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We observe that a term of the WZW-type can be added to the Lagrangian of the Poisson σ-model in such a way that the algebra of the first class constraints remains closed. This leads to a natural generalization of the concept of Poisson geometry. The resulting “WZW–Poisson” manifold M is characterized by a bivector Π and by a closed three-form H such that 1/2[Π,Π]Schouten=H,ΠΠΠ. 相似文献
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In the framework of noncommutative geometry we describe spinor fields with nonvanishing winding number on a truncated (fuzzy) sphere. The corresponding field theory actions conserve all basic symmetries of the standard commutative version (space isometries and global chiral symmetry), but due to the noncommutativity of the space the fields are regularized and they contain only a finite number of modes.Part of the Project P8916-PHY of the Fonds zur Förderung der wissenschaftlichen Forschung in Österreich. 相似文献
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C. Klimĉík 《Communications in Mathematical Physics》2001,217(1):203-228
A two dimensional gauge theory is canonically associated to every Drinfeld double. For particular doubles, the theory turns
out to be e.g. the ordinary Yang–Mills theory, the G/G gauged WZNW model or the Poisson σ-model that underlies the Kontsevich
quantization formula. We calculate the arbitrary genus partition function of the latter. The result is the q-deformation of the ordinary Yang–Mills partition function in the sense that the series over the weights is replaced by the
same series over the q-weights. For q equal to a root of unity the series acquires the affine Weyl symmetry and its truncation to the alcove coincides with the
Verlinde formula.
Received: 10 December 1999 / Accepted: 8 October 2000 相似文献
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We present a simple derivation of the spectra of the action variables of the quantized compactified Ruijsenaars-Schneider system. We obtain the spectra by combining K?hler quantization with the identification of the classical action variables as a standard toric moment map on a complex projective space. The result is consistent with the Schr?dinger quantization of the system previously developed by van Diejen and Vinet. 相似文献
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A lattice-type regularization of the supersymmetric field theories on a supersphere is constructed by approximating the ring
of scalar superfields by an integer-valued sequence of finite dimensional rings of supermatrices and by using the differencial
calculus of non-commutative geometry. The regulated theory involves only finite number of degrees of freedom and is manifestly
supersymmetric.
Received: 1 September 1996 / Accepted: 23 September 1996 相似文献
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Kazimierz W?odarczyk Dorota Klim 《Journal of Mathematical Analysis and Applications》2004,295(2):291-302
For holomorphic noncontractive maps on (not necessarily bounded) domains in complex Banach spaces, we establish the conditions guaranteeing locally uniform convergence of random iterations and study the existence of fixed points and boundary behaviour of iterations. In particular, we show that the problem, concerning the existence of the horospheres determined by Carathéodory-Reiffen-Finsler pseudometrics defined on unbounded domains, has the solution and we prove new results of type of Julia's lemma and Wolff's theorem. 相似文献
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C. Klimčík 《Letters in Mathematical Physics》1991,21(1):23-33
In and out scalar vertex operators are constructed perturbatively in a class of recently discovered UV finite nonlinear -models describing the string evolution in gravitational plane wave backgrounds. They exhibit peculiar singularities in the target space related to the focusing phenomena in such backgrounds well known from the classical and quantum gravity theories. The computation is performed up to three loops of the usual perturbation expansion and to all loops of the weak field limit. An argument is given that the vertex operator singularities should persist, even when summing up the all perturbation expansions. 相似文献
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Dynamic processes and fixed points of set-valued nonlinear contractions in cone metric spaces 总被引:1,自引:0,他引:1
Investigations concerning the existence of dynamic processes convergent to fixed points of set-valued nonlinear contractions in cone metric spaces are initiated. The conditions guaranteeing the existence and uniqueness of fixed points of such contractions are established. Our theorems generalize recent results obtained by Huang and Zhang [L.-G. Huang, X. Zhang, Cone metric spaces and fixed point theorems of contractive maps, J. Math. Anal. Appl. 332 (2007) 1467–1475] for cone metric spaces and by Klim and Wardowski [D. Klim, D. Wardowski, Fixed point theorems for set-valued contractions in complete metric spaces, J. Math. Anal. Appl. 334 (1) (2007) 132–139] for metric spaces. The examples and remarks provided show an essential difference between our results and those mentioned above. 相似文献