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Following the construction of the projection operators on T2 presented by Gopakumar, Headrick and Spradlin, we construct a set of projection operators on the integral noncommutative orbifold T2/ G( G= Z N, N=2, 3, 4, 6) which correspond to a set of solitons on T2/ Z N in noncommutative field theory. In this way, we derive an explicit form of projector on T2/ Z6 as an example. We also construct a complete set of projectors on T2/ Z N by series expansions for integral case. [ABSTRACT FROM AUTHOR]

We study the algebra A[sub n], the basis of the Hilbert space H[sub n] in terms of θ functions of the positions of n solitons. Then we embed the Heisenberg group as the quantum operator factors in the representation of the transfer matrices of various integrable models. Finally we generalize our result to the generic θ case. [ABSTRACT FROM AUTHOR]

The quantum and classical algebras connected with the Zn-symmetric elliptic solution of the Yang–Baxter equation are derived; their structure constants and the relations between the quantum algebra and the classical one are investigated in detail. Moreover, the trigonometric limit of these algebras is worked out. [ABSTRACT FROM AUTHOR]

In this paper, it is the intent to apply the Riemann–Hilbert transformation developed by Hauser and Ernst [J. Math. Phys. 21, 1126, 1418 (1980)] in providing a new representation of the Virasoro group. It is found that the Geroch group that acts on the solution space of the Einstein field equations is extended to the semidirect product of the Virasoro and Kac–Moody groups; also, the relationship between the infinitesimal transformation given previously [B. Y. Hou and W. Li, Lett. Math. Phys. 13, 1 (1987); J. Phys. A 20, L897 (1987); W. Li, Phys. Lett. A 129, 301 (1988)] and the infinitesimal Riemann–Hilbert transformation is pointed out. Finally, it is shown that the well-known Neugebauer–Backlund transformation can be derived from the Riemann–Hilbert transformation. [ABSTRACT FROM AUTHOR]

Using the natural connection form on a principal bundle P(M,G) and the bundle [ATOTHER]@FA[/ATOTHER]([ATOTHER]@FA[/ATOTHER]/G,G) a systematic derivation of the double-cohomological series constituted by the exterior differential d on space-time M and arbitrary, horizontal, and vertical variations in connection space is given. The relationship between these cohomologies and the family index theorem is clarified. The formalism is then used to analyze Abelian gauge structure inside non-Abelian gauge theory. The pertinent functional U(1) connection form, curvature form, and three-form ‘‘curvature’’ are identified and computed, and are related to the θ vacuum, anomalous commutation relation, and Jacobi identity, respectively. Some of the results differ from those obtained by Wu and Zee [Nucl. Phys. B 258, 157 (1985)] and Niemi and Semenoff [Phys. Rev. Lett. 55, 227 (1985)] and the results of this paperrecover theirs under certain conditions. Finally the generalization of the formalism to a nontrivial principal bundle by introduction of a fixed background connection form is discussed. [ABSTRACT FROM AUTHOR]