Asymptotic completeness, global existence and the infrared problem for the maxwell-dirac equations

Memoirs of the American Mathematical Society

Volumn , Issue 606, 1997, Pages 1-311

  Flato, Moshé ^a   Simon, Jacques C H ^a   Taflin, Erik ^a,b  

^a UNIVERSITÉ DE BOURGOGNE   (France)

^b Union des Assurances de Paris   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031139067     PISSN: 00659266     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (34)

1. [1] Bayen, F., Flato, M., Fronsdal, C., Lichnerowicz, A. and Sternheimer, D.: Deformation theory and quantization I: Deformation of symplectic structures. Ann. Phys. 111, 61-110 (1978).
2. [2] Bayen, F., Flato, M., Fronsdal, C., Lichnerowicz, A. and Sternheimer, D.: Deformation theory and quantization II: Physical applications. Ann. Phys. 111, 111-151 (1978).
3. [3] Bornaveas, N.: Local Existence for the Maxwell-Dirac Equations in Three Space-Time Dimensions. Ph.D. Thesis (1993), Princeton University.
4. [4] Calderon, A.P.: Lebesgue spaces of differentiable functions and distributions. Proc. Symp. Pure Math. IV, AMS 1961, 33-49.
5. [5] Chadam, J.M.: Global solutions of the Cauchy problem for the (classical) coupled Maxwell-Dirac equations in one space dimension. J. Funct.Anal. 13, 173-184 (1973).
6. [6] Christodoulou, D. and Klainerman, S.: The Global Nonlinear Stability of the Minkowski Space. Princeton Mathematical Series, 41, 1993. Princeton University Press.
7. [7] Dito, J.: Star-products and nonstandard quantization for Klein-Gordon equation. J. Math. Phys. 33, 791-801 (1992).
8. [8] Dixmier, J. and Malliavin, P.: Factorisation de fonctions et de vecteurs indéfiniment différentiables. Bull. des Sciences Math. 102, 305-330 (1978).
9. [9] Esteban, M., Georgiev, V. and Séré, E.: Stationary solutions of the Maxwell-Dirac and Klein-Gordon-Dirac equations. ICTP preprint IC/95/68. To appear in: Calculus of Variations, (1996).
10. e série, 10, 405-418 (1977).
11. [11] Flato, M. and Simon, J.C.H.: Non-linear equations and covariance. Lett. Math. Phys. 2, 155-160 (1979).
12. [12] Flato, M. and Simon, J.C.H.: Yang-Mills equations are formally linearizable. Lett. Math. Phys. 3, 279-283 (1979).
13. [13] Flato, M., Simon, J.C.H., Sternheimer, D and Taflin, E.: Nonlinear relativistic: wave equations in general dimensions. RIMS-preprint 1050, Dec. 1995. To be published in Pitman Series, Longman, 1996.
14. [14] Flato, M., Simon, J.C.H. and Taflin, E.: On global solutions of the Maxwell-Dirac Equations. Commun. Math. Phys. 112, 21-49 (1987).
15. [15] Flato, M., Simon, J.C.H. and Taflin, E.: The Maxwell-Dirac equations: Asymptotic completeness and infrared problem. Reviews in Math. Phys. 6, N° 5a, 1071-1083 (1994).
16. [16] Georgiev, V.: Small Amplitude Solutions of the Maxwell-Dirac Equations. Indiana Univ. Math. Journ. 40, 845-883 (1991).
17. [17] Gross, L.: The Cauchy problem for the coupled Maxwell and Dirac equations. Commun. Pure Appl. Math 19, 1-15 (1966).
18. [18] Hörmander, L.: The analysis of linear partial differential operators. Vol. I, Berlin, Heidelberg, New-York: Springer 1985.
19. [19] Hörmander, L.: Remarks on the Klein-Gordon equation. Journée Équations aux dérivées partielles, Saint-Jean de Monts 1987, Soc. Math. France (1987).
20. [20] Hörmander, L.: Non-Linear Hyperbolic Differential Equations, Lectures 1986-1987, N° 1988:2 /ISSN 0327-8475, Dept. Mathematics, Lund.
21. [21] Hörmander, L.: On Sobolev spaces associated with some Lie algebras, in "Current topics in partial differential equations", Tokyo: Kinokuniya Company Ltd 1985, pp. 261-287.
22. [22] Kato, K.: Linear evolution equations of "hyperbolic" type, II. J. Math. Soc. Japan 25, 648-666 (1973).
23. [23] Kato, T.: Quasilinear equations of evolution, with application to partial differential equations. Lecture Notes in Mathematics, Vol. 448. Berlin, Heidelberg, New-York: Springer 1975, pp. 25-70.
24. [24] Morawetz, C.S. and Strauss, W.A.: On a Nonlinear Scattering Operator. Commun. Pure Appl. Math. 26,47-54 (1973).
25. e série, 5, 599-660 (1972).
26. [26] Simon, J.C.H.: A wave operator for a non-linear Klein-Gordon equation. Lett. Math. Phys. 7, 387-398 (1983).
27. [27] Simon, J.C.H. and Taflin, E.: Wave operators and analytic solutions for systems of non-linear Klein-Gordon equations and non-linear Schrödinger equations. Commun. Math. Phys. 99, 541-562 (1985).
28. [28] Simon, J.C.H. and Taflin, E.: The Cauchy problem for non-linear Klein-Gordon equations. Commun. Math. Phys. 152, 433-478 (1993).
29. [29] Simon, J.C.H. and Taflin, E.: Initial data for non-linear evolution equations and differentiable vectors of group representations. In: Modern Group Theoretical Methods in Physics, J. Bertrand et al.(eds.), Mathematical Physics Studies 18 (Kluwer Academic Publishers, Dordrecht, 1995) 243-253.
30. [30] Sternheimer, D.: Recent developments in non linear representations and evolution equations. Lecture Notes in Physics 313 (Springer, Berlin, 1988), 65-73.
31. [31] Taflin, E.: Formal linearization of nonlinear massive representations of the connected Poincaré group. Jour. Math. Phys. 25, 765-771 (1984).
32. [32] Tsutsumi, Y.: Global Existence and Asymptotic Behavior of Solutions for the Maxwell-Schrödinger Equations in Three Space Dimensions. Commun. Math. Phys. 151, 543-576 (1993).
33. p decay rates for homogeneous wave equations. Math. Z. 120, 93-106 (1971).
34. [34] Warner, G.: Harmonic analysis on semi-simple Lie group I, Die Grundlehren der mathematischen Wissenschaften vol. 188, Berlin, Heidelberg, New-York: Springer 1972.