Relativistic Wave Equations
Les rencontres physiciens-mathématiciens de Strasbourg -RCP25, Tome 18 (1973), Exposé no. 4, 24 p.
@article{RCP25_1973__18__A4_0,
     author = {Seiler, R.},
     title = {Relativistic {Wave} {Equations}},
     journal = {Les rencontres physiciens-math\'ematiciens de Strasbourg -RCP25},
     note = {talk:4},
     publisher = {Institut de Recherche Math\'ematique Avanc\'ee - Universit\'e Louis Pasteur},
     volume = {18},
     year = {1973},
     language = {en},
     url = {http://www.numdam.org/item/RCP25_1973__18__A4_0/}
}
TY  - JOUR
AU  - Seiler, R.
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JO  - Les rencontres physiciens-mathématiciens de Strasbourg -RCP25
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PY  - 1973
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VL  - 18
PB  - Institut de Recherche Mathématique Avancée - Université Louis Pasteur
UR  - http://www.numdam.org/item/RCP25_1973__18__A4_0/
LA  - en
ID  - RCP25_1973__18__A4_0
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Seiler, R. Relativistic Wave Equations. Les rencontres physiciens-mathématiciens de Strasbourg -RCP25, Tome 18 (1973), Exposé no. 4, 24 p. http://www.numdam.org/item/RCP25_1973__18__A4_0/

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P.A.M. Dirac For a detailed account of the history of the Dirac equation we refer to A. S. Wightman in Aspects of Quantum Theory, Edited by A. Salam and E.P. Wigner (Cambridge University Press, 1972).

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C. S. Morawetz and W. A. Strauss, Comm. Pure Appl. Math. 25, 1 (1972) | MR 303097 | Zbl 0228.35055

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John M. Chadam Indiana University Preprint, Bloomington, Indiana (1972)

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H. Joos Fortschr. Physik 10, 65 (1962) | Zbl 0131.44002

19) P. Moussa and R. Stora, International School of Elementary Particle Physics, Herceg-Novi, Yugoslavia (1966)

20) A. S. Glass Princeton Thesis 1971, unpublished

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22) For a most complet review on relativistic wave equations without interaction see ref. 20)

23) see ref. 2) and ref. 30)

P. Minkowski and R. Seiler, Phys. Rev. D 4, 359 (1971) | MR 342072

25) J. Bellissard and R. Seiler, to be published in Lettere al Nouovo Cimento

26) A. S. Wightman ref. 9) p. 107

27) J. Bellissard Université de Provence-Centres Saint-Charles, Thèse; unpublished

28) J. Leray and Y. Ohya Systèmes lineaires hyperboliques non stricts Colloques CBM Louvain (1964) ; | Zbl 0135.14804

J. Leray and Y. Ohya Reprint in Battelle Rencontres on Hyperbolic Equations and Waves, Seattle 1968

29) R. Seiler, in preparation

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31) Spin zero particle in external field, ref. 30).

32) Spin 1/2 particle in external field R. Seiler, Comm. Math. Phys. 25, 127 (1972)

33) Existence already follows from classical theorems by Scale resp. Scale and Stinespring

34) There is a close connection between the kernel I(x,y) comming up in the formal expression for the S-matrix in perturbation theory S= in 0|S|0 in :expdxdyϕ in + (x)I(x,y)ϕ in (y): and the fundamental solution S R (x,y;A) resp. S A (x,y;A) of the wave equation (11). G=G 0 +G 0 IG 0 where G 0 denotes the fundamental solution of the free equation with Feynman boundary conditions. Then G is a solution of the equation G=G 0 -iG 0 ¬AG On the other hand S R resp. S A are solutions of the Yang-Feldman equation (12) S R A (x,y;A)=S R A 0 (x-y)-idzS R A 0 (x-z)¬A(z)S R A (z,y;A).

35) A. S. Wightman, private communication