2004 Fiscal Year Final Research Report Summary
Towards A New Formulation of Unified Model with Gravity on a Lattice
| Project/Area Number |
13640250
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
素粒子・核・宇宙線
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| Research Institution | HOKKAIDO UNIVERSITY |
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Principal Investigator |
KAWAMOTO Noboru Hokkaido University, Graduate School of Sci., Professor, 大学院・理学研究科, 教授 (50169778)
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| Project Period (FY) |
2001 – 2004
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| Keywords | Quantum Gravity / Lattice Gravity / Supersymmetry on the Lattice / Twisted Supersymmetry / Topological Field Theory / Dirac-kahler Fermion |
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| Research Abstract |
My research thema in this period can be classified into the following 4 categories :
1)Continuation from the previous investigations.
2)Fermion Formulation with Non-commutativity on a Lattice.
3)A Proposal of New Superspace Formulation.
4)Supersymmetry on a Lattice.
1)Based on the generalized gauge theory formulation which we discovered, we applied a truncated version of generalized Yang-Mills theory with SU(2|1) gauge group and derived Weinberg-Salam model. Numerical evaluation of the c-dependence of the fractal dimension of two-dimensional quantum surface was investigated and the result is perfect agreement with the analytic result which we obtained previously.
2)We may introduce mild non-commutativity for the lattice difference operator tosatisfy the Leibniz rule. We can then define differential form on a lattice and introduce associative Clifford product. We have clarified the Dirac-Kahler fermion formulation with non-commutativity on a lattice.
3)It was already recognized that the twisting appeared in the quantization of topological field theory can be identified as a Dirac-Kahler fermion formulation. We found that this twisting mechanism is a universal characteristic which appears in the quantization of topological field theory and a twisted superspace formulation is hidden behind the formulation. N=2 twisted superspace formulation was formulated in two dimensions. Then this formulation is extended into N=4 in four dimensions.
4)Twisted superspace formulation is successfully formulated on a lattice with the introduction of the mild non-commutatibity for N=2 twisted superspace in two dimensions. It is now possible to apply this formulation to N=2 super Yang-Mills action on a lattice.
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