Quantum scattering by external metrics and Yang-Mills potentials
Annales de l'institut Henri Poincaré. Section A, Physique Théorique, Volume 31 (1979) no. 1, pp. 43-71.
@article{AIHPA_1979__31_1_43_0,
     author = {Cotta-Ramusino, P. and Kr\"uger, W. and Schrader, R.},
     title = {Quantum scattering by external metrics and {Yang-Mills} potentials},
     journal = {Annales de l'institut Henri Poincar\'e. Section A, Physique Th\'eorique},
     pages = {43--71},
     publisher = {Gauthier-Villars},
     volume = {31},
     number = {1},
     year = {1979},
     zbl = {0441.35055},
     mrnumber = {557051},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPA_1979__31_1_43_0/}
}
TY  - JOUR
AU  - Cotta-Ramusino, P.
AU  - Krüger, W.
AU  - Schrader, R.
TI  - Quantum scattering by external metrics and Yang-Mills potentials
JO  - Annales de l'institut Henri Poincaré. Section A, Physique Théorique
PY  - 1979
DA  - 1979///
SP  - 43
EP  - 71
VL  - 31
IS  - 1
PB  - Gauthier-Villars
UR  - http://archive.numdam.org/item/AIHPA_1979__31_1_43_0/
UR  - https://zbmath.org/?q=an%3A0441.35055
UR  - https://www.ams.org/mathscinet-getitem?mr=557051
LA  - en
ID  - AIHPA_1979__31_1_43_0
ER  - 
%0 Journal Article
%A Cotta-Ramusino, P.
%A Krüger, W.
%A Schrader, R.
%T Quantum scattering by external metrics and Yang-Mills potentials
%J Annales de l'institut Henri Poincaré. Section A, Physique Théorique
%D 1979
%P 43-71
%V 31
%N 1
%I Gauthier-Villars
%G en
%F AIHPA_1979__31_1_43_0
Cotta-Ramusino, P.; Krüger, W.; Schrader, R. Quantum scattering by external metrics and Yang-Mills potentials. Annales de l'institut Henri Poincaré. Section A, Physique Théorique, Volume 31 (1979) no. 1, pp. 43-71. http://archive.numdam.org/item/AIHPA_1979__31_1_43_0/

[1] S. Agmon., Spectral Properties of Schrödinger Operators and Scattering Theory, Annali Scuola Normale Superiore Pisa, Classe di Scienze, Serie IV, Vol. II, 1975, p. 151-218. | Numdam | MR | Zbl

[2] S. Albeverio, On Bound States in the Continuum of N-Body Systems and the Virial Theorem, Ann. Phys., t. 71, 1972, p. 167-276. | MR

[3] N. Aronszajn, A Unique Continuation Theorem for Solutions of Elliptic Partial Differential Equations or Inequalities of Second Order, J. Math. Pures Appl., t. 36, 1957, p. 235-249. | MR | Zbl

[4] R. Beals, On Spectral Theory and Scattering for Elliptic Operators with Singular Potentials, Report. Math. Dept., Yale Univ., 1969.

[5] A. Belavin, A. Polyakov, A.S. Schwarz, Y. Tyupkin, Pseudoparticle Solutions of the Yang-Mills Equations, Phys. Lett., t. 59 B, 1975, p. 85-87. | MR

[6] M.S. Birman, A Test for the Existence of Wave Operators, Doklady Akad. Nauk. SSSR, t. 147, 1962, p. 1008-1009. | MR | Zbl

[7] M.S. Birman, A Local Criterion for the Existence of Wave Operators, Izv. Ak. Nauk-Mat., t. 32, 1968, p. 914-942. | MR | Zbl

[8] M.S. Birman, Scattering Problems for Differential Operators with Constant Coefficients, Funkt. Anal. Publ., t. 3, 1969, p. 1-16. | MR | Zbl

[9] P.R. Chernoff, Essential Selfadjointness of Powers of Generators of Hyperbolic Equations, J. Funct. Anal., t. 12, 1973, p. 404-414. | MR | Zbl

[10] H.O. Cordes, Über die Bestimmtheit der Lösungen Elliptischer Differentialgleichungen durch Anfangsvorgaben, Nachr. Akad. Wiss. Göttingen, Math. Phys., Kl. II, t. 11, 1956, p. 239-258. | MR | Zbl

[11] H.O. Cordes, Selfadjointness of Powers of Elliptic Operators on Non-Compact Manifolds, Math. Ann., t. 195, 1972, p. 257-272. | MR | Zbl

[12] L.L. De Branges, Perturbations of Selfadjoint Transformations, Amer. J. Math., t. 84, 1962, p. 543-560. | MR | Zbl

[13] J. Dimock, Scalar Quantum Field in External Gauge Field, Suny et Buffalo preprint 1978; Scalar Quantum Field in an External Gravitational Field, Suny at Buffalo preprint, 1979. | MR

[14] V. Enss, Asymptotic Completeness for Quantum Mechanical Potential Scattering, Comm. Math. Phys., t. 61, 1978, p. 285-291. | MR | Zbl

[15] M.P. Gaffney, The Harmonic Operator for Exterior Differential Forms, Proc. Nat. Acad. Sci., USA, t. 37, 1951, p. 48-50. | MR | Zbl

[16] J.J. Giambiagi, K.D. Rothe, Regular N-Instanton Fields and Singular Gauge Transformations, Nucl. Phys., t. 129 B, 1977, p. 111-124.

