An Indefinite-Metric Formulation of a Free Massless Scalar Theory in Two Dimensions
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概要
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A free massless scalar field in two dimensions is studied in the framework of the indefinite-metric quantum field theory. Zero-frequency modes are analysed first in a finite-volume. It is inevitable to introduce extra unphysical operators. The infinite-volume limit is proved to exist. No infrared divergences appear in commutation relations and the Wightman function in the infinite-volume limit. Subsidiary conditions make it possible to define the positive semi-definite Hilbert space V_<phys> which contains the sero-norm subspace V_0. The positivity is recovered in the quotient physical space H_<phys>=V_<phys>/V_0 where the scalar field and its dual field are not independent. A kind of ambiguity with respect to the surface term appears in the definition of the Lorentz generator. However both the scalar and its dual fields cannot be a Lorentz scalar. Now that a free massless scalar theory is constructed successfully, spontaneous breaking of a continuous symmetry is possible in two dimensions in the idenfinite-metric field theory.
- 理論物理学刊行会の論文
- 1982-03-25
著者
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TAMEIKE Seiichi
Department of Physics, Kanazawa University
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Suzuki Tsuneo
Department Of Forensic Medicine Yamagata University School Of Medicine
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Tameike Seiichi
Department Of Physics Kanazawa University
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TAMEIKE Seiichi
Department of Physics, Kanazawa University:On leave from Department of Physics, Kyushu University
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