Project/Area Number  01540247 
Research Category 
GrantinAid for Scientific Research (C).

Research Field 
核・宇宙線・素粒子

Research Institution  Department of Physics Faculty of Science Osaka University 
Principal Investigator 
KIKKAWA Keiji Department of Physics Osaka University Professor, 理学部, 教授 (10011545)

CoInvestigator(Kenkyūbuntansha) 
KUBOTA Takahiro Department of Physics Osaka University Assistant, 理学部, 助手 (80161678)

Project Fiscal Year 
1989 – 1990

Project Status 
Completed(Fiscal Year 1990)

Budget Amount *help 
¥2,100,000 (Direct Cost : ¥2,100,000)
Fiscal Year 1990 : ¥900,000 (Direct Cost : ¥900,000)
Fiscal Year 1989 : ¥1,200,000 (Direct Cost : ¥1,200,000)

Keywords  Lorentz anomaly / BRST symmetry / PHI^3 model / Instanton / BornOppenheimer / Weyl invariance / Virasoro algebra / Lightcone gauge / ロレンツ異常項 / BRST対称性 / Φ^3模型 / インスタントン / ボルン・オッペンハイマ / ワイル不変性 / ヴィラソロ代数 / 光円錐ゲジ / 絃の場の理論 / ウヲド恒等式 / ボルソ・オッペンハイマ法 / ウイルソンの繰り込み群 / ヴィラソロ構造 / 絃理論 / モジュライ空間 / ポリヤコフの方法 / 絃理論の対称性 / 一般座標変換不変性 
Research Abstract 
We have started our research for constructing the unified theory of fundanmental interactions of elementary particles including gravity on the basis of string theories. Our aim is, in particular, to look for the string theory formulation in such a way that the theory does not depend on a particular background spacetime geometry. For this purpose we have set forth with concrete problems. Namely, we clarified mathematically complicated aspects of string theories left untouched so far, gained deep insights into the vacuum structures in the early universe, and tried to extend the stringy symmetries to the offmassshell. Let us survey what we have achieved. 1. We analyzed the mechanism of cancellation of the Lorentz anomaly known in the lightcone string field theory. By using the methods of Smatrix approach. And of path integral formalism. 2. we clarified mathematically complicated features of the PHI^3 theory, which has been put forward as a geometry independent formulation. In particula
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r, we proved the invariance under the general coordinate transformation by using the midpoint time prescription. 3. Going back to the original Einstein theory of gravity. We tackled the phase transition problem accompanied by topology change caused by gravitational instantons with no tunneling barrier. This study is expected to serve to scrutinize the vacuum structures in the early universe. We advocated the usefulness of the BornOppenheimer method which is supposed to replace the semiclassical approximation . 4. To grasp the connection between the two approaches based on the path integral method and the string field theory. We investigated the concept of "string emission vertex operator" . It has been proved that the requirement of the Weyl invariance the vertex in the first approach is equivalent to the classical equation of motion in the latter. The implications of the BRST symmetry in the field theory approach is investigated in terms of the actual offshell scattering amplitudes in the path integral approach. 5. A physical interpretation was given of the Virasoro algebra discovered in the twodimensional matrix models of gravity. Our interpretation is referred to the continuum noncritical string theory. 6. As a byproduct of our research. There is a paper on the algebraic extension of twodimensional quantum chromodynamics. There is also a comprehensive review article on the lightcone gauge string field theory. Less
