Book Review
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Ralph Abraham and Jerrold E. Marsden, Foundations of mechanics, Benjamin/Cummings Publishing Co., Inc., Advanced Book Program, Reading, Mass., 1978. Second edition, revised and enlarged; With the assistance of Tudor Raţiu and Richard Cushman. MR 515141
V. Arnold, Les méthodes mathématiques de la mécanique classique, Éditions Mir, Moscow, 1976 (French). Traduit du russe par Djilali Embarek. MR 0474391
M. F. Atiyah and J. D. S. Jones, Topological aspects of Yang-Mills theory, Comm. Math. Phys. 61 (1978), no. 2, 97–118. MR 503187
M. F. Atiyah and R. S. Ward, Instantons and algebraic geometry, Comm. Math. Phys. 55 (1977), no. 2, 117–124. MR 494098
5. R. J. Blattner, Lectures on representations of Lie groups and harmonic analysis, 5-16 Sept 1977, Liège, Belgium.
Y. Choquet-Bruhat, Géométrie différentielle et systèmes extérieurs, Monographies Universitaires de Mathématiques, No. 28, Dunod, Paris, 1968 (French). Préface de A. Lichnerowicz. MR 0236824
Victor Guillemin and Shlomo Sternberg, Geometric asymptotics, Mathematical Surveys, No. 14, American Mathematical Society, Providence, R.I., 1977. MR 0516965
Sigurđur Helgason, Differential geometry and symmetric spaces, Pure and Applied Mathematics, Vol. XII, Academic Press, New York-London, 1962. MR 0145455
Robert Hermann, Differential geometry and the calculus of variations, 2nd ed., Interdisciplinary Mathematics, Vol. XVII, Math Sci Press, Brookline, Mass., 1977. MR 0494184
Bertram Kostant, On Whittaker vectors and representation theory, Invent. Math. 48 (1978), no. 2, 101–184. MR 507800, DOI 10.1007/BF01390249
Masatake Kuranishi, Deformations of compact complex manifolds, Séminaire de Mathématiques Supérieures, No. 39 (Été 1969), Les Presses de l’Université de Montréal, Montreal, Que., 1971. MR 0355111
Peter D. Lax and Ralph S. Phillips, Scattering theory, 2nd ed., Pure and Applied Mathematics, vol. 26, Academic Press, Inc., Boston, MA, 1989. With appendices by Cathleen S. Morawetz and Georg Schmidt. MR 1037774
Peter D. Lax and Ralph S. Phillips, Scattering theory for automorphic functions, Annals of Mathematics Studies, No. 87, Princeton University Press, Princeton, N.J., 1976. MR 0562288
14. G. Mackey, Mathematical foundations of quantum mechanics, The Mathematical Physics Monograph Series, W. A. Benjamin, New York, 1963.
15. B. A. Dubrovin et al, Non-linear equations of Korteweg-deVries type, finite-zone linear operators, and Abelian varieties, Russian Math. Surveys 31 (1) (1976), 59-146.
Wulf Rossmann, Kirillov’s character formula for reductive Lie groups, Invent. Math. 48 (1978), no. 3, 207–220. MR 508985, DOI 10.1007/BF01390244
Rainer Kurt Sachs and Hung Hsi Wu, General relativity for mathematicians, Graduate Texts in Mathematics, Vol. 48, Springer-Verlag, New York-Heidelberg, 1977. MR 0503498
Irving Segal, Algebraic integration theory, Bull. Amer. Math. Soc. 71 (1965), 419–489. MR 178384, DOI 10.1090/S0002-9904-1965-11284-8
D. J. Simms, An application of polarisations and half-forms, Non-commutative harmonic analysis (Actes Colloq., Marseille-Luminy, 1974), Lecture Notes in Math., Vol. 466, Springer, Berlin, 1975, pp. 195–197. MR 0394760
J.-M. Souriau, Structure des systèmes dynamiques, Dunod, Paris, 1970 (French). Maîtrises de mathématiques. MR 0260238
Shlomo Sternberg, On the role of field theories in our physical conception of geometry, Differential geometrical methods in mathematical physics, II (Proc. Conf., Univ. Bonn, Bonn, 1977) Lecture Notes in Math., vol. 676, Springer, Berlin, 1978, pp. 1–80. MR 519606
Michael E. Taylor, Propagation, reflection, and diffraction of singularities of solutions to wave equations, Bull. Amer. Math. Soc. 84 (1978), no. 4, 589–611. MR 489757, DOI 10.1090/S0002-9904-1978-14501-7
V. S. Varadarajan, Geometry of quantum theory. Vol. I, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1968. MR 0471674
M. Vergne, On Rossmann’s character formula for discrete series, Invent. Math. 54 (1979), no. 1, 11–14. MR 549542, DOI 10.1007/BF01391173
25. J. F. Veverka, The Morse theory and its applications to solid state physics, Queen's Papers in Pure and Applied Math. no. 3 (1966).
