'All are every interesting topics treated with a high level of mathematical sophistication. One of the very useful tricks the author repeatedly resorts to is the introduction of one-parameter families of operators interpolating between two operators which appear naturally in the formalism. From this one-parameter family a differential equation for the determinant (or ratio of determinants) or for correlation functions is derived, which can then be solved. This is a very simple, elegant and powerful technique.'Mathematical Reviews ClippingsFunctional 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.

This monograph is written on topics in the subject of Continuum Quantum Geometric Path Integrals applied to Yang-Mills Theory and variants (QCD, Chern-Simons Theory, Ising Models, etc.)- the called Random Geometry in Quantum Field Theory, which are hoped to be useful to graduate students of quantum physics and applied mathematics, with a focused weight towards to those interested in applying the concepts of continuum quantum geometry in other branches of modern physics, like superconductivity, nuclear physics, polymer theory, string theory, etc. The methodology used to in this monograph is the same exposed in previous work in random classical physics: "Methods of Bosonic Path Integrals Representations- Random Systems in Classical Physics - Nova Publishers, (2006) U.S.A.': Expositions and formulas should be chewed, swallowed and digested. This process of analysis should not be abandoned until it yields a comprehension of the overall pattern of the proposed ideas and math, so after this step, one is ready to make improvements, corrections or criticisms on the path integrals representations of this book.

The special Internet categories are: Physics; Engineering Quantum Physics; and Applied Mathematics. The emphasis in this monograph is on non-trivial path integral variable change on previously obtained path integral solutions for difficult stochastic and functional equations by keeping the main objective to arrive at...another path integral which the author expects to be in a 'final' suitable form of become predictive. Note that path-integrals are mathematical objects specially tailored to the work of our modern 'slavers': computer machines.

Functional analysis is a well-established powerful method in mathematical physics, especially those mathematical methods used in modern non-perturbative quantum field theory and statistical turbulence. This book presents a unique, modern treatment of solutions to fractional random differential equations in mathematical physics. It follows an analytic approach in applied functional analysis for functional integration in quantum physics and stochastic Langevin-turbulent partial differential equations.