Related papers: Parafermionic derivation of Andrews-type multiple …
We describe a unified approach to calculating the partition functions of a general multi-level system with a free Hamiltonian. Particularly, we present new results for parastatistical systems of any order in the second quantized approach.…
We construct an evidently positive multiple series as a generating function for partitions satisfying the multiplicity condition in Schur's partition theorem. Refinements of the series when parts in the said partitions are classified…
The fermionic sector of the Standard Model of Elementary Particles emerges as the low energy limit of a single fermionic field freely propagating in a higher dimensional background. The local geometrical framework is obtained by enforcing…
All matter is made up of fermions -- one of the fundamental type of particles in nature. Fermions follow the Pauli exclusion principle, stating that two or more identical fermions cannot occupy the same quantum state. Antisymmetry of the…
Characters and linear combinations of characters that admit a fermionic sum representation as well as a factorized form are considered for some minimal Virasoro models. As a consequence, various Rogers-Ramanujan type identities are…
Parafermionic zero modes are non-Abelian excitations which have been predicted to emerge at the boundary of topological phases of matter. Contrary to earlier proposals, here we show that such zero modes may also exist in multilegged star…
We propose a method to construct a variety of partition identities at once. The main application is an all-moduli generalization of some of Andrews' results in [5]. The novelty is that the method constructs solutions to functional equations…
The (exclusion) statistics of parafermions is used to study degeneracies of quasiholes over the paired (or in general clustered) quantum Hall states. Focus is on the Z_k and su(3)_k/u(1)^2 parafermions, which are used in the description of…
Sum rules among superparticle masses are derived under the assumption that models beyond the MSSM are four-dimensional supersymmetric grand unified theories or five-dimensional supersymmetric orbifold grand unified theories. Sfermion sum…
The branching functions of the affine superalgebra $sl(2/1)$ characters into characters of the affine subalgebra $sl(2)$ are calculated for fractional levels $k=1/u-1$, u positive integer. They involve rational torus $A_{u(u-1)}$ and…
The algebra of multi-species anyons characterized by different statistical parameters $\nu_{ij}=e_{i}e_{j}\Phi_{i}\Phi_{j}/(2\pi)$, $i,j=1,...,n$ is redefined by basing on fermions and $k_{i}$-fermions ($k_{i}\in\bf{N}\rm /\{0,1\}$ with…
Inspired by Gansner's elegant $k$-trace generating function for rectangular plane partitions, we introduce two novel operators, $\varphi_{z}$ and $\psi_{z}$, along with their combinatorial interpretations. Through these operators, we derive…
We study cosets of the type $H_l/U(1)^r$, where $H$ is any Lie algebra at level $l$ and rank $r$. These theories are parafermionic and their characters are related to the string functions, which are generating functions for the…
The $K=4$ fractional superstring Fock space is constructed in terms of $\bZ_4$ parafermions and free bosons. The bosonization of the $\bZ_4$ parafermion theory and the generalized commutation relations satisfied by the modes of various…
In [arXiv:2212.04969], the authors stated some conjectures on the variance of certain sums of the divisor function $d_k(n)$ over number fields, which were inspired by analogous results over function fields proven in [arXiv:2107.01437].…
Tau functions expressed as fermionic expectation values are shown to provide a natural and straightforward description of a number of random processes and statistical models involving hard core configurations of identical particles on the…
We investigate the generation of entanglement in systems of identical fermions through a process involving particle detection, focusing on the implications that this kind of processes have for the concept of entanglement between fermionic…
${\mathbb Z}_2\times {\mathbb Z}_2$-graded mechanics admits four types of particles: ordinary bosons, two classes of fermions (fermions belonging to different classes commute among each other) and exotic bosons. In this paper we construct…
We use $p$-component fermions $(p=2,3,...)$ to present $(2p-2)N$-fold integrals as a fermionic expectation value. This yields fermionic representation for various $(2p-2)$-matrix models. Links with the $p$-component KP hierarchy and also…
We propose an elegant formulation of parafermionic algebra and parasupersymmetry of arbitrary order in quantum many-body systems without recourse to any specific matrix representation of parafermionic operators and any kind of deformed…