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Domains of bosonic Functional integrals and some applications to the mathematical physics of path integrals and String Theory

Since the result of R.P. Feynman on representing the initial value solution of Schrodinger Equation by means of an analytically time continued integration on a infinite dimensional space of functions, the subject of Euclidean Functional Integrals representations for Quantum Systems has became the mathematical operational framework to analyze Quantum Phenomena and stochastic systems as showed in the previous decades of research on Theoretical Physics ([1]–[3]). One of the most important open problem in the mathematical theory of Euclidean Functional Integrals is that related to implementation of sound mathematical approxima-