Spis treści: Methods of Bosonic and Fermionic Path Integrals Representations


About This Monograph, s. xi

1 Loop Space Path Integrals Representations for Euclidean Quantum Fields Path Integrals and the Covariant Path Integral, s. 1

  • 1.1. Introduction, s. 1
  • 1.2. The Bosonic Loop Space Formulation of the O(N)-Scalar Field Theory, s. 1
  • 1.3. A Fermionic Loop Space for QCD, s. 4
  • 1.4. Invariant Path Integration and the Covariant Functional Measure for Einstein Gravitation Theory, s. 6
  • 1.4.1. Introduction, s. 6
  • 1.4.2. Invariant Integration, s. 7
  • 1.4.3. A Quantum Path Measure for Einstein Theory, s. 8

2 Path Integrals Evaluations in Bosonic Random Loop Geometry - Abelian Wilson Loops, s. 35

  • 2.1. Introduction, s. 35
  • 2.2. Abelian Wilson Loop Interaction at Finite Temperature, s. 35
  • 2.3. The Static Confining Potential for Q.C.DS. in the Mandelstam Model through Path Integrals, s. 41

3 The Triviality - Quantum Decoherence of Quantum Chromodynamics SU (∞) in the Presence of an External Strong White-Noise Eletromagnetic Field, s. 59

  • 3.1. Introduction, s. 59
  • 3.2. The Triviality - Quantum Decoherence Analysis, s. 60
  • 3.3. Random Surface Dynamical Factor in the Analytical Regularization Scheme, s. 64
  • 3.4. The Non-relativistic Case, s. 67
  • 3.5. The Static Confining Potential in a Tensor Axion Model, s. 69
  • 3.6. The Confining Potential on the Axion-String Model in the Axion Higher-Energy Region, s. 70
  • 3.7. A λφ4 String Field Theory as a Dynamics of Self Avoiding Random Surfaces, s. 75

4 The Confining Behaviour and Asymptotic Freedom for QCD(SU(°°)) - A Constant Gauge Field Path Integral Analysis, s. 87

  • 4.1. Introduction, s. 87
  • 4.2. The Model and Its Confining Behavior, s. 88
  • 4.3. The Path-Integral Triviality Argument for the Thirring Model at SU(°°), s. 94
  • 4.4. The Loop Space Argument for the Thirring Model Triviality, s. 100

5 Triviality - Quantum Decoherence of Fermionic Quantum Chromodynamics SU (Nc) in the Presence of an External Strong U (°°) Flavored Constant noise Field, s. 105

  • 5.1. Introduction, s. 105
  • 5.2. The Triviality - Quantum Decoherence Analysis for Quantum Chromodynamics, s. 106

6 Fermions on the Lattice by Means of Mandelstam-Wilson Phase Factors: A Bosonic Lattice Path-Integral Framework, s. 115

  • 6.1, s. 115
  • 6.2.  The Framework, s. 115

7 A Connection between Fermionic Strings and Quantum Gravity States - A Loop Space Approach, s. 121

  • 7.1. Introduction, s. 121
  • 7.2. The Loop Space Approach for Quantum Gravity, s. 122
  • 7.3. The Wheeler - De Witt Geometrodynamical Propagator, s. 127
  • 7.4. A λφ4 Geometrodynamical Field Theory for Quantum Gravity, s. 130

8 A Fermionic Loop Wave Equation for Quantum Chromodynamics at Nc — +∞, s. 137

  • 8.1. Introduction, s. 137
  • 8.2. The Fermionic Loop Wave Equation, s. 137

9 String Wave Equations in Polyakov's Path Integral Framework, s. 141

  • 9.1. Introduction, s. 141
  • 9.2. The Wave Equation in Covariant Particle Dynamics, s. 141
  • 9.3. The Wave Equation in the Covariant Bosonic String Dynamics, s. 143
  • 9.4. A String Solution for the QCD[SU(°°)] Bosonic Contour Average Equation, s. 147
  • 9.5. The Neveu-Schwarz String Wave Equation, s. 150

10 A Random Surface Membrane Wave Equation for Bosonic Q.C.D. (SU (∞), s. 163

  • 10.1. Introduction, s. 163
  • 10.2. The Random Surface Wave Functional, s. 163
  • 10.3. A Connection with Q.C.D(SU(<*>)), s. 166

11 Covariant Functional Diffusion Equation for Polyakov's Bosonic String, s. 173

  • 11.1. Introduction, s. 173
  • 11.2. The Covariant Equation, s. 173
  • 11.3. The Wheeler - De Witt Equation as a Functional Diffusion Equation, s. 177

12 Covariant Path Integral for Nambu-Goto String Theory, s. 183

  • 12.1. Introduction, s. 183
  • 12.2. The Nambu-Goto Full Path Integral, s. 183

13 Topological Fermionic String Representation for Chern-Simons Non-Abelian Gauge Theories, s. 191

  • 13.1. Introduction, s. 191
  • 13.2. The Fermionic String Representation, s. 191

14 Fermionic String Representation for the Three-Dimensional Ising Model, s. 195

  • 14.1. Introduction, s. 195
  • 14.2. The Proposed String Theory, s. 196

15 A Polyakov Fermionic String as a Quantum State of Einstein Theory of Gravitation, s. 201

  • 15.1. Introduction, s. 201
  • 15.2. The Quantum Gravity String, s. 201

16 A Scattering Amplitude in the Quantum Geometry of Fermionic Strings, s. 209

  • 16.1. Introduction, s. 209
  • 16.2. The Scattering Amplitude, s. 209

17 Path-Integral Bosonization for the Thirring Model on a Riemann Surface 217

  • 17.1, s. 217
  • 17.2. The Path-Integral Bosonization on a Riemann Surface, s. 217

18 A Path-Integral Approach for Bosonic Effective Theories for Fermion Fields in Four and Three Dimensions, s. 225

  • 18.1. Introduction, s. 25
  • 18.2. The Bosonic High-Energy Effective Theory, s. 225
  • 18.3. The Bosonic Low-Energy Effective Theory, s. 228
  • 18.4. Polyakov's Fermi-Bose Transmutation in 3D Abelian-Thirring Model, s. 231
  • 18.5. Effective Four-Dimensional Bosonic Actions - Some Comments, s. 237
  • 18.6. The Triviality of the Abelian-Thirring Quantum Field Model, s. 239

19 Domains of Bosonic Functional Integrals and Some Applications to the Mathematical Physics of Path Integrals and String Theory, s. 245

  • 19.1. Introduction, s. 245
  • 19.2. The Euclidean Schwinger Generating Functional as a Functional Fourier Transform, s. 246
  • 19.3. The Support of Functional Measures - The Minlos Theorem, s. 248
  • 19.4. Some Rigorous Quantum Field Path Integral in the Analytical Regularization Scheme, s. 256
  • 19.5. Remarks on the Theory of Integration of Functionals on Distributional Spaces and Ffilbert-Banach Spaces, s. 261

20 Non-linear Diffusion in RD and in Hilbert Spaces, a Path Integral Study, s. 279

  • 20.1. Introduction, s. 279
  • 20.2. The Non-linear Diffusion, s. 279
  • 20.3. The Linear Diffusion in the Space L2(Q.), s. 285

21 Basics Integrals Representations in Mathematical Analysis of Euclidean Functional Integrals, s. 295

22 Supplementary Appendixes, s. 307

Index, s. 331

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