相关论文: Set partitions, fermions, and skein relations

Mixed dimensional theories have been used to describe condensed matter systems where fermions are constrained to a plane while the gauge fields they interact with remain four-dimensional. Here we investigate dynamical breaking of chiral…

We compare the structures and methods in the theory of causal fermion systems with approaches to fundamental physics based on division algebras, in particular the octonions. We find that octonions and, more generally, tensor products of…

We study noncommutative differential structures on the group of permutations $S_N$, defined by conjugacy classes. The 2-cycles class defines an exterior algebra $\Lambda_N$ which is a super analogue of the Fomin-Kirillov algebra $\CE_N$ for…

Quantum mechanical wave functions of N identical fermions are usually represented as anti-symmetric functions of ordered configurations. Leinaas and Myrheim proposed how a fermionic wave function can be represented as a function of…

We provide a new geometric representation of a family of fragmentation processes by nested laminations, which are compact subsets of the unit disk made of noncrossing chords. We specifically consider a fragmentation obtained by cutting a…

We present an application of the Grassmann algebra to the problem of the monomer-dimer statistics on a two-dimensional square lattice. The exact partition function, or total number of possible configurations, of a system of dimers with a…

We study the restrictions, the strict fixed points, and the strict quotients of the partition complex $|\Pi_n|$, which is the $\Sigma_n$-space attached to the poset of proper nontrivial partitions of the set $\{1,\ldots,n\}$. We express the…

This work investigates the invariance of the non-necessarily finite uniform dimension and related concepts for subextensions in skew polynomial rings \mbox{$ \mathbb{S}=R[ \mathbf{\mathrm{X}}; \mathbf{\alpha} , \mathbf{\delta} ]$} of…

For each positive integer $n$, let $G_n$ be the graph of integer partitions of $n$, where two partitions are adjacent if one is obtained from the other by an elementary transfer of a cell in the Ferrers diagram, followed by reordering.…

In this paper, we explain a connection between a family of free-fermionic six-vertex models and a discrete time evolution operator on one-dimensional Fermionic Fock space. The family of ice models generalize those with domain wall boundary,…

The partition function on the three-sphere of N=3 Chern-Simons-matter theories can be formulated in terms of an ideal Fermi gas. In this paper we show that, in theories with N=2 supersymmetry, the partition function corresponds to a gas of…

We determine the dispersion relations of fermionic quasiparticles in ultradegenerate plasmas by a complete evaluation of the on-shell hard-dense-loop-resummed one-loop fermion self energy for momenta of the order of the Fermi momentum and…

Let $K[X_n]$ be the commutative polynomial algebra in the variables $X_n=\{x_1,\ldots,x_n\}$ over a field $K$ of characteristic zero. A theorem from undergraduate course of algebra states that the algebra $K[X_n]^{S_n}$ of symmetric…

We examine two associative products over the ring of symmetric functions related to the intransitive and Cartesian products of permutation groups. As an application, we give an enumeration of some Feynman type diagrams arising in Bender's…

Recent research has revealed that the CRT symmetry for fermions exhibits a fractionalization distinct from the $\mathbb{Z}_2^{\mathcal{C}}\times\mathbb{Z}_2^{\mathcal{R}}\times\mathbb{Z}_2^{\mathcal{T}}$ for scalar bosons. In fact, the CRT…

We extend the existing skew polynomial representations of matrix algebras which are direct sum of matrix spaces over division rings. In this representation, the sum-rank distance between two tuples of matrices is captured by a weight…

In this article we study in detail the supersymmetric structures that underlie the system of fermionic zero modes around a superconducting cosmic string. Particularly, we extend the analysis existing in the literature on the one dimensional…

We consider the behaviour of fermions in the background of instanton-anti\-instanton type configurations. Several different physics problems, from the high energy electroweak interactions to the study of vacuum structure of QCD and of large…

We report on recent results of the QCDSF/UKQCD Collaboration on investigations of baryon structure using configurations generated with N_f=2+1 dynamical flavours of O(a) improved Wilson fermions. With the strange quark mass as an additional…

Since any string theory involves a path integration on the world-sheet metric, their partition functions are volume forms on the moduli space of genus g Riemann surfaces M_g, or on its super analog. It is well known that modular invariance…