Orbifolds,Hopf algebras,and the Moonshine

We describe the modular properties and fusion rules of holomorphic orbifold models by Hopf algebraic techniques, using the representation theory of the orbifold quantum group. We apply this theory to the construction of generalized Thompson series, and discuss its connections with Moonshine.     

Symmetric Products,Permutation Orbifolds and Discrete Torsion

Symmetric product orbifolds, i.e. permutation orbifolds of the full symmetric group S _n are considered by applying the general techniques of permutation orbifolds. Generating functions for various quantities, e.g. the torus partition functions and the Klein-bottle amplitudes are presented, as well as a simple expression for the discrete torsion coefficients.     

Orbifolds and Topological Defects

We study orbifolds of two-dimensional topological field theories using defects. If the TFT arises as the twist of a superconformal field theory, we recover results on the Neveu–Schwarz and Ramond sectors of the orbifold theory, as well as bulk-boundary correlators from a novel, universal perspective. This entails a structure somewhat weaker than ordinary TFT, which however still describes a sector of the underlying conformal theory. The case of B-twisted Landau–Ginzburg models is discussed in detail, where we compute charge vectors and superpotential terms for B-type branes. Our construction also works in the absence of supersymmetry and for generalised “orbifolds” that need not arise from symmetry groups. In general, this involves a natural appearance of Hochschild (co)homology in a 2-categorical setting, in which among other things we provide simple presentations of Serre functors and a further generalisation of the Cardy condition.     

Coherent states and partition function

The concept of coherent states for arbitrary Lie group is suggested as a tool for explicitly obtaining an integral representation of the partition function, whenever the Hamiltonian has a dynamical group. Two examples are thoroughly discussed: the case of the nilpotent group of Weyl related to a generic many-body problem with two-body interactions, and the case of SU(1, 1)() relevant for a superfluid system.     

Gerbes over Orbifolds and Twisted K-Theory

In this paper we construct an explicit geometric model for the group of gerbes over an orbifold X. We show how from its curvature we can obtain its characteristic class in H³(X) via Chern-Weil theory. For an arbitrary gerbe , a twisting K_orb(X) of the orbifold K-theory of X is constructed, and shown to generalize previous twisting by Rosenberg [28], Witten [35], Atiyah-Segal [2] and Bowknegt et. al. [4] in the smooth case and by Adem-Ruan [1] for discrete torsion on an orbifold.The first author was partially supported by the National Science Foundation and Conacyt-México     

Solitons in Affine and Permutation Orbifolds

We consider properties of solitons in general orbifolds in the algebraic quantum field theory framework and constructions of solitons in affine and permutation orbifolds. Under general conditions we show that our construction gives all the twisted representations of the fixed point subnet. This allows us to prove a number of conjectures: in the affine orbifold case we clarify the issue of fixed point resolutions; in the permutation orbifold case we determine all irreducible representations of the orbifold, and we also determine the fusion rules in a nontrivial case, which imply an integral property of chiral data for any completely rational conformal net.Supported in part by NSF.Supported in part by GNAMPA-INDAM and MIUR.Supported in part by NSF.     

Rotational partition function of methane

An analytical formula for the quantum-mechanical rotational partition function of tetrahedral XY₄ molecules is shown to be accurate to better than 1% for methane at temperatures T ≥ 40°K.     

Strutinsky smoothing and the partition function approach

The Strutinsky shell correction is analytically shown to be equivalent to the shell correction obtained from the partition function approach, provided certain restrictions on the Strutinsky smoothing parameter are met.     

Hyperbolicity of partition function and quantum gravity

We study a geometry of the partition function which is defined in terms of a solution of the five-term relation. It is shown that the 3-dimensional hyperbolic structure or the Euclidean AdS₃ naturally arises in the classical limit of this invariant. We discuss that the oriented ideal tetrahedron can be assigned to the partition function of string.     

Anomaly in the lattice partition function

The lattice partition function Z(T)=σ_(Si) exp(−H/k_BT), where H, k_B and T are the Hamiltonian of the system, the Boltzmann constant and the absolute temperature, respectively, leads to a vanishing spontaneous magnetisation for all temperatures, independently of the lattice considered. This feature is related to the symmetry breaking in these systems. In comparing this relation to the well-known partition function Z(T)=σ_n exp(−E_n/k_BT) where E_n is energy, we observe an incompatibility which could be the reason that this partition function leads to a vanishing spontaneous magnetisation.     

Densities of states and the complex partition function

A Fourier transform technique based on the method of Dubner and Abate is here applied to the energy-level density problem for quantum partition functions. It is shown that, for typical molecular systems at realistic energies, the integrated level count, W(E), is obtainable to near ‘spectroscopic’ accuracy and in reasonable computing time. A smooth Fourier resolution of the simple density function, g(E), is likewise possible. Though somewhat less economical, this procedure entirely removes the slight discrepancies found in the steepest-descent method and can reasonably be claimed to dispose once and for all of the problem of quantum level-density computations in molecular rate theory.     

自由粒子配分函数的zeta函数正规化处理

zeta函数正规化技术在现代物理中有着重要应用.本文探讨其在大学物理中的应用,即采用zeta函数正规化处理自由粒子的配分函数,并导出相应的热力学量.考虑粒子被囚禁在体积有限的立方容器中,给出了热力学量在有限体积下的一级修正.     

The partition function of a two-dimensional plasma

The stability of the canonical partition function of a two-dimensional classical plasma with respect to condensation phenomena is discussed.