Alan Weinstein, Lectures on symplectic manifolds, Regional Conference Series in Mathematics, No. 29, American Mathematical Society, Providence, R.I., 1977. Expository lectures from the CBMS Regional Conference held at the University of North Carolina, March 8–12, 1976. MR 0464312
R. O. Wells Jr., Complex manifolds and mathematical physics, Bull. Amer. Math. Soc. (N.S.) 1 (1979), no. 2, 296–336. MR 520077, DOI 10.1090/S0273-0979-1979-14596-8
- 1.
- R. Abraham and J. Marsden, Foundations of mechanics, 2nd ed., Addison-Wesley, Reading, Mass. 1978. MR 0515141
- 2.
- V. Arnold, Mathematical methods of classical mechanics, Graduate Texts in Math., vol. 60, Springer-Verlag, Berlin and New York, 1978. MR 690288
- 3.
- M. F. Atiyah and J. D. Jones (Oxford), Topological aspects of Yang-Mills theory, Comm. Math. Phys. 61 (1978), 97-118. MR 503187
- 4.
- M. F. Atiyah and R. S. Ward, Instantons and algebraic geometry, Comm. Math. Phys. 55 (1977), 117-124. MR 494098
- 5.
- R. J. Blattner, Lectures on representations of Lie groups and harmonic analysis, 5-16 Sept 1977, Liège, Belgium.
- 6.
- Y. Choquet-Bruhat, Géométrie différentielle et systèmes extérieurs, Monographies Universitaires de Math. No. 28, Dunod, Paris, 1968. MR 236824
- 7.
- V. Guillemin and S. Sternberg, Geometric asymptotics, Math. Surveys, no. 14, Amer. Math. Soc., Providence, R. I., 1977. MR 516965
- 8.
- S. Helgason, Differential geometry and symmetric spaces, Academic Press, New York, 1962 (2nd ed., 1979). MR 145455
- 9.
- R. Hermann, Differential geometry and the calculus of variations, Math. Sci. Press, Brook-line, 2nd ed., 1977. MR 494184
- 10.
- B. Kostant, Whittaker vectors and representation theory, Invent. Math. 48 (1978), 101-184. MR 507800
- 11.
- M. Kuranishi, Deformations of compact complex manifolds, Les Presses de l'Université de Montréal (1971). MR 355111
- 12.
- P. D. Lax and R. S. Phillips, Scattering theory, Academic Press, New York, 1967. MR 1037774
- 13.
- P. D. Lax and R. S. Phillips, Scattering theory for automorphic functions, Ann. of Math. Studies, Princeton Univ. Press, 1976. MR 562288
- 14.
- G. Mackey, Mathematical foundations of quantum mechanics, The Mathematical Physics Monograph Series, W. A. Benjamin, New York, 1963.
- 15.
- B. A. Dubrovin et al, Non-linear equations of Korteweg-deVries type, finite-zone linear operators, and Abelian varieties, Russian Math. Surveys 31 (1) (1976), 59-146.
- 16.
- W. Rossmann, Kirillov's character formula for reductive Lie groups, Invent. Math. 48 (1978), 207-220. MR 508985
- 17.
- R. K. Sachs and H. Wu, General relativity for mathematicians, Graduate Texts in Math., vol. 48, Springer-Verlag, Berlin and New York, 1977. MR 503498
- 18.
- I. E. Segal, Algebraic integration theory, Bull. Amer. Math. Soc. 71 (1965), 419-489. MR 178384
- 19.
- D. J. Simms, An application of polarizations on half-forms, Non-commutative Harmonic Analysis, Lecture Notes in Math., vol. 466, Springer-Verlag, Berlin and New York, 1975. MR 394760
- 20.
- J.-M. Souriau, Structure des systèmes dynamique, Dunod, Paris 1970. MR 260238
- 21.
- S. Sternberg, On the role of field theories in our Physical conception of geometry, Differential Geometrical Methods in Mathematical Physics, Lecture notes in Math., vol. 676, 1978, pp. 1-81. MR 519606
- 22.
- M. E. Taylor, Propagation, reflection, and diffraction of singularities of solutions to wave equations, Bull. Amer. Math. Soc. 84 (1978), 589-612. MR 489757
- 23.
- V. S. Varadarajan, Geometry of quantum theory. I, II, D. Van Nostrand, Princeton, N. J., 1968. MR 471674
- 24.
- M. Vergne, On Rossmann's character formula for discrete series, Invent Math. 54 (1979), 11-15. MR 549542
- 25.
- J. F. Veverka, The Morse theory and its applications to solid state physics, Queen's Papers in Pure and Applied Math. no. 3 (1966).
- 26.
- A. Weinstein, Lectures on symplectic manifolds, CBMS Regional Conf. Ser. in Math., no. 29, Amer. Math. Soc., Providence, R. I., 1977. MR 464312
- 27.
- R. O. Wells, Jr., Complex manifolds and mathematical physics, Bull. Amer. Math. Soc. (N. S.) 1 (1979), 296-337. MR 520077
Review Information:
Reviewer:
Bent Ørsted
Journal:
Bull. Amer. Math. Soc.
3 (1980), 878-885
DOI:
https://doi.org/10.1090/S0273-0979-1980-14837-5
