Supersymmetric Calogero–Moser–Sutherland models and Jack superpolynomials

Nuclear Physics B - Tập 606 - Trang 547-582 - 2001
Patrick Desrosiers1, Luc Lapointe2, Pierre Mathieu1
1Département de Physique, Université Laval, Québec, Canada G1K 7P4
2Department of Mathematics and Statistics, McGill University, Montréal, Québec, H3A 2K6, Canada

Tài liệu tham khảo

Calogero, 1969, Ground state of one-dimensional N body system, J. Math. Phys., 10, 2197, 10.1063/1.1664821 Calogero, 1969, Solution of a three body problem in one dimension, J. Math. Phys., 10, 2191, 10.1063/1.1664820 Calogero, 1971, Solution of the one-dimensional N body problems with quadratic and/or inversely quadratic pair potentials, J. Math. Phys., 12, 419, 10.1063/1.1665604 Moser, 1975, Three integrable Hamiltonian systems connected with isospectral deformations, Adv. Math., 16, 197, 10.1016/0001-8708(75)90151-6 Sutherland, 1971, Quantum many body problem in one dimension: ground state, J. Math. Phys., 12, 246, 10.1063/1.1665584 Sutherland, 1971, Exact results for a quantum many body problem in one dimension, Phys. Rev. A, 4, 2019, 10.1103/PhysRevA.4.2019 Sutherland, 1972, Exact results for a quantum many body problem in one dimension II, Phys. Rev. A, 5, 1372, 10.1103/PhysRevA.5.1372 Olshanetsky, 1981, Classical integrable finite dimensional systems related to Lie algebras, Phys. Rep., 71, 313, 10.1016/0370-1573(81)90023-5 Olshanetsky, 1983, Quantum integrable systems related to Lie algebras, Phys. Rep., 94, 313, 10.1016/0370-1573(83)90018-2 Airault, 1977, Rational and elliptic solutions of the Korteweg – de Vries equation and a related many-body problem, Commun. Pure Appl. Math., 30, 95, 10.1002/cpa.3160300106 Murthy, 1994, Thermodynamics of a one-dimensional ideal gas with fractionnal exclusion statistics, Phys. Rev. Lett., 73, 3331, 10.1103/PhysRevLett.73.3331 Bernard Polychronakos Prange, 1990 Azuma, 1994, Explicit relation of the quantum Hall effect and the Calogero–Sutherland model, Phys. Lett. B, 331, 107, 10.1016/0370-2693(94)90949-0 Fradkin, 1991 Ouvry Haldane, 1991, ‘Fractional statistics’ in arbitrary dimensions: a generalization of the Pauli principle, Phys. Rev. Lett., 67, 937, 10.1103/PhysRevLett.67.937 Haldane, 1988, Exact Jastrow–Gutzwiller resonating valence bond ground state of the spin 1/2 antiferromagnetic Heisenberg chain with 1/R2 exchange, Phys. Rev. Lett., 60, 635, 10.1103/PhysRevLett.60.635 Sriram Shastry, 1988, Exact solution of an S=1/2 Heisenberg antiferromagnetic chain with long ranged interactions, Phys. Rev. Lett., 60, 639, 10.1103/PhysRevLett.60.639 Haldane, 1992, Yangian symmetry of integrable quantum chains with long-range interactions and a new description of states in conformal field theory, Phys. Rev. Lett., 69, 2021, 10.1103/PhysRevLett.69.2021 Polychronakos, 1992, Exchange operator formalism for integrable systems of particles, Phys. Rev. Lett., 69, 703, 10.1103/PhysRevLett.69.703 Minahan, 1993, Integrable systems for particles with internal degrees of freedom, Phys. Lett. B, 302, 299, 10.1016/0370-2693(93)90395-X Minahan Frahm, 1993, Spectrum of a spin chain with inverse square exchange, J. Phys. A, 26, L473, 10.1088/0305-4470/26/10/002 Polychronakos, 1994, Exact spectrum of SU(n) spin chain with inverse square exchange, Nucl. Phys. B, 419, 553, 10.1016/0550-3213(94)90344-1 Fendley, 1995, Solving the 1D log gas using Jack polynomials and functional relations, J. Stat. Phys., 79, 799, 10.1007/BF02181204 Simons, 1994, Matrix models, one-dimensional fermions, and quantum chaos, Phys. Rev. Lett., 72, 64, 10.1103/PhysRevLett.72.64 Caselle, 1995, Distribution of transmission eigenvalues in disordered wires, Phys. Rev. Lett., 74, 2776, 10.1103/PhysRevLett.74.2776 Gibbons, 1999, Black holes and Calogero models, Phys. Lett. B, 454, 187, 10.1016/S0370-2693(99)00266-X D'Hoker, 1999, Seiberg–Witten theory and Calogero–Moser systems, Prog. Theor. Phys. Suppl., 135, 75, 10.1143/PTPS.135.75 Dunkl, 1989, Differential-difference operators associated to reflection groups, Trans. Am. Math. Soc., 311, 1, 10.1090/S0002-9947-1989-0951883-8 Jack, 1970, A class of symmetric polynomials with a parameter, Proc. R. Soc. Edinburgh Sect. A, 69, 1 Jack, 1972, A