July 4, 1984
Utrecht University
Thesis advisor: Gerard 't Hooft




CONTENTS Parts not published elsewhere in italics;
available as scanned GIF files

• Chapter I: General Introduction ... 1
• Chapter II: Some results for SU(N) gauge fields on the hypertorus ... 17
  Published as: Comm. Math. Phys. 85 (1982) 529-548
  • 1. Introduction ... 17
  • 2. The structure of the gauge fields on the hypertorus ... 18
  • 3. The Pontryagin number on T⁴ ... 21
  • 4. Orthogonal twist, zero action configurations ... 27
  • 5. Conclusions ... 30
  • Appendix ... 31
  • References ... 35
• Chapter III: The Hamiltonian formalism for gauge fields on the hypertorus ... 36
  • 1. Introduction ... 37
  • 2. The Hamiltonian and the Hilbert space ... 38
  • 3. The Wilson loop ... 44
  • 4. The identification of e and m ... 47
  • 5. Translational invariance ... 55
  • 6. Finite temperature on the torus ... 58
  • Appendix ... 61
  • References ... 71
• Chapter IV: SU(N) Yang-Mills solutions with constant field strength on T⁴ ... 72
  Published as: Comm. Math. Phys. 94 (1984) 397-419
  • 1. Introduction ... 73
  • 2. The solutions and their fluctuations ... 76
  • 3. The fluctuation spectrum ... 83
  • 4. Stability and selfduality ... 89
  • 5. Discussion ... 97
  • Appendix A ... 99
  • Appendix B ... 105
  • References ... 109
• Chapter V: Surviving extrema for the action on the twisted SU(infinity) one point lattice ... 110
  Published as: Comm. Math. Phys. 92 (1983) 1-18
  • 1. Introduction ... 110
  • 2. Construction of twist eating configurations ... 111
  • 3. Examples ... 113
  • 4. Extrema for the TEK-action ... 114
  • 5. Applications ... 117
  • 6. Discussion ... 120
  • Appendix ... 121
  • References ... 126
• Chapter VI: Instantons versus factorization in large-N field theories ... 128
  Published as: Phys. Lett. 140B (1984) 375-378
  • Appendix ... 136
  • References ... 145
• Chapter VII: Hot twists for the single-point model of large-N QCD ... 146
  Published as: Nucl. Phys. B237 (1984) 274-284, co-author F.R. Klinkhamer
  • 1. Introduction ... 146
  • 2. Reduction ... 147
  • 3. Loop equations ... 149
  • 4. Construction of hot twists ... 151
  • 5. Planar graphs ... 154
  • 6. Discussion ... 155
  • References ... 156

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