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| Material Type: | Internet resource |
|---|---|
| Document Type: | Book, Internet Resource |
| All Authors / Contributors: |
A P Balachandran; S Kürkçüoğlu; S Vaidya |
| ISBN: | 9812704663 9789812704665 |
| OCLC Number: | 137289528 |
| Description: | xiii, 181 pages ; 24 cm |
| Contents: | 2 Fuzzy Spaces 5 -- 2.1 Fuzzy C[superscript 2] 5 -- 2.2 Fuzzy S[superscript 3] and Fuzzy S[superscript 2] 5 -- 2.3 The Fuzzy Sphere S[Characters not reproducible] 5 -- 2.4 Observables of S[Characters not reproducible] 8 -- 2.5 Diagonalizing L[superscript 2] 9 -- 2.6 Scalar Fields on S[Characters not reproducible] 9 -- 2.7 The Holstein-Primakoff Construction 10 -- 2.8 CP[superscript N] and Fuzzy CP[superscript N] 11 -- 2.9 The CP[superscript N] Holstein-Primakoff Construction 14 -- 3 Star Products 17 -- 3.2 Properties of Coherent States 19 -- 3.3 The Coherent State or Voros *-Product on the Moyal Plane 20 -- 3.4 The Moyal *-Product on the Groenewold-Moyal Plane 23 -- 3.4.1 The Weyl Map and the Weyl Symbol 23 -- 3.5 Properties of *-Products 24 -- 3.5.1 Cyclic Invariance 24 -- 3.5.2 A Special Identity for the Weyl Star 25 -- 3.5.3 Equivalence of *c and *w 25 -- 3.5.4 Integration and Tracial States 26 -- 3.5.5 The [Theta]-Expansion 27 -- 3.6 The *-Products for the Fuzzy Sphere 28 -- 3.6.1 The Coherent State *-Product *c 28 -- 3.6.2 The Weyl *-Product *w 31 -- 4 Scalar Fields on the Fuzzy Sphere 35 -- 4.1 Loop Expansion 37 -- 4.2 The One-Loop Two-Point Function 39 -- 4.3 Numerical Simulations 43 -- 4.3.1 Scalar Field Theory on Fuzzy S[superscript 2] 45 -- 4.3.2 Gauge Theory on Fuzzy S[superscript 2] x S[superscript 2] 46 -- 5 Instantons, Monopoles and Projective Modules 47 -- 5.1 Free Modules, Projective Modules 47 -- 5.2 Projective Modules on A = C[Infinity] (S2) 49 -- 5.3 Equivalence of Projective Modules 51 -- 5.4 Projective Modules on the Fuzzy Sphere 54 -- 5.4.1 Fuzzy Monopoles and Projectors P[Characters not reproducible] 54 -- 5.4.2 The Fuzzy Module for the Tangent Bundle and the Fuzzy Complex Structure 56 -- 6 Fuzzy Nonlinear Sigma Models 59 -- 6.2 CP[superscript 1] Models and Projectors 60 -- 6.3 An Action 63 -- 6.4 CP[superscript 1]-Models and Partial Isometries 65 -- 6.4.1 Relation Between P([superscript [Kappa]]) and P[subscript [Kappa]] 68 -- 6.5 Fuzzy CP[superscript 1]-Models 69 -- 6.5.1 The Fuzzy Projectors for [Kappa]> 0 69 -- 6.5.2 The Fuzzy Projectors for [Kappa] <0 70 -- 6.5.3 The Fuzzy Winding Number 71 -- 6.5.4 The Generalized Fuzzy Projector: Duality or BPS States 71 -- 6.5.5 The Fuzzy Bound 71 -- 6.6 CP[superscript N]-Models 73 -- 7 Fuzzy Gauge Theories 77 -- 7.1 Limits on Gauge Groups 78 -- 7.2 Limits on Representations of Gauge Groups 79 -- 7.3 Connection and Curvature 80 -- 7.4 Instanton Sectors 81 -- 7.5 The Partition Function and the [Theta]-parameter 82 -- 8 The Dirac Operator