Asymptotic observables and Coulomb scattering for the Dirac equation

 Access to full text

 Full (PDF)

1. [1] P.R. Chernoff, Essential self-adjointness of powers of generators of hyperbolic equations. J. Func. Anal., t. 12, 1973, p. 401-414. Zbl0263.35066MR369890
2. [2] J. Dollard and G. Velo, Asymptotic behaviour of a Dirac particle in a Coulomb field. Il Nuovo Cimento, t. 45, 1966, p. 801-812. 
3. [3] V. Enss, Geometric methods in spectral and scattering theory of Schrödinger operators. In: Rigorous Atomic and Molecular Physics, G. Velo, A. S. Wightman (eds). New York, Plenum, 1981. 
4. [4] V. Enss, Asymptotic observables on scattering states. Commun. Math. Phys., t. 89, 1983, p. 245-268. Zbl0543.47008MR709466
5. [5] V. Enss, Propagation properties of quantum scattering states. J. Func. Anal., t. 52, 1983, p. 219-251. Zbl0543.47009MR707205
6. [6] V. Enss, Quantum scattering theory for two and three-body systems with potentials of short and long range. In: Schrödinger Operators, S. Graffi (ed.), Lecture Notes in Mathem., 1159, Springer, Berlin, 1985, p. 39-176. Zbl0585.35023MR824987
7. [7] W. Hunziker, On the space-time behaviour of Schrödinger wavefunctions. J. Math. Phys., t. 7, 1966, p. 300-304. Zbl0151.43801MR193939
8. [8] A.J. Kalnay, The localization problem. In: Problems in the Foundations of Physics, t. 4, M. Bunge (ed.). Berlin, Springer, 1971. 
9. [9] M. Klaus and R. Wüst, Characterization and uniqueness of distinguished self–adjoint extensions of Dirac-operators. Commun. Math. Phys., t. 64, 1979, p. 171-176. Zbl0408.47022MR519923
10. [10] Pl. Muthuramalingam, Scattering theory by Enss' method for operator valued matrices: Dirac operator in an electric field, J. Math. Soc. Japan, t. 37, 1985, p. 415-432. Zbl0581.47006MR792984
11. [11] Pl Muthuramalingam and K.B. Sinha, Asymptotic completeness in long-range scattering II. Ann. scient. Ec. Norm. Sup., t. 18, 1985, p. 57-87. Zbl0584.47009MR803195
12. [12] G. Nenciu, Self-adjointness and invariance of the essential spectrum for Dirac operators defined as quadratic forms. Commun. Math. Phys., t. 48, 1976, p. 235-247. Zbl0349.47014MR421456
13. [13] P.A. Perry, Scattering theory by the Enss Method. Mathematical Reports, t. 1, Harwood, Chur., 1983. Zbl0529.35004MR752694
14. [14] C. Radin and B. Simon, Invariant domains for the time-dependent Schrödinger equation. J. Diff. Equ., t. 29, 1978, p. 289-296. Zbl0351.34004MR502354
15. [15] M. Reed and B. Simon, Methods of Modern Mathematical Physics I, Functional Analysis. New York, Academic Press, 1972. Zbl0242.46001MR493419
16. [16] M. Reed and B. Simon, Methods of Modern Mathematical Physics II, Fourier Analysis, Self-Adjointness. New York, Academic Press, 1975. Zbl0308.47002MR493420
17. [17] M. Reed and B. Simon, Methods of Modern Mathematical Physics III, Scattering Theory. New York, Academic Press, 1979. Zbl0405.47007MR529429
18. [18] E. Schrödinger, Sitzungsb. Preuss. Akad. Wiss., Phys.-Math. Kl., t. 24, 1930, p. 418. JFM56.0754.06
19. [19] K.B. Sinha and Pl. Muthuramalingam, Asymptotic evolution of certain observables and completeness in Coulomb scattering I. J. Func. Anal., t. 55, 1984, p. 323- 343. Zbl0531.47008MR734802
20. [20] R. Wüst, Distinguished self-adjoint extension of Dirac operators constructed by means of cut-off potentials. Math. Z., t. 141, 1975, p. 93-98. Zbl0311.47020MR365233
21. [21] B. Thaller, Relativistic scattering theory for long-range potentials of non-electrostatic type. Lett. Math. Phys., to appear 1986. Zbl0643.35078MR849249
22. [22] Pl Muthumaralingam and K.B. Sinha, Existence and completeness of wave operators for the Dirac operator in an electro-magnetic field with long-range potentials. Preprint, New Delhi, 1986. MR989018

1. Hiroshi Isozaki, Inverse scattering theory for Dirac operators
2. Anne Boutet de Monvel-Berthier, Dragos Manda, Radu Purice, Limiting absorption principle for the Dirac operator
3. Thierry Daudé, Propagation estimates for Dirac operators and application to scattering theory
4. J.-P. Nicolas, Scattering of linear Dirac fields by a spherically symmetric Black-Hole