A New Concept of the Analytic Operator-Valued Feynman Integral on Wiener Space

ABSTRACT

In this article we introduce a new concept of an analytic operator-valued Feynman integral for functionals on Wiener space, which we then use to explain various physical phenomena. We then establish the existence of some analytic operator-valued Feynman integrals that prove useful in establishing various applications in quantum mechanics.

KEYWORDS:

• Analytic operator-valued Feynman integral
• (an)harmonic oscillator
• diffusion equation
• Feynman–Kac formula
• Schrödinger equation

MATHEMATICS SUBJECT CLASSIFICATION:

• 60J65
• 28C20

Acknowledgments

The authors thank the referees for their helpful suggestions which led to the present version of this article.