By Zhang M. L. (Ed)
This volumes offers a complete assessment of interactions among differential geometry and theoretical physics, contributed through many best students in those fields. The contributions promise to play a huge position in selling the advancements in those fascinating components. in addition to the plenary talks, the assurance comprises: types and similar themes in statistical physics; quantum fields, strings and M-theory; Yang-Mills fields, knot conception and similar issues; K-theory, together with index conception and non-commutative geometry; replicate symmetry, conformal and topological quantum box conception; improvement of integrable platforms; and random matrix concept"
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Extra resources for Differential Geometry and Physics: Proceedings of the 23rd International Conference of Differential Geometric Methods in Theoretical Physics
35. B. B. Zamolodchikov, Ann. Phys. 120 (1979) 253. 36. Y. L. Ge, K. Xue, Comm. Math. Phys. 136 (1991) 195. 37. L. Ge, K. Xue, Phys. Lett. A. 120 (1991) 266. 38. A. Belavin, Phys. Lett. B 283 (1992) 67. 39. R. R. Werthamer, Phys. Rev. 131 (1963) 1553. 40. C M . L. Ge and K. Xue, Directional Transitions in spin systems and representations of Y(sl(2)), Nankai preprint, APCTP-98-026. 41. J. Erickson, D. Levron, W. Happer, S. Kadlecek, B. W. G. Walker, Phys. Rev. Lett. 85 (2000) 4237. 42. W. Happer, Degeneracies of the Hamiltonian x(K+ 1/2)SZ+K- S, preprint, Princeton University, November, 2000.
10) iy£j where /ij and h (not Planck constant) are arbitrary parameters. 8). When % = 1,2, Y(SU(2)) makes transition between spin singlet and triplet. Now Y(SU(3)) transits SU(3) singlet and Octet. For instance, setting = \du), \n°) = 4=(l««> - \dd}), \K~) = \du), \K°) = \ds), V2 1 \uu) + \dd) + \ss)). 11) | O Special interest is the following. -M. -L. Ge, K. -B. Zhang |KJ> JK°> 1+ 1 0 * o I- *|7r+> " k°> \v°) i / f |K-> |K°) Fig. 1. , (I± + fl±)\rf' > = ±2V3/i|7r ± >, (17+ + / 1 7 + ) | / > = —2v/3/i|-Kr° >, (CT_ + fU-)\r)0' > = 2V3/i|^° >, (V± + /V±)|T7 0 ' > = -2v / 3/i|if :F >, (h + fh)\v°' >= -V6h\n° >, (ls + fh)\r?
Looking at J = / x i S 1 + M 2 S 2 - i ( / i i + / i 2 ) ( S i + S 2 ) + 7 ( S 1 + S 2 ) + 2 A S 1 x S 2 . 5) When 7 = | , /x2 — Mi = cosa and A = ^sina, it reduces to the form in the interacting picture. Putting Sx + S 2 = S, 2A = - - ( / i is not Plank constant). 6) In accordance with the convention we have 2 h 1 J = 7 S + J2MiSi + - S i x S 3 - -(/ii + M2)S = 7 S + Y. 7) i=\ Since J —• ^S + J still satisfies Yangian relations, it is natural to appear the term 7S. The interacting Hamiltonian then reads HT(t) = - 7 B ( t ) • S - B(i) • Y.
Differential Geometry and Physics: Proceedings of the 23rd International Conference of Differential Geometric Methods in Theoretical Physics by Zhang M. L. (Ed)