Abstract
Let ℝv∋ξ →Σess(ξ) denote the bottom of the essential spectrum for the ber Hamiltonians of the translation invariant massive Nelson model, which describes a v-dimensional electron linearly coupled to a scalar massive radiation eld. We prove that, away from a locally nite set, Σess is an analytic function of total momentum.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
F.A. Berezin, The method of second quantization, 1 ed., Academic Press, New York, San Francisco, London, 1966.
L. Bruneau and J. Dereziński, Pauli-Fierz Hamiltonians defined as quadratic forms, Rep. Math. Phys., 54 (2004), 169–199.
J.B. Conway, Functions of one complex variable, 2 ed., Graduate texts in mathematics, vol. 11, Springer-Verlag, New York, 1978.
J. Dereziński and C. Gérard, Asymptotic completeness in quantum field theory. massive Pauli-Fierz Hamiltonians, Rev. Math. Phys. 11 (1999), 383–450.
R.P. Feynman, Statistical mechanics. A set of lectures, Frontiers in physics, W.A. Benjamin, Inc., Reading, Massechusets, 1972.
J. Fröhlich, On the infrared problem in a model of scalar electrons and massless scalar bosons, Ann. Inst. Henri Poincaré 19 (1973), 1–103.
J. Fröhlich, Existence of dressed one-electron states in a class of persistent models, Fortschr. Phys. 22 (1974), 159–198.
R.C. Gunning and H. Rossi, Analytic functions of several complex variables, Series in modern analysis, Prentice-Hall, Inc., Englewood Cliffs, N. J., 1965.
J.S. Møller, The translation invariant massive Nelson model: I. The bottom of the spectrum, Ann. Henri Poincaré 6 (2005) 1091–1135.
“The Fröhlich polaron revisited”. Submitted.
H. Spohn, The polaron at large total momentum, J. Phys. A 21 (1988), 1199–1211.
H. Spohn, Dynamics of charged particles and their radiation field, Cambridge University Press, 2004.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer
About this chapter
Cite this chapter
Schach-Møller, J. (2006). On the Essential Spectrum of the Translation Invariant Nelson Model. In: Asch, J., Joye, A. (eds) Mathematical Physics of Quantum Mechanics. Lecture Notes in Physics, vol 690. Springer, Berlin, Heidelberg . https://doi.org/10.1007/3-540-34273-7_15
Download citation
DOI: https://doi.org/10.1007/3-540-34273-7_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-31026-6
Online ISBN: 978-3-540-34273-1
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)