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Generalized Scaling Operators in White Noise Analysis and Applications to Hamiltonian Path Integrals with Quadratic Action

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Stochastic and Infinite Dimensional Analysis

Part of the book series: Trends in Mathematics ((TM))

Abstract

We give an outlook, how to realize the ideas of complex scaling from [15–17] to phase space path integrals in the framework of White Noise Analysis. The idea of this scaling method goes back to [9]. Therefore we extend the concept complex scaling to scaling with suitable bounded operators.

On the occasion of the 75th birthday of Ludwig Streit

This work is supported by the FCT-project: PTDC/MAT-STA/1284/2012

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Acknowledgements

Dear Ludwig Streit, I wish you all the best to your 75th birthday. The author would like to thank the organizing and programme committee of the Stochastic and Infinite Dimensional Analysis conference for an interesting and stimulating meeting. The author thanks the FCT for financial support within the project PTDC/MAT-STA/1284/2012.

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Authors and Affiliations

  1. CMAF Avenida Prof. Gama Pinto 2, 1649-009, Lisboa, Portugal

    Wolfgang Bock

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  1. Wolfgang Bock
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Correspondence to Wolfgang Bock .

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Editors and Affiliations

  1. Research Center for Theoretical Physics Central Visayan Institute Foundation, Jagna, Bohol, Philippines

    Christopher C. Bernido

  2. Research Center for Theoretical Physics Central Visayan Institute Foundation, Jagna, Bohol, Philippines

    Maria Victoria Carpio-Bernido

  3. Fachbereich Mathematik, Technische Universität Kaiserslautern, Kaiserslautern, Germany

    Martin Grothaus

  4. Department of Mathematics and Physics, University of Reading, Reading, United Kingdom

    Tobias Kuna

  5. Departamento de Ciências e Tecnologia, Universidade Aberta, Lisbon, Portugal

    Maria João Oliveira

  6. Universidade da Madeira Faculdade de Ciências Exatas e da Engenharia, Funchal, Madeira, Portugal

    José Luís da Silva

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Bock, W. (2016). Generalized Scaling Operators in White Noise Analysis and Applications to Hamiltonian Path Integrals with Quadratic Action. In: Bernido, C., Carpio-Bernido, M., Grothaus, M., Kuna, T., Oliveira, M., da Silva, J. (eds) Stochastic and Infinite Dimensional Analysis. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-07245-6_4

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