| Observable Algebra in Field Algebra of G-spin Models |
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| 作者姓名： | 蒋立宁 |
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| 作者单位： | DepartmentofMathematics,BeijingInstituteofTechnology,Beijing100081,China |
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| 基金项目： | Supported by the National Natural Science Foundationof China (No.10 0 0 10 2 0 ) |
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| 摘 要： | Field algebra of G-spin models can provide the simplest examples of lattice field theory exhibiting quantum symmetry. Let D(G) be the double algebra of a finite group G and D(H), a sub-algebra of D(G) determined by subgroup H of G. This paper gives concrete generators and the structure of the observabl ealgebra AH, which is a D(H)-invariant sub-algebra in the field algebra of G-spin models F, and shows that AH is a C^*-algebra. The correspondence between H and AH is strictly monotonic. Finally, a duality between D(H) and A. is given via an irreducible vacuum C^* -representation of F.
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| 关 键 词： | G-螺旋模型 场代数 可观测代数 格论 有限群 |
Observable Algebra in Field Algebra of G-spin Models |
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| JIANG Lining.Observable Algebra in Field Algebra of G-spin Models[J].Tsinghua Science and Technology,2003,8(5):573-576. |
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| Authors: | JIANG Lining |
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| Institution: | JIANG LiningDepartment of Mathematics,Beijing Institute of Technology,Beijing 100081,China |
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| Abstract: | Field algebra of G-spin models can provide the simplest examples of lattice field theory exhibiting quantum symmetry. Let D(G) be the double algebra of a finite group G and D(H), a sub-algebra of D(G) determined by subgroup H of G. This paper gives concrete generators and the structure of the observable algebra A H, which is a D(H)-invariant sub-algebra in the field algebra of G-spin models F, and shows that A H is a C *-algebra. The correspondence between H and A H is strictly monotonic. Finally, a duality between D(H) and A H is given via an irreducible vacuum C *-representation of F. |
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| Keywords: | G-spin models field algebra observable algebra duality |
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