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On the deformation aspects of the replica thermalisation of the SU (2)-invariant Thirring model

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Conférence Moshé Flato 1999

Part of the book series: Mathematical Physics Studies ((MPST,volume 21/22))

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Abstract

We introduce an S-matrix preserving replica-thermalisation of integrable massive quantum field theories in 1 + 1-dimensions within the context of form factors. The deformation character of the methods used therein is being highlighted. We then solve a deformed version of the SU(2)-invariant Thirring model employing hypergeometric solutions of the rational sl 2-type quantum Knizhnik-Zamolodchikov equation at generic level and multiperiodic Barnes functions.

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References

  1. Bayen, F., Flato, M. Fronsdal, C., Lichnerowicz, A., and Sternheimer, D.: Deformation Theory and Quantization I & II, Ann. Physics 111 (1978), 61–110 & 111–151.

    Article  MathSciNet  MATH  Google Scholar 

  2. Pillin, M.: On the deformability of Heisenberg algebras, Comm. Math. Phys. 180 (1996), 23–38.

    Article  MathSciNet  MATH  Google Scholar 

  3. Flato, M., Fr0nsdal, C., and Sternheimer, D.: Singletons, Physics in AdS universe and oscillations of composite neutrinos, Lett. Math. Phys. 48 (1999), 109–119.

    Article  MathSciNet  MATH  Google Scholar 

  4. Smirnov, F. A.: Lectures on integrable massive models of QFT, in: M. L. Ge and B. H. Zhao, (eds.), Introduction to quantum group and integrable massive models of quantum field theory (Nankai, 1989), Nankai Lectures Math. Phys., World Sci. Publishing, River Edge, NJ, 1990, pp. 1–68.

    Google Scholar 

  5. Bisognano, J. and Wichmann, E.: On the duality condition for a Hermitian scalar field, J. Math. Phys. 16 (1975), 985–1007;

    Article  MathSciNet  MATH  Google Scholar 

  6. Bisognano, J. and Wichmann, E.: On the duality condition for quantum fields, J. Math. Phys. 17(1976), 303–321.

    Article  MathSciNet  Google Scholar 

  7. Callan, C. and Wilczek, F.: On geometric entropy, Phys. Lett. B 333 (1994), 55–61.

    Article  MathSciNet  Google Scholar 

  8. Niedermaier, M.: Varying the Unruh temperature in integrable QFTs, Nucl. Phys. B 535 (1998), 621–649;

    Article  MathSciNet  MATH  Google Scholar 

  9. Niedermaier, M.: Form factors, thermal states and modular structures, Nucl. Phys. B 519 (1998), 517–550;

    Article  MathSciNet  MATH  Google Scholar 

  10. Niedermaier, M.: A derivation of the cyclic form factor equation, Comm. Math. Phys. 196 (1998), 411–428.

    Article  MathSciNet  MATH  Google Scholar 

  11. Karowski, M. and Weisz, P.: Exact form factors in 1+1-dimensional field theoretic models with soliton behaviour, Nucl. Phys. B 139 (1978), 455–476.

    Article  MathSciNet  Google Scholar 

  12. Nakayashiki, A., Pakuliak, S., and Tarasov, V.: On solutions of the KZ and qKZ equations at level zero, preprint q-alg/9712002.

    Google Scholar 

  13. Jimbo, M. and Miwa, T.: Algebraic analysis of solvable lattice models, CBMS Regional Conference Series in Mathematics, 85, Amer. Math. Soc, Providence, RI, 1995.

    Google Scholar 

  14. Pillin, M.: Exact two-particle matrix elements in S-matrix preserving deformation of integrable QFTs, Phys. Lett. B 448 (1999), 227–233.

    Article  MathSciNet  MATH  Google Scholar 

  15. Tarasov, V. and Varchenko, A.: Geometry of g-hypergeometric functions as a bridge between Yangians and quantum affine algebras, Invent. Math. 128 (1997), 501–588.

    Article  MathSciNet  Google Scholar 

  16. Pillin, M.: Replica-deformation of the SU(2)-invariant Thirring model via solutions of the qKZ equation, preprint KCL-MTH-99–29 (1999), hep-th/9907147.

    Google Scholar 

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© 2000 Kluwer Academic Publishers

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Pillin, M. (2000). On the deformation aspects of the replica thermalisation of the SU (2)-invariant Thirring model. In: Dito, G., Sternheimer, D. (eds) Conférence Moshé Flato 1999. Mathematical Physics Studies, vol 21/22. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-1276-3_19

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  • DOI: https://doi.org/10.1007/978-94-015-1276-3_19

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-5551-4

  • Online ISBN: 978-94-015-1276-3

  • eBook Packages: Springer Book Archive

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