[17] E. Heinz, Über die Eindeutigkeit beim Cauchy'schen Anfangswertproblem einer Elliptischen Differentialgleichung, Nachr. Akad. Wiss. Göttingen, Math. Phys. Kl. II, t. 1, 1955, 1-12. | MR | Zbl

[18] H. Hess, R. Schrader, D.A. Uhlenbrock, Domination of Semigroups and Generalization of Kato's Inequality, Duke Math. J., t. 44, 1977, p. 893-904. | MR | Zbl

[19] H. Hess, R. Schrader, D.A. Uhlenbrock, Kato's Inequality and Spectral Distribution of Laplace Operators on Compact Riemannian Manifolds, to appear in J. Diff. Geom. | Zbl

[20] G. 'Thooft, Symmetry Breaking through Bell-Jackiw Anomalies, Phys. Rev. Lett., t. 37, 1976, p. 8-11.

[21] 'Thooft G., Computation of the Quantum Effects due to a Fourdimensional Pseudo-particle, Phys. Rev., t. 14 D, 1976, p. 3432-3435.

[22] L. Hörmander, The Existence of Wave Operators in Scattering Theory, Math. Z., t. 140, 1976, p. 69-91. | MR | Zbl

[23] T. Ikebe, J. Uchiyama, On the Asymptotic Behaviour of Eigenfunctions of Second Order Elliptic Operators, J. Math. Kyoto Univ., t. 11, 1971, p. 425-448. | MR | Zbl

[24] W. Jäger, Zur Theorie der Schwingungsgleichung mit variablen Koeffizienten in Aussengebieten, Math. Z., t. 102, 1967, p. 62-68. | MR | Zbl

[25] T. Kato, Perturbation Theory for Linear Operators, Springer, Berlin-Heidelberg- New York, 1966. | MR | Zbl

[26] T. Kato, Scattering Theory with two Hilbert Spaces, J. Funct. Anal., t. 1, 1967, p. 269-324. | MR | Zbl

[27] T. Kato, Schrödinger Operators with Singular Potentials, Israel J. Math., t. 13, 1972, p. 135-149. | MR | Zbl

[28] J. Kupsch, W. Sandhas, Møller Operators for Scattering on Singular Potentials, Comm. Math. Phys., t. 2, 1966, p. 147-154. | MR | Zbl

[29] S. Kuroda, Scattering Theory of Differential Operators I, Operator Theorems, J. Math. Soc. Japan, t. 25, 1973, p. 75-104. | MR | Zbl

[30] S. Kuroda, Scattering Theory of Differential Operators II, Self Adjoint Elliptic Operators, J. Math. Soc. Japan, t. 25, 1973, p. 222-234. | MR | Zbl

[31] M. Reed, B. Simon, The Scattering of Classical Waves from Inhomogeneous Media, Math. Z., t. 155, 1977, p. 163-180. | MR | Zbl

[32] M. Reed, B. Simon, Methods of Modern Mathematical Physics, Vol. II and Vol. IV, Academic Press, New York, San Francisco, London, 1975-1978. | Zbl

[33] M. Reed, B. Simon, Methods of Modern Mathematical Phys., Vol. III, Scattering Theory, to appear. | MR | Zbl

[34] F. Rellich, Über das Asymptotische Verhalten der Lösungen von Δu + λu = 0 in unendlichen Gebieten, Jber. Deutsch. Math. Verein, t. 53, 1943, 57-65. | MR | Zbl

[35] W. Roelcke, Über den Laplace Operator auf Riemann'schen Mannigfaltigkeiten mit diskontinuierlichen Gruppen, Math. Nachr., t. 21, 1960, p. 132-149. | MR | Zbl

[36] S.N.M. Ruijsenaars, The S-Operator for Spin-O and Spin-1/2 Particles in Time-dependent External Fields, p. 414-416, Erice Proc. 77 (ed. G. Velo, A. S. Wightman), Berlin-Heidelberg-New York, 1978.

[37] M. Schechter, Scattering Theory for Elliptic Operators of Arbitrary Order, Comm. Math. Helv., t. 49, 1974, p. 84-113. | MR | Zbl

[38] M. Schechter, Nonhomogeneous Elliptic Systems and Scattering, Tohoku Math. J., t. 27, 1975, p. 601-606. | MR | Zbl

[39] S. Sciuto, Topics on Instantons, CERN Preprint (1977) to be published in Rivista del Nuovo Cimento.

[40] B. Simon, Phase Space Analysis of Simple Scattering Systems: Extensions of Some Work of Enss, Princeton Univ. preprint, 1978. | MR

[41] W.F. Stinespring, A Sufficient Condition for an Integral Operator to have a Trace, J. reine angew. Math., t. 200, 1958, p. 200-207. | MR | Zbl

[42] R.S. Strichartz, Multipliers on Fractional Sobolev Spaces, J. Math. Mech., t. 16, 1967, p. 1031-1060. | MR | Zbl

[43] J. Von Neumann, E.P. Wigner, Über Merkwürdige Diskrete Eigenwerte, Z. Phys., t. 30, 1929, p. 465-467. | JFM

[44] S. Weinberg, Gravitation and Cosmology, J. Wiley, New York, London, Sidney, Toronto, 1972.

[45] J. Avron, I. Herbst, B. Simon, Schrödinger Operators with Magnetic Fields; I. General Interaction, Duke Math. J., t. 45, 1978, p. 847-883. | MR | Zbl