Lecture Notes in Topics in Path Integrals and String Representations

Functional Integrals is a well-established method in mathematical physics, especially those mathematical methods used in modern non-perturbative quantum field theory and string theory. This book presents a unique, original and modern treatment of strings representations on Bosonic Quantum Chromodynamics and Bosonization theory on 2d Gauge Field Models, besides of rigorous mathematical studies on the analytical regularization scheme on Euclidean quantum field path integrals and stochastic quantum field theory. It follows an analytic approach based on Loop space techniques, functional determinant exact evaluations and exactly solubility of four dimensional QCD loop wave equations through Elfin Botelho fermionic extrinsic self avoiding string path integrals.

Contents:

• Bosonic Free Strings and Non-Supersymetric QCD(SU(∞)): A Constant Gauge Field Path Integral Study
• Basics Polyakov's Quantum Surface Theory on the Formalism of Functional Integrals and Applications
• Critical String Wave Equations and the QCD(U(Nc)) String
• The Formalism of String Functional Integrals for the Evaluation of the Interquark Potential and Non Critical Strings Scattering Amplitudes
• The D → -∞ Saddle-Point Spectrum Analysis of the Open Bosonic Polyakov String in RD x SO(N) — The QCD(SU(∞)) String
• The Electric Charge Confining in Abelian Rank Two Tensor Field Model
• Infinities on Quantum Field Theory: A Functional Integral Approach
• Some Comments on Rigorous Finite-Volume Euclidean Quantum Field Path Integrals in the Analytical Regularization Scheme
• On the Rigorous Ergodic Theorem for a Class of Non-Linear Klein Gordon Wave Propagations
• A Note on Feynman-Kac Path Integral Representations for Scalar Wave Motions
• A Note on the Extrinsic Phase Space Path Integral Method for Quantization on Riemannian Manifold Particle Motions — An Application of Nash Embedding Theorem

Readership: Applied mathematicians, mathematical physicists and theoretical physicists.