Loop groups, anyons and the Calogero-Sutherland model

Communications in Mathematical Physics

Volumn 201, Issue 1, 1999, Pages 1-34

  Carey, Alan L ^a   Langmann, Edwin ^b  

^a UNIVERSITY OF ADELAIDE   (Australia)

^b ROYAL INSTITUTE OF TECHNOLOGY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033241456     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200050547     Document Type: Review

References (45)

1. [AMOS1] Awata, H., Matsuo, Y., Odake, S., Shiraishi, J.: Excited states of Calogero-Sutherland model and singular vectors of the W(N) algebra. Nucl. Phys. B449, 347 (1995)
2. [AMOS2] Awata, H., Matsuo, Y., Odake, S., Shiraishi, J.: Collective field theory, Calogero-Sutherland model and generalized matrix models. Phys. Lett. B347, 49 (1995)
3. ∞ parafermions. Nucl. Phys. B343, 185 (1990)
4. [BHKV] Brink, L., Hansson, T.H., Konstein, S., and Vasiliev, M.A.: The Calogero model: anyonic representations, fermionic extensions and supersymmetry. Nucl. Phys. B401, 591 (1993)
5. [BMT] Buchholz, D., Mack, G., and Todorov, I.: Localized automorphisms of the U(1) current algebra on the circle: An instructive example. In: Kastler, D. (ed.) The algebraic theory of superselection sectors: introduction and recent results. Proceedings, Palermo 1989, Singapore: World Scientific, 1989, p. 356
6. [CHa] Carey, A.L. and Hannabuss, K.C.: Temperature states on the loop groups, theta functions and the Luttinger model. J. Funct. Anal. 75, 128 (1987)
7. [CHMS] Carey, A.L., Hannabuss, K.C., Mason, L. and Singer, M.: The Landau-Lifshitz Equation, Elliptic curves and the Ward transform. Commun. Math. Phys. 154, 25 (1993)
8. [CHu] Carey, A.L. and Hurst, C.A.: A note on the boson-fermion correspondence and infinite dimensional groups. Commun. Math. Phys. 98, 435 (1985)
9. [CR] Carey, A.L. and Ruijsenaars, S.N.M.: On fermion gauge groups, current algebras and Kac-Moody algebras. Acta Appl. Mat. 10, 1 (1987)
10. [CRW] Carey, A.L., Ruijsenaars, S.N.M. and Wright, J.D.: The massless Thirring model: positivity of Klaiber's n-point functions. Commun. Math. Phys. 99, 347 (1985)
11. [C] Coleman, S.: Quantum sine-Gordon equation as the massive Thirring model. Phys. Rev. D 11, 2088 (1975)
12. [DFZ] Dell'Antonio, G.F., Frishman, Y., and Zwanziger, D.: Thirring model in terms of currents; solutions and light cone expansions. Phys. Rev. D 6, 988 (1972)
13. [F] Frenkel, I.B.: Two constructions of affine Lie algebra representations and boson-fermions correspondence in quantum field theory. J. Funct. Anal. 44, 259 (1981)
14. 2 quantum many body system. J. Stat. Phys. 72, 39 (1993)
15. 2 quantum many body system. J. Stat. Phys. 72, 39 (1993)
16. 2 quantum many body system'. Nucl. Phys. B416, 377 (1994); see also Ref. [AMOS1]
17. [GJ] Glimm, J. and Jaffe, A.: Quantum Physics. New York: Springer Verlag, 1981
18. [GL] Grosse, H. and Langmann, E.: A super-version of quasi-free second quantization. I. Charged particles. J. Math. Phys. 33, 1032 (1992)
19. [H] Ha, Z.N.C.: Fractional statistics in one dimension: View from an exactly solvable model. Nucl. Phys. B435 [FS], 604 (1995)
20. [HLV] Hansson, T.H., Leinaas, J.M., Viefers, S.: Field theory of any ions in the lowest Landau level. Nucl. Phys. B470, 291 (1996)
21. [I] Iso, S.: Anyon basis in c = 1 conformal field theory. Nucl. Phys. B443 [FS], 581 (1995)
22. [K] Kac, V.G.: Infinite dimensional Lie algebras. Cambridge: Cambridge University Press, 1985
