Related papers: Free fermions, KdV charges, generalised Gibbs ense…
We provide a concise exposition with original proofs of combinatorial formulas for the 2D Ising model partition function, multi-point fermionic observables, spin and energy density correlations, for general graphs and interaction constants,…
One the base of Maxwell and Dirac equations the one biquaternionic model of electro-gravimagnetic (EGM) fields is considered. The closed system of biquaternionic wave equations is constructed for determination of free system of electric and…
We provide a concrete formula for a dual system as well as for a conjugate system of $q$-Gaussians represented on the $q$-deformed Fock space. Moreover, using this formula, we prove the existence of a free Gibbs potential and that the…
We find all the integer charge solutions to the equations for the cancellation of local gauge anomalies in a class of gauge theories which extend the Standard Model (SM) by a gauge group of the form $G \times U(1)$, where $G$ is an…
We study the eigenvalues of Dirac operators in QCD with two mass degenerate dynamical fermions. The gauge configurations have been obtained with HMC and the so-called Chirally Improved fermionic action. We compare eigenvalues obtained for…
We study quantum spin chains solvable via hidden free fermionic structures. We study the algebras behind such models, establishing connections to the mathematical literature of the so-called ``graph-Clifford'' or ``quasi-Clifford''…
Let G be any of the complex classical groups GL(n), SO(2n+1), Sp(2n), O(2n), let g denote the Lie algebra of G, and let Z(g) denote the subalgebra of G-invariants in the universal enveloping algebra U(g). We derive a Taylor-type expansion…
A geometric approach to the standard model in terms of the Clifford algebra $% C\ell_{7}$ is advanced. The gauge symmetries and charge assignments of the fundamental fermions are seen to arise from a simple geometric model involving extra…
In this paper we connect the well established discrete frame theory of generalized shift invariant systems to a continuous frame theory. To do so, we let $\Gamma_j$, $j \in J$, be a countable family of closed, co-compact subgroups of a…
Recently, a new way of deriving the moduli space of quiver gauge theories that arise on the world-volume of D3-branes probing singular toric Calabi-Yau cones was conjectured. According to the proposal, the gauge group, matter content and…
There exist chiral gauge models in two dimensions that have massless composite fermions. Two examples are presented and it is suggested that they be accepted as benchmark test-cases for generic proposals of non-perturbatively regulating…
A Yukawa-Higgs model with Ginsparg-Wilson (GW) fermions, proposed recently by Bhattacharya, Martin and Poppitz as a possible lattice formulation of chiral gauge theories, is studied. A simple argument shows that the gauge boson always…
For sigma-PWB extensions, we extend to modules the theory of Gr\"obner bases of left ideals presented in [5]. As an application, if A is a bijective quasi-commutative sigma-PWB extension, we compute the module of syzygies of a submodule of…
The G/G WZW model results from the WZW-model by a standard procedure of gauging. G/G WZW models are members of Dirac sigma models, which also contain twisted Poisson sigma models as other examples. We show how the general class of Dirac…
We study the effects on a non-universal $U(1)_{X}$ extension of the Standard Model given the alternative value obtained by the Budapest-Marseille-Wuppertal (BMW) group for the anomalous magnetic moment of the muon $g-2$. The model explains…
The Ginibre ensemble of complex random Hamiltonian matrices $H$ is considered. Each quantum system described by $H$ is a dissipative system and the eigenenergies $Z_{i}$ of the Hamiltonian are complex-valued random variables. For generic…
We consider an asymptotically free vectorial gauge theory, with gauge group $G$ and $N_f$ fermions in a representation $R$ of $G$, having an infrared (IR) zero in the beta function at $\alpha_{IR}$. We present general formulas for…
The classification of topological phases of matter in the presence of interactions is an area of intense interest. One possible means of classification is via studying the partition function under modular transforms, as the presence of an…
For a CSA group $G$ and a wide class of abelian groups $A$ we give an explicit construction for the tensor $A$-completion of $G$ using free products with amalgamations. We apply the obtained results to the study of basic properties of…
We evaluate averages involving characteristic polynomials, inverse characteristic polynomials and ratios of characteristic polynomials for a $N\times N$ random matrix taken from a $L$-deformed Chiral Gaussian Unitary Ensemble with an…