Quantization of field theories generalizing Gravity-Yang-Mills systems on the cylinder

  • P. Schaller
  • T. Strobl
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 436)


Gauge Theory Gauge Transformation Integral Surface Coadjoint Orbit Space Time Manifold 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [1]
    S.G. Rajeev,, Phys. Lett. B 212 (1988) 203. A. Migdal, Sov. Phys. Jept. 42 (1976) 413. K.S. Gupta, R.J. Henderson, S.G. Rajeev, O.T. Turgut, Yang-Mills Theory on a Cylinder Coupled to Point Particles, preprint UR-1327, ER-40685-777.Google Scholar
  2. [2]
    J.E. Hetrick and Y. Hosotani, Phys. Lett. B 230 (1989) 88. E. Langmann and G.W. Semenoff, Phys. Lett. B 296 (1992) 117; B 303 (1993) 303. S. Shabanov, Phys. Lett. 318B (1993) 323; 2D Yang-Mills theories, gauge orbit spaces, and the path integral quantization, preprint T93/139, hepth/9312160.Google Scholar
  3. [3]
    J.E. Hetrick, Canonical Quantization of Two Dimensional Gauge Fields, preprint UvA-ITFA 93-15, hep-th/9305020. L. Chandar and E. Ercolessi, Inequivalent Quatizations of Yang-Mills Theory on a Cylinder, preprint SU-4240-537.Google Scholar
  4. [4]
    C.G. Callan, S.B. Giddings, J.A. Harvey, A. Strominger, Phys. Rev. D 45/4 (1992) R1005. H. Verlinde, in The Sixth Marcel Grossmann Meeting on General Relativity, edited by M. Sato (World Scientific, Singapore, 1992). D Cangemi and R. Jackiw, Ann. Phys. (NY) 225, (1993) 229. D. Christensen and R.B. Mann, Class. Quan. Grav. 9 (1992) 1. S.A. Hayward, Cosmic Censorship in 2-dimensional dilaton gravity, Max Planck Inst. preprint 1992. A. Mikovic, Phys. Lett. B304 (1993) 70. H. Kawai and R. Nakayama, Quantum R 2 Gravity in Two Dimensions, preprint KEK 92-212.Google Scholar
  5. [5]
    M. O. Katanaev and I. V. Volovich, Phys. Lett. 175B (1986) 413; M. O. Katanaev, J. Math. Phys. 32 (1991) 2483; J. Math. Phys. 34/2 (1991) 700; W. Kummer, D.J. Schwarz, Nucl.Phys. B382 (1992) 171; F. Haider, W. Kummer, Int.Journ.Mod.Phys. 9 (1994) 207; N. Ikeda and K.I. Izawa, Prog.Theor.Phys., 89 (1993) 223Google Scholar
  6. [6]
    D. Amati, S. Elitzur, E. Rabinovici, On Induced Gravity in 2-d Topological Theories, preprint hep-th/9212003.Google Scholar
  7. [7]
    C. Teitelboim, Phys. Lett. 1268 (1983) 41; R. Jackiw, 1984 Quantum Theory of Gravity, ed S. Christensen (Bristol: Hilger) p 403.Google Scholar
  8. [8]
    T. Fukuyama and K. Kamimura, Phys. Lett. 1608 (1985) 259; K. Isler and C. Trugenberger, Phys. Rev. Lett. 63 (1989) 834; A. Chamsedine and D. Wyler, Phys. Lett. 228B (1989) 75; Nucl. Phys. 340B (1990) 595.Google Scholar
  9. [9]
    Kostant, B. (1970) Quantization and unitary representations. In Lectures in modern analysis III (ed. C.T. Taam). Lecture notes in mathematics, Vol. 170. Springer, Berlin. Souriau, J.-M (1970) Structure des systmes dynamiques Dunod, ParisGoogle Scholar
  10. [10]
    Kirillov, A.A. (1976) Elements of the theory of representations Springer, Berlin. Woodhouse, N.M.J. Geometric Quantization, second Ed. 1992, Clarendon Press, Oxford.Google Scholar
  11. [11]
    C.J. Isham in Recent Aspects of Quantum Fields, ed. Gausterer et. al. LNP 396, p.123, Springer Berlin Heidelberg 1991.Google Scholar
  12. [12]
    P. Schaller and T. Strobl, Diffeomorphisms versus Nonabelian Gauge Transformations: An Example of 1+1 Dimensional Gravity, preprint TUW9325, hep-th/9401110, to be published in Phys. Letts. B. Google Scholar
  13. [13]
    P. Schaller and T. Strobl, Class. Quan.Grav. 11 (1993) 331.Google Scholar
  14. [14]
    T. Strobl, Quantization and the Issue of Time for Various Two-Dimensional Models of Gravity, hep-th/9308155, to be publ. in J.Mod.Phys. D, (Proceedings of Journees Relativistes).Google Scholar
  15. [15]
    T. Strobl, Dirac Quantization of Gravity-Yang-Mills Systems in 1+1 Dimensions, preprint TUW9326, hep-th/9403121. P. Schaller and T. Strobl, Poisson Structure Induced (Topological) Field Theories, preprint TUW9403, hep-th/9405110.Google Scholar
  16. [16]
    Y. Choquet-Bruhat, C. DeWitt-Morette, Analysis, Manifolds and Physics, Part II: 92 Applications, North-Holland Physics 1989.Google Scholar
  17. [17]
    P.A.M. Dirac, Lectures on Quantum Mechanics, Yeshiva University, New York 1964. M. Henneaux and C. Teitelboim, Quantisation of Gauge Systems, Princeton University Press 1992.Google Scholar
  18. [18]
    J.F. Adams, Infinite Loop Spaces, Annals of Mathamatics Studies 90, Princeton University Press, Princeton 1978.Google Scholar
  19. [19]
    J. Goldstone and R. Jackiw, Phys. Lett. 74B (1978) 81.Google Scholar
  20. [20]
    D. Finkelstein and C. W. Misner, Ann. Phys. (NY) 6, 230 (1959); cf. also K. A. Dunn, T. A. Harriott, J. G. Williams, J. Math. Phys. 33/4 (1992) 1437, where, however, the solutions in chapter V do not correspond to constant curvature solutionsGoogle Scholar
  21. [21]
    A. Ashtekar Lectures on Non-Perturbative Canonical Gravity, World Scientific, Singapore, 1991.Google Scholar

Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • P. Schaller
    • 1
  • T. Strobl
    • 1
  1. 1.Inst. f. Theor. PhysikTechn. Univ. ViennaWienAustria

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