Westerkamp, Werner: Recent results in infinite dimensional analysis and applications to Feynman integrals. 1995
Inhalt
- Introduction
- Preliminaries
- Generalized functions in infinite dimensional analysis
- Measures on linear topological spaces
- Concept of distributions in infinite dimensional analysis
- Appell polynomials associated to the measure µ
- The dual Appell system and the representation theorem for P´(N´)
- Test functions on a linear space with measure
- Distributions
- Integral transformations
- Characterization theorems
- The Wick product
- Positive distributions
- Change of measure
- Gaussian analysis
- The Hida spaces (N) and (N)´
- The nuclear triple of Kondratiew
- The spaces G and M
- The Meyer-Yan triple
- The scaling operator
- Donsker`s delta "function"
- Concept of path integration in a white noise framework
- The free Feynman integrand
- The unperturbed harmonic oscillator
- An example: Quantum mechanics on a circle
- Feynman integrals and complex scaling
- Quantum mechanical propagators in terms of white noise distributions
- An extension of the Khandekar Streit method
- Verifying the Schrödinger equation
- The Feynman integrand for the perturbed harmonic oscillator
- The Feynman integrand for the Albeverio Høegh-Krohn class
- A new look at Feynman Hibbs
- Transition amplitudes
- Relation to operator notation
- A functional form of the canonical commutation relations
- Ehrenfest's theorem
- Bibliography