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تسجيل مستخدم جديدSymplectic Quantum Mechanics and Chern-Simons Gauge Theory II: Mapping Tori of Tori
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Lisa C. Jeffrey
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We compute the semiclassical formulas for the partition functions obtained using two different Lagrangians: the Chern-Simons functional and the symplectic action functional.
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In this article we describe the relation between the Chern-Simons gauge theory partition function and the partition function defined using the symplectic action functional as the Lagrangian. We show that the partition functions obtained using these t
wo Lagrangians agree, and we identify the semiclassical formula for the partition function defined using the symplectic action functional.
The discrete orthogonality of special function families, called $C$- and $S$-functions, which are derived from the characters of compact simple Lie groups, is described in Hrivnak and Patera (2009 J. Phys. A: Math. Theor. 42 385208). Here, the result
s of Hrivnak and Patera are extended to two additional recently discovered families of special functions, called $S^s-$ and $S^l-$functions. The main result is an explicit description of their pairwise discrete orthogonality within each family, when the functions are sampled on finite fragments $F^s_M$ and $F^l_M$ of a lattice in any dimension $ngeq2$ and of any density controlled by $M$, and of the symmetry of the weight lattice of any compact simple Lie group with two different lengths of roots.
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We compute the gravitational Chern-Simons term explicitly for an adiabatic family of metrics using standard methods in general relativity. We use the fact that our base three-manifold is a quasi-regular K-contact manifold heavily in this computation.
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Three types of numerical data are provided for simple Lie groups of any type and rank. This data is indispensable for Fourier-like expansions of multidimensional digital data into finite series of $C-$ or $S-$functions on the fundamental domain $F$ o
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