23. [KRd] Kac, V.G. and Radul, A.: Quasifinite highest weight modules over the Lie algebra of differential operators on the circle. Commun. Math. Phys. 157, 429 (1993); see also Bilal, A., Phys. Lett. B227, 406 (1989); Bakas, I., Phys. Lett. B228, 57 (1989)
24. [KRd] Kac, V.G. and Radul, A.: Quasifinite highest weight modules over the Lie algebra of differential operators on the circle. Commun. Math. Phys. 157, 429 (1993); see also Bilal, A., Phys. Lett. B227, 406 (1989); Bakas, I., Phys. Lett. B228, 57 (1989)
25. [KRd] Kac, V.G. and Radul, A.: Quasifinite highest weight modules over the Lie algebra of differential operators on the circle. Commun. Math. Phys. 157, 429 (1993); see also Bilal, A., Phys. Lett. B227, 406 (1989); Bakas, I., Phys. Lett. B228, 57 (1989)
26. [KRi] Kac, V.G. and Raina, A.K.: Highest weight representations of infinite dimensional Lie algebras. Singapore: World Scientific, 1987
27. [K1] Klaiber, B.: The Thirring model. In: Barut A. O. and Brittin W. E. (eds.) Quantum theory and statistical physics. Vol. XA, Lectures in Theoretical Physics, New York: Gordon & Breach, 1967 p 141; see also Hagen, C.H. Nuovo Cim. 51B, 169 (1967)
28. [K1] Klaiber, B.: The Thirring model. In: Barut A. O. and Brittin W. E. (eds.) Quantum theory and statistical physics. Vol. XA, Lectures in Theoretical Physics, New York: Gordon & Breach, 1967 p 141; see also Hagen, C.H. Nuovo Cim. 51B, 169 (1967)
29. [McD] Macdonald, I.G.: Symmetric functions and Hall polynomials. Oxford Mathematical Monographs. Oxford: Clarendon Press, 1979
30. [M] Mandelstam, S.: Soliton operators for the quantized sine-Gordon equations. Phys. Rev. D11, 3026 (1975)
31. [MS] Marotta, V. and Sciarrino, A.: From vertex operators to Calogero-Sutherland models. Nucl. Phys. B476, 351 (1996)
32. [P] Polychronakos, A.P.: Nonrelativistic bosonization and fractional statistics. Nucl. Phys. B324, 597 (1989)
33. [PS] Pressley, A., and Segal, G.: Loop Groups. Oxford: Oxford Mathematical Monographs, 1986
34. [RS1] Reed, M. and Simon, B.: Methods of Modern Mathematical Physics Vol. I, New York, London: Academic Press, 1972
35. [RS2] Reed, M. and Simon, B.: Methods of Modern Mathemtical Physics. Vol. II, New York, London: Academic Press, 1975
36. [R] Ruijsenaars, S.N.M.: On Bogoliubov transformations for systems of relativistic charged particles. J. Math. Phys. 18, 517 (1977)
37. [S] Sato, M.: Soliton equations as dynamical systems on infinite dimensional Grassmanian manifolds. RIMS Kokyuroka, 439, 30-40 (1981)
38. [Se] Segal, G.B.: Unitary representations of some infinite dimensional groups. Commun. Math. Phys. 80, 301 (1981)
39. [SeW] Segal, G.B. and Wilson, G.: Loop Groups and equations of KdV type. Publ. Math I.H.E.S. 61, 5 (1985)
40. [Sk] Skyrme, T.H.R.: Particle states of a quantized meson field. Proc. Roy. Soc. A262, 237 (1961)
41. [StJ Stanley, R.P.: Some properties of Jack symmetric functions. Adv. in Math. 77, 76 (1989); see Ref. [McD].
42. [StW] Streater, R.F. and Wilde, I.F.: Fermion states of a boson field. Nucl. Phys. B24, 561 (1970)
43. [Su] Sutherland, B.: Exact results for a quantum many body problem in one-dimension. Phys. Rev. A4 2019 (1971); ibid. A5 1372 (1972); Calogero F., J. Math. Phys. 10 2197 (1969)
44. [Su] Sutherland, B.: Exact results for a quantum many body problem in one-dimension. Phys. Rev. A4 2019 (1971); ibid. A5 1372 (1972); Calogero F., J. Math. Phys. 10 2197 (1969)
45. [Su] Sutherland, B.: Exact results for a quantum many body problem in one-dimension. Phys. Rev. A4 2019 (1971); ibid. A5 1372 (1972); Calogero F., J. Math. Phys. 10 2197 (1969)