Relativistic Wave Equations

Seiler, R.

Les rencontres physiciens-mathématiciens de Strasbourg -RCP25, Tome 19 (1973), p. 1-24 / Harvested from Numdam

Détail

Publié le : 1973-01-01

Bibliographie

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

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27) J. Bellissard Université de Provence-Centres Saint-Charles, Thèse; unpublished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

30) B. Schroer, A. Swieca and R. Seiler, Phys. Rev. D 2, 2927 (1970) | Zbl 1227.81201

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 $S=_{\text{in}}\langle 0 | S | 0 \rangle_{\text{in}}:exp\int dxdy\phi _\text{in}^+(x)I(x,y)\phi _\text{in}(y):$ and the fundamental solution $S_R(x,y;A)$ resp. $S_A(x,y;A)$ of the wave equation (11). $G=G^0+G^0IG^0$ where $G^0$ denotes the fundamental solution of the free equation with Feynman boundary conditions. Then $G$ is a solution of the equation $G=G^0-iG^0\not{A}G$ On the other hand $S_R$ resp. $S_A$ are solutions of the Yang-Feldman equation (12) $S_{R\atop A}(x,y;A)=S_{R\atop A}^0(x-y)-i \int dz S_{R\atop A}^0(x-z) \not{A}(z) S_{R\atop A}(z,y;A)$.

35) A. S. Wightman, private communication