Some rigorous results on the Pauli-Fierz model of classical electrodynamics
Annales de l'I.H.P. Physique théorique (1993)
- Volume: 58, Issue: 2, page 155-171
- ISSN: 0246-0211
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topBambusi, Dario, and Galgani, Luigi. "Some rigorous results on the Pauli-Fierz model of classical electrodynamics." Annales de l'I.H.P. Physique théorique 58.2 (1993): 155-171. <http://eudml.org/doc/76601>.
@article{Bambusi1993,
author = {Bambusi, Dario, Galgani, Luigi},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {Coulomb gauge; global existence and uniqueness of solution of Cauchy problem; space of finite energy states; stability for family of solitary wave solutions; Fourier transform; time evolution of energy spectral distribution},
language = {eng},
number = {2},
pages = {155-171},
publisher = {Gauthier-Villars},
title = {Some rigorous results on the Pauli-Fierz model of classical electrodynamics},
url = {http://eudml.org/doc/76601},
volume = {58},
year = {1993},
}
TY - JOUR
AU - Bambusi, Dario
AU - Galgani, Luigi
TI - Some rigorous results on the Pauli-Fierz model of classical electrodynamics
JO - Annales de l'I.H.P. Physique théorique
PY - 1993
PB - Gauthier-Villars
VL - 58
IS - 2
SP - 155
EP - 171
LA - eng
KW - Coulomb gauge; global existence and uniqueness of solution of Cauchy problem; space of finite energy states; stability for family of solitary wave solutions; Fourier transform; time evolution of energy spectral distribution
UR - http://eudml.org/doc/76601
ER -
References
top- [1] E. Fermi, Quantum Theory of Radiation, Rev. Mod. Phys., Vol. 4, 1932, pp. 87-132. Zbl0003.41503
- [2] W. Heitler, The Quantum Theory of Radiation, Oxford, Clarendon, 1950. Zbl0040.42303
- [3] P.A.M. Dirac, The Principles of Quantum Mechanics, Oxford, Clarendon, 1967. Zbl0012.18104
- [4] A. Kramers, Die Wechselwirkung zwischen geladenen Teilchen und Strahlungsfeld, Nuovo Cimento, Vol. 15, 1938, pp. 108-114. Zbl64.1485.02JFM64.1485.02
- [5] A. Kramers, Quantum Mechanics, North Holland, P. C., 1958. Zbl0077.20802
- [6] W. Pauli and M. Fierz, Zur Theorie der Emission langwelliger Lichtquanten, Nuovo Cimento, Vol. 15, 1938, pp. 167-188. JFM64.1487.01
- [7] P. Blanchard, Discussion mathématique du modèle de Pauli et Fierz relatif à la catastrophe infrarouge, Commun. Math. Phys., Vol. 15, 1969, pp. 156-172. MR256676
- [8] A. Arai, An Asymptotic Analysis and its Application to the nonrelativistic Limit of the Pauli-Fierz and Spin-boson Model, J. Math. Phys., Vol. 31, 1990, pp. 2653-2663. Zbl0734.47046MR1075749
- [9] T. Okamoto and K. Yajima, Complex Scaling Technique in non-Relativistic QED, Ann. Inst. H. Poincaré A, Vol. 42, 1985, pp. 311-327. Zbl0594.58057MR797278
- [10] L. Galgani, C. Angaroni, L. Forti, A. Giorgilli and F. Guerra, Classical Electrodynamics as a Nonlinear Dynamical System, Phys. Lett. A, Vol. 139, 1989, pp. 221- 230.
- [11] P. Bocchieri, A. Crotti and A. Loinger, A Classical Solvable Model of a Radiant Cavity, Lett. Nuovo Cimento, Vol. 4, 1972, pp.741-744.
- [12] G. Benettin, L. Galgani and A. Giorgilli, Boltzmann's Ultraviolet Cutoff and Nekhoroshev's Theorem on Arnold Diffusion, Nature, Vol. 311, 1984, pp. 444-445.
