Michael MOVSHEV |
MAT 570: Concepts of Quantum Mechanics |
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Week 5: |
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Week 6: |
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Week 7: |
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Week 9: |
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Week 10: |
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Week 11: |
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Week 12: |
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Books:
[Alvarez]Alvarez, Orlando Lectures on quantum mechanics and the index theorem. Geometry and quantum field theory (Park City, UT, 1991), 271--322, IAS/Park City Math. Ser., 1, Amer. Math. Soc., Providence, RI, 1995.
[Atiyah, M. F.,Bott R.]Atiyah, M. F.; Bott, R.The moment map and equivariant cohomology. Topology 23 (1984), no. 1, 1--28.
[Berezin(ru)]Berezin, Felix Alexandrovich Introduction to superanalysis. Edited and with a foreword by A. A. Kirillov. With an appendix by V. I. Ogievetsky. Translated from the Russian by J. Niederle and R. Koteck\'y. Translation edited by Dimitri Le\u\i tes. Mathematical Physics and Applied Math
[Bryant]Bryant, Robert L.An introduction to Lie groups and symplectic geometry. Geometry and quantum field theory (Park City, UT, 1991), 5--181, IAS/Park City Math. Ser., 1, Amer. Math. Soc., Providence, RI, 1995.
[Deligne Freed] Deligne, Pierre; Freed, Daniel S. Classical field theory. Quantum fields and strings: a course for mathematicians, Vol. 1, 2 (Princeton, NJ, 1996/1997), 137--225, Amer. Math. Soc., Providence, RI, 1999.
[Grosche] Christian Grosche An Introduction into the Feynman Path Integral arXiv:hep-th/9302097v1
[Guillemin V.."Moment_maps..."] Guillemin, Victor Moment maps and combinatorial invariants of Hamiltonian $T\sp n$-spaces. Progress in Mathematics, 122. Birkhäuser Boston, Inc., Boston, MA, 1994. viii+150 pp. ISBN: 0-8176-3770-2
[Guillemin, Sternberg] Guillemin, Victor; Sternberg, Shlomo Geometric asymptotics. Mathematical Surveys, No. 14. American Mathematical Society, Providence, R.I., 1977. xviii+474 pp. (one plate).
[Henneaux_Teitelboim] Henneaux, Marc; Teitelboim, Claudio Quantization of gauge systems. Princeton University Press, Princeton, NJ, 1992. xxviii+520 pp. ISBN: 0-691-08775-X; 0-691-03769-8
[Kazhdan]Kazhdan, David Introduction to QFT. Quantum fields and strings: a course for mathematicians, Vol. 1, 2 (Princeton, NJ, 1996/1997), 377--418, Amer. Math. Soc., Providence, RI, 1999.
[Kontsevich]Kontsevich, Maxim Deformation quantization of Poisson manifolds. Lett. Math. Phys. 66 (2003), no. 3, 157--216.
[Manin]Manin, Yuri I. Gauge field theory and complex geometry. Translated from the Russian by N. Koblitz and J. R. King. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 289. Springer-Verlag, Berlin, 1988. x+297 pp. ISBN: 3-540-1
[Palais(ru)]Palais, Richard S. Seminar on the Atiyah-Singer index theorem. With contributions by M. F. Atiyah, A. Borel, E. E. Floyd, R. T. Seeley, W. Shih and R. Solovay. Annals of Mathematics Studies, No. 57 Princeton University Press, Princeton, N.J. 1965 x+366 pp.
[Stasheff]Stasheff, Jim Homological reduction of constrained Poisson algebras. J. Differential Geom. 45 (1997), no. 1, 221--240.
[Schwarz1] Schwarz, Albert Topological quantum field theories. XIIIth International Congress on Mathematical Physics (London, 2000), 123--142, Int. Press, Boston, MA, 2001.
[Schwarz2]Schwarz, Albert Semiclassical approximation in Batalin-Vilkovisky formalism. Comm. Math. Phys. 158 (1993), no. 2, 373--396.
[Takhtajan] Takhtajan L.A. A Neoclassic Introduction to Quantum Mechanics.(DRAFT)
[Woodhouse] Woodhouse, Nicholas Geometric quantization. Oxford Mathematical Monographs. The Clarendon Press, Oxford University Press, New York, 1980. xi+316 pp. ISBN: 0-19-853528-7