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Introduction to path integrals, matrix models and strings

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Field Theory, Topology and Condensed Matter Physics

Part of the book series: Lecture Notes in Physics ((LNP,volume 456))

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References

  1. A general reference for aspects of path integral quantization is: Faddeev, L.D.: The Feynman Integral for Singular Lagrangians, Theo. Math. Phys. Vol.No.1,3 (1969)

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  2. Treatment of ordering associated with changes of variables in path integral is given in: Gervais, J.-L., Jevicki, A: Nucl.Phys. B110 (1976) 93

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  3. Path integral for spin is considered in: Jevicki, A., Papanicolaou N.: Ann.Phys. 120 (1979) 107 and in geometric terms for example, by Polyakov, A: Mod. Phys. Lett. A3 No. 3 (1988) 325

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  4. Path integral quantization of the SU(2) top is due originally to: Schulman, L.: Phys. Rev. 176 (1968) 1558

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  5. The basic reference on String Theory is: Green, M., Schwarz, J., Witten, E.: Superstring Theory, (1987) Cambridge University Press

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  6. The spectrum of 2-Dimensional string theory can be found in: Polyakov, A.M.: Mod. Phys. Lett. A6 (1991) 635; Wakimoto, M., Yamada, H.: Hiroshima Math. J. 16, (1986) 427

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  11. The formulation of Yang-Mills on a circle (plaquet) was described in: Jevicki, A., Sakita, B.: Phys. Rev. D22 (1980) 467

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  12. The Schurr polynomial (character) eigenstates and the conformal field theory description is given in: Jevicki, A.: Nucl. Phys. B376 (1992) 75

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  13. For recent application and latest developments on the 1/N expansion of 2d Yang-Mills theory see: Douglas, M.: Conformal field Techniques in Large N Yang-Mills Theory, RU-93-57 preprint, to appear in the Cargese Workshop on Strings and Topological Field Theory; Gross, D., Taylor, W.: Nucl. Phys. B403 (1983) 395

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  16. The field theoretic approach to 2d string theory that we described is given in: Das, S.R., Jevicki, A.: Mod. Phys. Lett. A5 (1990) 1639

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  17. For perturbative calculations see: Demeterfi, K., Jevicki, A., Rodrigues, J.P.: Nucl. Phys. B362 (1991) 173; Nucl. Phys. B365 (1991) 449

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  18. The classical solution of collective field theory is given by: Polchinski, J.: Nucl. Phys. B362 (1991) 125

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  19. The ω∞ symmetry was introduced in: Avan, J., Jevicki, A.: Phys. Lett. B266 (1991) 35; Phys. Lett. B272 (1991) 17

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  20. and given a conformal field theory interpretation by: Witten, E.: Nucl. Phys. B373 (1992) 187

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  22. The loop space approach to field theory of strings is formulated in Jevicki, A., Rodrigues, J.P.: Nucl. Phys. B421 (1994)

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  23. Schwinger-Dyson equations for matrix models are studied in: David, F.: Mod. Phys. Lett. A5 (1990) 1019; Fukuma, M., Kawai, H., Nakayama, R.: Intern. Journ. Mod. Phys. A6 (1991) 1385; Dijkgraaf, R., Verlinde, E., Verlinde, H.: Nucl. Phys B348 (1991) 435.

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  24. For an independent attempt of constructing a field theory of noncritical strings see: Ishibashi, N., Kawai, H.: KEK Preprint KEK-Th 364 (July 1993)

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  25. The stochastic approach to solving loop equations is originally used in: Rodrigues, J.P.: Nucl. Phys B260 (1985) 350

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Authors and Affiliations

  1. Department of Physics, Brown University, Box 1843, 02912, Providence, RI, USA

    Antal Jevicki

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  1. Antal Jevicki
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Hendrik B. Geyer

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© 1995 Springer-Verlag

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Jevicki, A. (1995). Introduction to path integrals, matrix models and strings. In: Geyer, H.B. (eds) Field Theory, Topology and Condensed Matter Physics. Lecture Notes in Physics, vol 456. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0113368

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  • DOI: https://doi.org/10.1007/BFb0113368

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  • Print ISBN: 978-3-540-60138-8

  • Online ISBN: 978-3-540-49455-3

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