Temperature states on gauge groups
Annales de l'I.H.P. Physique théorique, Tome 57 (1992) no. 3, pp. 219-257.
@article{AIHPA_1992__57_3_219_0,
     author = {Carey, A. L. and Hannabuss, K. C.},
     title = {Temperature states on gauge groups},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     pages = {219--257},
     publisher = {Gauthier-Villars},
     volume = {57},
     number = {3},
     year = {1992},
     mrnumber = {1185334},
     zbl = {0769.46052},
     language = {en},
     url = {http://www.numdam.org/item/AIHPA_1992__57_3_219_0/}
}
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Carey, A. L.; Hannabuss, K. C. Temperature states on gauge groups. Annales de l'I.H.P. Physique théorique, Tome 57 (1992) no. 3, pp. 219-257. http://www.numdam.org/item/AIHPA_1992__57_3_219_0/

[1] H. Araki, On quasi-free states of the CAR and Bogoliubov automorphisms, Publ. Res. Inst. Math. Sci., Vol. 6, 1970, pp. 385-442. | MR | Zbl

[2] H. Araki and E.J. Woods, Representations of the canonical commutation relations describing a non-relativistic free Bose-gas, J. Math. Phys., Vol. 4, 1963, pp. 637-662. | MR

[3] H. Araki, Bogoliubov automorphisms and Fock representations of canonical anticommutation relations, in Contemporary Mathematics, Amer. Math. Soc., Vol. 62, 1987, pp. 23-141. | MR | Zbl

[4] L. Baggett and A. Kleppner, Multiplier representations of abelian groups, J. Func. Analysis, Vol. 14, 1978, pp. 299-324. | MR | Zbl

[5] O. Bratteli and D.W. Robinson, Operator algebras and quantum statistical mechanics II, Springer, New York, 1979. | MR | Zbl

[6] A.L. Carey and S.N.M. Ruijsenaars, On fermion gauge groups, current algebras and Kac-Moody algebras, Acta App. Math., Vol. 10, 1987, pp. 1-86. | MR | Zbl

[7] A.L. Carey, Some infinite dimensional groups and bundles, Publ. R.LM.S., Kyoto, Vol. 20, 1984, pp. 1103-1117. | MR | Zbl

[8] A.L. Carey, C.A. Hurst and D.M. O'Brien, Automorphisms of the canonical anticommutation relations and index theory, J. Func. Analysis, Vol. 48, 1982, pp, 360- 393. | MR | Zbl

[9] A.L. Carey and D.M. O'Brien, Absence of vacuum polarisation in Fock space, Lett. Math. Phys., Vol. 6, 1982, pp. 335-340. | MR | Zbl

[10] A.L. Carey and K.C. Hannabuss, Temperature states on loop groups theta functions and the Luttinger model, J. Func. Analysis, Vol. 75, 1987, pp. 128-160. | MR | Zbl

[11] A.L. Carey and C.A. Hurst, A note on the boson-fermion correspondence and infinite dimensional groups, Commun. Math. Phys., Vol. 98, 1985, pp. 435-448. | MR | Zbl

[12] A.L. Carey, S.N.M. Ruijsenaars and J.D. Wright, The massless Thirring model: positivity of Klauber's n-point functions, Commun. Math. Phys., Vol. 99, 1985, pp. 347- 364. | MR

[13] A. Connes, Non-commutative differential geometry, Publ. I.H.E.S., Vol. 62, 1985. | Numdam | Zbl

[14] L. Dolan and R. Jackiw, Symmetry behaviour at finite temperature, Phys. Rev., Vol. D9, 1974, pp. 3320-3329.

[15] R.G. Douglas, Banach algebra techniques in operator theory, Academic Press, New York, 1972. | MR | Zbl

[16] I.B. Frenkel, Two constructions of affine Lie algebra representations and the boson-fermion correspondence in quantum field theory, J. Func. Analysis, Vol. 44, 1981, pp. 259-357. | MR | Zbl

[17] I.B. Frenkel and V.G. Kac, Basic representations of affine Lie algebras and dual resonance models, Invent. Math., Vol. 62, 1980, pp. 23-66. | MR | Zbl

[18] K.C. Hannabuss, Representations of nilpotent locally compact groups, J. Func. Analysis, Vol. 34, 1979, pp. 164-165. | MR | Zbl

[19] K.C. Hannabuss, Characters and contact transformations, Math. Proc. Camb. Phil. Soc., Vol. 90, 1981, pp. 465-476. | MR | Zbl

[20] J. Lewis and V. Pulé, The equilibrium states of the free Boson gas, Commun. Math. Phys., Vol. 36, 1974. | MR

[21] J. Lewis, The free boson gas, in Mathematics of Contemporary Physics, R. F. STREATER Ed., Academic Press, London, 1972.

[22] L.E. Lundberg, Quasi-free second quantisation, Commun. Math. Phys., Vol. 50, 1976, pp. 103-112. | MR | Zbl

[23] G.W. Mackey, Acta Math., Vol. 99, 1958, pp. 265-311. | MR | Zbl

[24] J. Milnor, Remarks on infinite-dimensional Lie groups, Les Houches, Summer School, 1983, B. DEWITT Ed. | MR | Zbl

[25] G.K. Pedersen, C*-algebras and their automorphism groups, Academic Press, London- New York, 1979. | MR | Zbl

[26] R. Powers and E. Størmer, Free states of the canonical anticommutation relations, Commun. Math. Phys., Vol. 16, 1970, pp. 1-33. | MR | Zbl

[27] M. Reed and B. Simon, Methods of modern mathematical physics IV: scattering theory, Academic Press, New York, 1979. | MR | Zbl

[28] F. Rocca, M. Sirugue and D. Testard, Commun. Math. Phys., Vol. 19, 1970, pp. 119- 141. | MR

[29] G.B. Segal, Unitary representations of some infinite dimensional groups, Commun. Math. Phys., Vol. 80, 1981, pp. 301-362. | MR | Zbl

[30] G.B. Segal, Jacobi's identity and an isomorphism between a symmetric algebra and an exterior algebra, Oxford lectures and unpublished manuscript.

[31] G.B. Segal, Loop groups, Springer Lecture Notes in Math., Vol. III, 1984, pp. 155- 168, and A.N. Pressley and G.B. Segal, Loop groups, Oxford University Press, Oxford, 1986. | Zbl

[32] A. Van Daele and A. Verbeure, Quasi-equivalence of quasifree states on the Weyl algebra, Commun. Math. Phys., Vol. 21, 1971, pp. 171-191. | MR | Zbl