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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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yl group. Fundamental domains of even affine and dual even affine Weyl groups, governing the argument and label symmetries of the even orbit functions, are determined. The discrete orthogonality relations are formulated on finite sets of points from the refinements of the dual weight lattices. Explicit counting formulas for the number of points of the discrete transforms are deduced. Real-valued Hartley orbit functions are introduced and all ten types of the corresponding discrete Hartley transforms are detailed.
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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