and Axial Anomaly 85 -- 8.2 A Review of the Ginsparg-Wilson Algebra 85 -- 8.3 Fuzzy Models 88 -- 8.3.1 Review of the Basic Fuzzy Sphere Algebra 88 -- 8.3.2 The Fuzzy Dirac Operator (No Instantons or Gauge Fields) 89 -- 8.3.3 The Fuzzy Gauged Dirac Operator (No Instanton Fields) 91 -- 8.4 The Basic Instanton Coupling 93 -- 8.4.1 Mixing of Spin and Isospin 94 -- 8.4.2 The Spectrum of the Dirac operator 94 -- 8.5 Gauging the Dirac Operator in Instanton Sectors 95 -- 8.6 Further Remarks on the Axial Anomaly 96 -- 9 Fuzzy Supersymmetry 99 -- 9.1 osp(2, 1) and osp(2, 2) Superalgebras and their Representations 100 -- 9.2 Passage to Supergroups 106 -- 9.3 On the Superspaces 107 -- 9.3.1 The Superspace C[superscript 2, 1] and the Noncommutative C[Characters not reproducible] 107 -- 9.3.2 The Supersphere S[superscript (3, 2)] and the Noncommutative S[superscript (3, 2)] 108 -- 9.3.3 The Commutative Supersphere S[superscript (2, 2)] 108 -- 9.3.4 The Fuzzy Supersphere S[Characters not reproducible] 112 -- 9.4 More on Coherent States 114 -- 9.5 The Action on the Supersphere S[superscript (2, 2)] 116 -- 9.6 The Action on the Fuzzy Supersphere S[Characters not reproducible] 119 -- 9.6.1 The Integral and Supertrace 119 -- 9.6.2 OSp(2, 1) IRR's with Cut-Off N 121 -- 9.6.3 The Highest Weight States and the osp(2, 2)-Invariant Action 121 -- 9.6.4 The Spectrum of V 122 -- 9.6.5 The Fuzzy SUSY Action 124 -- 9.7 The *-Products 125 -- 9.7.1 The *-Product on S[Characters not reproducible] 125 -- 9.7.2 The *-Product on Fuzzy "Sections of Bundles" 127 -- 9.8 More on the Properties of K[subscript ab] 129 -- 9.9 The O(3) Nonlinear Sigma Model on S[superscript (2, 2)] 131 -- 9.9.1 The Model on S[superscript (2, 2)] 131 -- 9.9.2 The Model on S[Characters not reproducible] 132 -- 9.9.3 Supersymmetric Extensions of Bott Projectors 133 -- 9.9.4 The SUSY Action Revisited 134 -- 9.9.5 Fuzzy Projectors and Sigma Models 135 -- 10 SUSY Anomalies on the Fuzzy Supersphere 137 -- 10.1.1 The Fuzzy Sphere 137 -- 10.1.2 SUSY 138 -- 10.1.3 Irreducible Representations 139 -- 10.1.4 Casimir Operators 140 -- 10.1.5 Tensor Products 141 -- 10.1.6 The Supertrace and the Grade Adjoint 141 -- 10.1.7 The Free Action 141 -- 10.2 SUSY Chirality 143 -- 10.3 Eigenvalues of V[subscript 0] 144 -- 10.4 Fuzzy SUSY Instantons 145 -- 10.5 Fuzzy SUSY Zero Modes and their Index Theory 146 -- 10.5.1 Spectrum of K[subscript 2] 147 -- 10.5.2 Index Theory and Zero Modes 149 -- 11 Fuzzy Spaces as Hopf Algebras 151 -- 11.3 The Group and the Convolution Algebras 154 -- 11.4 A Prelude to Hopf Algebras 155 -- 11.5 The *-Homomorphism G* [right arrow] S[Characters not reproducible] 159 -- 11.6 Hopf Algebra for the Fuzzy Spaces 161 -- 11.7 Interpretation 165 -- 11.8 The Presnajder Map 166. |
| Responsibility: | A.P. Balachandran, S. Kürkçüoğlu, S. Vaidya. |
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