Supersymmetric Calogero–Moser–Sutherland models and Jack superpolynomials
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