- [13] G. Casati, I. Guarneri and F. Valz-Gris, Preliminaries to the Ergodic Theory of Infinite-Dimensional Systems: A Model of Radiant Cavity, J. Stat. Phys., Vol. 30, 1983, pp. 195-217. MR710740
- [14] L. Gross, The Cauchy Problem for the Coupled Maxwell and Dirac Equations, Comm. Pure Appl. Math., Vol. 19, 1966, pp. 1-15. Zbl0137.32401MR190520
- [15] T. Kato, Quasi-linear Equations of Evolution, with Applications to Partial Differential Equations, in Lect. Notes Math., No. 448, Springer, New York, 1975. Zbl0315.35077MR407477
- [16] J.M. Chadam, Global Solutions of the Cauchy Problem for the (Classical) Coupled Maxwell-Dirac Equations in One Space Dimension, J. Funct. Anal., Vol. 13, 1973, pp. 173-184. Zbl0264.35058MR368640
- [17] M. Abraham, Prinzipien der Dynamik des Elektrons, Ann. der Phys., Vol. 10, 1903, pp. 105-179. Zbl34.0915.02JFM34.0915.02
- [18] I. Segal, Nonlinear Semigroups, Ann. of Math., Vol. 78, 1963, pp. 339-364. Zbl0204.16004
- [19] S.B. Kuksin, Perturbation Theory for Quasiperiodic Solutions of Infinite Dimensional Hamiltonian Systems. 1. Symplectic structures and Hamiltonian Scales of Hilbert Spaces. Preprint of Max Planck Institut für Mathematik MPI/90-99. S.B. Kuksin, Perturbation Theory for Quasiperiodic Solutions of Infinite Dimensional Hamiltonian Systems. 2. Statement of the main theorem and its consequences, Preprint of Max Planck Institut für Mathematik MPI/90-100. Zbl0678.58037
- [20] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer Verlag, New York, 1993. MR710486
- [21] J.E. Marsden and J.R. Hughes, Mathematical Foundations of Elasticity, Prentice Hall, Englewood Cliff, 1983. Zbl0545.73031
- [22] M. Phillips, Classical Electrodynamics, in Handbuch der Physik, Springer Verlag, Berlin, 1962. MR148344
- [23] P.A.M. Dirac, Classical Theory of Radiating Electrons, Proc. Roy. Soc., Vol. A167, 1938, pp. 148-168. Zbl0023.42702JFM64.1481.03
- [24] F. Rohrlich, Classical Charged particles, Addison-Wesley, Redwood City, 1965. Zbl0131.43602MR1200457
- [25] J. Jeans, On the Vibrations set up in Molecules by Collisions, Phil. Mag., Vol. 6, 1903, p. 279; J. Jeans, On the Partition of Energy between Matter and Aether, Phil. Mag., Vol. 10, 1905, p. 91. See also L. Galgani, Relaxation times and the Foundations of Classical Statistical Mechanics, in Nonlinear Evolution and Cahotic Phenomena, G. GALLAVOTTI and P. ZWEIFEL Eds., Nato ASI series B176, pp. 147-160, Plenum Press, New York, 1988. JFM34.0833.02
- [26] M. Grillakis, J. Shatah and W. Strauss, Stability of Solitary Waves in the Presence of Symmetry, I, J. Funct. Anal., Vol. 74, 1987, pp. 160-197. Zbl0656.35122MR901236
- [26] M. Grillakis, J. Shatah and W. Strauss, Stability of Solitary Waves in the Presence of Symmetry, II, J. Funct. Anal., Vol. 94, 1990, pp. 308-348. Zbl0711.58013MR1081647
- [28] P. Blanchard, J. Stubbe and L. Vazquez, On the Stability of Solitary Waves for Classical Scalar Fields, Ann. Inst. Henri Poincaré, Vol. 47, 1987, pp. 309-336. Zbl0649.35076MR921309
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