the σ-formalism) for the string model is transcribed into a few equivalent formalisms. In the λ-formalism the invariance of DWE against the "Hilbert transform" becomes manifest. Finite "gauge transformations", under which the theory is invariant, are explicitly obtained for the consideration of their structural meaning. The original string model is generalized to the hybrid model, where each element constituting the string is endowed with internal "Fermi oscillator variables", in the framework of DWE, which now fixes the Regge intercept at the value lower than the original one by 1/2 unit or its multiples. In particular the hybrid model with vector Fermi variables, which implies "double-string" consisting of Dirac-like elements, is treated, where our vector Fermi variables differ from those in similar models by other authors with respect to their reality and Lorentz properties and are free from the introduction of additional indefinite metric. Moreover our theory is invariant under space reflection.

著者

Takabayasi Takehiko

出版者

一般社団法人日本物理学会

雑誌

Progress of theoretical physics (ISSN:0033068X)

巻号頁・発行日

vol.52, no.6, pp.1910-1928, 1974-12-25

被引用文献数

9

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Theory of "geometric" string, recently employed as a model of hadrons, is represented in a form covariant under general transformation of parameters ("coordinates") by the aid of tensor analysis. It is shown that this approach is essentially simple and transparent and works to clarify subtle points in the relativistic kinematics and mechanics of the geometric string. The method is applied to the treatment of conformal invariance, "static solutions" and single-time formalism. Relativistic string with intrinsic rotational degrees is presented, also on the basis of the general-covariant approach. This new model allows a charge distribution along the string. Analogy of the "general-covariant" string theory to general relativity as well as its distinction therefrom is explained.