surface integral and symmetric functions, Proc. R. Soc. Edinburgh Sect. A, 69, 347 Cheredenik, 1995, Double affine Hecke algebras and Macdonald's conjectures, Ann. Math., 141, 191, 10.2307/2118632 Macdonald, 1996, Affine Hecke algebras and orthogonal polynomials, Astérisque, 247, 189 Fomin, 1999, Quadratic algebras, Dunkl elements and Schubert calculus, Prog. Math., 172, 147 Flower, 1993, Invariants of the Haldane–Shastry SU(N) chain, Phys. Rev. Lett., 70, 2325, 10.1103/PhysRevLett.70.2325 Bernard, 1993, Yang–Baxter equation in long range interacting system, J. Phys. A, 26, 5219, 10.1088/0305-4470/26/20/010 Stanley, 1988, Some combinatorial properties of Jack symmetric functionsl, Adv. Math., 77, 76, 10.1016/0001-8708(89)90015-7 Forrester, 1992, Selberg correlation integrals and the 1/r2 quantum many-body system, Nucl. Phys. B, 388, 671, 10.1016/0550-3213(92)90559-T Lapointe, 1995, A Rodrigues formula for the Jack polynomials and the Macdonald–Stanley conjecture, Int. Math. Res. Notices, 1995, 419, 10.1155/S1073792895000298 Lapointe, 1996, Exact operator solution of the Calogero–Sutherland model, Commun. Math. Phys., 178, 425, 10.1007/BF02099456 Awata Awata, 1995, Excited states of Calogero–Sutherland model and singular vectors of the W(N) algebra, Nucl. Phys. B, 449, 347, 10.1016/0550-3213(95)00286-2 Hikami, 1993, Infinite symmetry of the spin systems with inverse square interactions, J. Phys. Soc. Japan, 62, 4203, 10.1143/JPSJ.62.4203 Hikami, 1994, Integrable systems with long range interactions, w-infinity algebra and energy spectrum, Phys. Rev. Lett., 73, 1191, 10.1103/PhysRevLett.73.1191 Knop, 1997, A recursion and a combinatorial formula for the Jack polynomials, Invent. Math., 128, 9, 10.1007/s002220050134 Lapointe, 2000, Determinantal formula and recursion for Jack polynomials, Electron. J. Comb., 7, 467 Ujino, 1996, Rodrigues formula of the hi-Jack symmetric polynomials associated with the quantum Calogero model, J. Phys. Soc. Japan, 65, 2423, 10.1143/JPSJ.65.2423 Macdonald, 1995 Symmetric Functions and Orthogonal Polynomials, Dean Jacqueline B. Lewis Memorial Lectures presented at Rutgers University, American Mathematical Society, 1998 Lapointe, 1997, Rodrigues formula for the Macdonald polynomials, Adv. Math., 130, 261, 10.1006/aima.1997.1662 Ruijsenaars, 1986, A new class of integrable systems and its relation to solitons, Ann. Phys., 170, 370, 10.1016/0003-4916(86)90097-7 Ruijsenaars, 1987, Complete integrability of relativistic Calogero–Moser systems and elliptic function identities, Commun. Math. Phys., 110, 191, 10.1007/BF01207363 Awata, 2000, Hidden algebraic structure of the Calogero–Sutherland model, integral formula for Jack polynomial and their relativistic analog, 23 Freedman, 1990, An exactly solvable N particle system in supersymmetric quantum mechanics, Nucl. Phys. B, 344, 317, 10.1016/0550-3213(90)90364-J Witten, 1981, Dynamical breaking of supersymmetry, Nucl. Phys. B, 188, 513, 10.1016/0550-3213(81)90006-7 Witten, 1982, Constraints on supersymmetry breaking, Nucl. Phys. B, 202, 253, 10.1016/0550-3213(82)90071-2 Sriram Shastry, 1993, Superlax pairs and infinite symmetries in the 1/r2 system, Phys. Rev. Lett., 70, 4029, 10.1103/PhysRevLett.70.4029 Brink, 1993, The Calogero model: anyonic representation, fermionic extension and supersymmetry, Nucl. Phys. B, 401, 591, 10.1016/0550-3213(93)90315-G Brink, 1998, Hidden algebras of the (super) Calogero and Sutherland models, J. Math. Phys., 39, 1285, 10.1063/1.532380 Wyllard, 2000, (Super)conformal many-body quantum mechanics with extended supersymmetry, J. Math. Phys., 41, 2826, 10.1063/1.533273 Bordner, 2000, Calogero–Moser models. V: Supersymmetry and quantum lax pair, Prog. Theor. Phys., 103, 463, 10.1143/PTP.103.463 Ghosh Dargis, 1993, Nonlocal conservation laws for supersymmetric KdV equation, Phys. Lett. A, 176, 67, 10.1016/0375-9601(93)90318-T Nicolai, 1976, Supersymmetry and spin systems, J. Phys. A, 9, 1497, 10.1088/0305-4470/9/9/010 Nicolai, 1977, Extensions of supersymmetric spin systems, J. Phys. A, 10, 2143, 10.1088/0305-4470/10/12/022 Cooper, 1995, Supersymmetry and quantum mechanics, Phys. Rep., 251, 267, 10.1016/0370-1573(94)00080-M Mathieu Desrosiers