no. 3
The wave equation with one point interaction and the (linearized) classical electrodynamics of a point particle
Annales de l'I.H.P. Physique théorique, Tome 68 (1998) no. 3, pp. 351-377. 
@article{AIHPA_1998__68_3_351_0,
     author = {Noja, Diego and Posilicano, Andrea},
     title = {The wave equation with one point interaction and the (linearized) classical electrodynamics of a point particle},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     pages = {351--377},
     publisher = {Gauthier-Villars},
     volume = {68},
     number = {3},
     year = {1998},
     mrnumber = {1622543},
     zbl = {0923.35172},
     language = {en},
     url = {http://www.numdam.org/item/AIHPA_1998__68_3_351_0/}
}
TY  - JOUR
AU  - Noja, Diego
AU  - Posilicano, Andrea
TI  - The wave equation with one point interaction and the (linearized) classical electrodynamics of a point particle
JO  - Annales de l'I.H.P. Physique théorique
PY  - 1998
SP  - 351
EP  - 377
VL  - 68
IS  - 3
PB  - Gauthier-Villars
UR  - http://www.numdam.org/item/AIHPA_1998__68_3_351_0/
LA  - en
ID  - AIHPA_1998__68_3_351_0
ER  - 
%0 Journal Article
%A Noja, Diego
%A Posilicano, Andrea
%T The wave equation with one point interaction and the (linearized) classical electrodynamics of a point particle
%J Annales de l'I.H.P. Physique théorique
%D 1998
%P 351-377
%V 68
%N 3
%I Gauthier-Villars
%U http://www.numdam.org/item/AIHPA_1998__68_3_351_0/
%G en
%F AIHPA_1998__68_3_351_0
Noja, Diego; Posilicano, Andrea. The wave equation with one point interaction and the (linearized) classical electrodynamics of a point particle. Annales de l'I.H.P. Physique théorique, Tome 68 (1998) no. 3, pp. 351-377. http://www.numdam.org/item/AIHPA_1998__68_3_351_0/

[ABD] S. Albeverio, Z. Brzeżniak and L. Dabrowski, Fundamentals Solutions of the Heat and Schrödinger Equations with Point Interactions. J. Funct. Anal., Vol. 130, 1995, pp. 220-254. | MR | Zbl

[AGHH] S. Albeverio, F. Gesztesy, R. Hoegh-Krohn and H. Holden, Solvable Models in Quantum Mechanics. New York: Springer-Verlag 1988. | MR | Zbl

[A] A. Arai, Rigorous Theory of Spectra and Radiation for a Model in Quantum Electrodynamics. J. Math. Phys., Vol. 24, 1983, pp. 1896-1910. | MR | Zbl

[B] D. Bambusi, A Proof of the Lorentz-Dirac Equation for Charged Point Particles. Preprint Univ. Milano 1996.

[BG] D. Bambusi and L. Galgani, Some Rigorous Results on the Pauli-Fierz Model of Classical Electrodynamics. Ann. Inst. H.Poincaré, Vol. 58A, 1993, pp. 155-171. | Numdam | MR | Zbl

[BN] D. Bambusi and D. Noja, Classical Electrodynamics of Point Particles and Mass Renormalization. Some Preliminary Results. Lett. Math. Phys. Vol. 37, 1996, pp. 449-460. | MR | Zbl

[Be] H.A. Bethe, The Electromagnetic Shift of Energy Levels. Phys. Rev., Vol. 72, 1947, pp. 339-341. | Zbl

[Bl] P. Blanchard P., Discussion Mathematique du Modèle de Pauli-Fierz relatif au Catastrophe Infrarouge. Commun. Math. Phys., Vol. 15, 1969, pp. 156-172. | MR

[CN] S. Coleman and R.E. Norton, Runaway Modes in Model Field Theory. Phys. Rev., Vol. 125, 1962, pp. 1422-1428. | MR | Zbl

[DFT] G.F. Dell'Antonio, R. Figari and A. Teta, Diffusion of a Particle in Presence of N Moving Point Sources. Preprint Univ. di Roma "La Sapienza" 1996.

[D] P.A.M. Dirac, Classical Theory of Radiating Electrons. Proc. Roy. Soc., Vol. A167, 1938, pp. 148-168. | JFM | Zbl

[EIH] A. Einstein, L. Infeld and B. Hoffmann, The Gravitational Equations and the Problem of Motion. Ann. Math., Vol. 39, 1938, pp. 65-100. | JFM | MR | Zbl

[F] H.O. Fattorini, Second Order Linear Differential Equations in Banach Spaces. Amsterdam: North-Holland 1985. | MR | Zbl

[H] W. Heitler, The Quantum Theory of Radiation. Oxford: Clarendon 1950.

[IW] L. Infeld and P.R. Wallace, The Equation of Motions in Electrodynamics. Phys. Rev., Vol. 57, 1940, pp. 797-806. | JFM | MR | Zbl

[K] J. Kijowski, Electrodynamics of Moving Particles. Gen. Rel. Grav. Vol. 26, 1994, pp. 167-201. | MR

[Ki] J. Kisyńsky, On the Cosine Operator Functions and One-Parameter Groups of Operators. Studia Math. , Vol. 44, 1972, pp. 93-105. | MR | Zbl

[Kr] H.A. Kramers, Nonrelativistic Quantum Electrodynamics and the Correspondence Principle, in: R. Stoops (ed.), Rapports et Discussions du Huitieme conseil de Physique Solvay. Brussels 1950.

[L] H.A. Lorentz, The Theory of Electrons ( 2 nd edition). New York: Dover 1952.

[PF] W. Pauli and M. Fierz, Zur Theorie der Emission langwelliger Lichtquanten. Nuovo Cimento, Vol. 15, 1938, pp. 168-188. | JFM

[S1] M. Sova, Cosine Operator Functions. Dissertationes Math., Vol. 49, 1966, pp. 1-47. | MR | Zbl

[S2] M. Sova, Semigroups and Cosine Functions of Normal Operators in Hilbert Spaces. Časopis Pešt. Mat., Vol. 93, 1968, pp. 386-421. | MR | Zbl

[T] A. Teta, Quadratic Forms for Singular Perturbations of the Laplacian. Publ. RIMS Kyoto Univ., Vol. 26, 1990, pp. 803-819 | MR | Zbl

[VK] N.G. Vankampen., Contributions to the Quantum Theory of Light Scattering. Kgl. Danske. Videnskab. Selskab, Mat. Fys. Medd, Vol. 26, 1951, No. 15. | MR | Zbl