Related papers: The Euler-Riemann Gases, and Partition Identities
We examine "partition zeta functions" analogous to the Riemann zeta function but summed over subsets of integer partitions. We prove an explicit formula for a family of partition zeta functions already shown to have nice properties -- those…
Working within the path-integral framework we first establish a duality between the partion functions of two $U(1)$ gauge theories with a theta term in $d=4$ space-time dimensions. Then, after a dimensional reduction to $d=3$ dimensions we…
The partition function of gravitons with Casimir-type boundary conditions is worked out. The simplest box that allows one to achieve full analytical control consists of a slab geometry with two infinite parallel planes separated by a…
The thermodynamical partition function of the Duffin-Kemmer-Petiau theory is evaluated using the imaginary-time formalism of quantum field theory at finite temperature and path integral methods. The DKP partition function displays two…
The generating functional of two dimensional $BF$ field theories coupled to fermionic fields and conserved currents is computed in the general case when the base manifold is a genus g compact Riemann surface. The lagrangian density…
In this paper, we use basic asymptotic analysis to establish some uniform asymptotic formulas for the Fourier coefficients of the inverse of Jacobi theta functions. In particular, we answer and improve some problems suggested and…
We present a bosonized effective field theory for a 2d Fermi surface in a weak magnetic field using the coadjoint orbit approach, which was recently developed as a nonlinear bosonization method in phase space for Fermi liquids and non-Fermi…
It is commonly believed that there are only two types of particle exchange statistics in quantum mechanics, fermions and bosons, with the exception of anyons in two dimension. In principle, a second exception known as parastatistics, which…
The factorization theorem for organizing multiple electroweak boson emissions at future colliders with energy far above the electroweak scale is formulated. Taking the inclusive muon-pair production in electron-positron collisions as an…
We study the problem of particle indistinguishability for the three cases known in nature: identical classical particles, identical bosons and identical fermions. By exploiting the fact that different types of particles are associated with…
In Hawking's Euclidean path integral approach to quantum gravity, the partition function is computed by summing contributions from all possible topologies. The behavior such a sum can be estimated in three spacetime dimensions in the limit…
Some new representations of the supersymmetric transformations are derived, and the supermultiplets are introduced. Based on these representations, various formulations (equations, commutation relations, propagators, Jacobi identities,…
We present a unified and simple method for deriving work theorems for classical and quantum Hamiltonian systems, both under equilibrium conditions and in a steady state. Throughout the paper, we adopt the partitioning of the total…
Let $p_k(n)$ be given by the $k$-th power of the Euler Product $\prod _{n=1}^{\infty}(1-q^n)^k=\sum_{n=0}^{\infty}p_k(n)q^{n}$. By investigating the properties of the modular equations of the second and the third order under the Atkin…
We present explicit expressions for the central piece of a variational method developed by Shi et al. which extends variational wave functions that are efficiently computable on classical computers beyond mean-field to generalized Gaussian…
A full treatment of decoherence and dephasing effects in BEC interferometry has been developed based on using quantum correlation functions for treating interferometric effects. The BEC is described via a phase space distribution functional…
We develop the theory of copartitions, which are a generalization of partitions with connections to many classical topics in partition theory, including Rogers-Ramanujan partitions, theta functions, mock theta functions, partitions with…
We study a model of quantum mechanical fermions with matrix-like index structure (with indices $N$ and $L$) and quartic interactions, recently introduced by Anninos and Silva. We compute the partition function exactly with $q$-deformed…
We investigate multipartite entanglement in a non-interacting fermion gas, as a function of fermion separation, starting from the many particle fermion density matrix. We prove that all multiparticle entanglement can be built only out of…
We describe a method to compute thermodynamic quantities in the harmonic approximation for identical bosons and fermions in an external confining field. We use the canonical partition function where only energies and their degeneracies…