Abstract
The interaction of a particle with a boson field is considered. The matrix elements of the cut-off Green function are expressed in terms of a discrete time Poisson process and shown to converge to a finite limit, under some stringent conditions on the boson field. A renormalization process is set up to extend the result to more physical situations.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Maslov, V.P. and Chebotarev A.P. (1978), Viniti Itogui Nauki, 15, p.5.
Combe, P., Hoegh-Krohn, R., Rodriguez, R., Sirugue, M., and Sirugue-Collin, M., Comm. Math. Phys., 77, p. 269 (1980)
Combe, P., Hoegh-Krohn, R., Rodriguez, R., Sirugue, M., and Sirugue-Collin, M., J. Math. Phys., 23, p. 405, (1982).
Bertrand, J., and Rideau, G., (1981), Stochastic jump processes in the phase space representation of quantum mechanics, in Mathematical problems in theoretical physics, Lecture Notes in Physics, 153, Springer-Verlag.
Bertrand, J., Gaveau, B. and Rideau, G. (1984), Poisson processes and quantum field theory: a model, in Lecture Notes in Mathematics, 1136, Springer-Verlag.
Bertrand, J., Gaveau, B. and Rideau, G. (1985), Quantum fields and Poisson processes, I. Interaction of a cut-off boson field with a quantum particle, Lett. Math. Phys., 9, pp. 73–82.
Bertrand, J., Gaveau, B. and Rideau, G. (1985), Quantum fields and Poisson processes, II. Interaction of boson-boson and boson-fermion fields with a cut-off, Lett. Math. Phys., 9, pp. 353–362.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1995 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Gaveau, B., Bertrand, J., Rideau, G. (1995). Poisson Path Integral Representation of Green Functions for Certain Field Theories. In: Bertrand, J., Flato, M., Gazeau, JP., Irac-Astaud, M., Sternheimer, D. (eds) Modern Group Theoretical Methods in Physics. Mathematical Physics Studies, vol 18. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8543-9_13
Download citation
DOI: https://doi.org/10.1007/978-94-015-8543-9_13
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4598-0
Online ISBN: 978-94-015-8543-9
eBook Packages: Springer Book Archive