Related papers: Discrete Dirac Operators, Critical Embeddings and …
Partition functions are an important research object in combinatorics and mathematical physics [Barvinok, 2016]. In this work, we consider the partition function of the Ising antiferromagnet on random regular graphs and characterize its…
We solve for spectrum, obtain explicitly and study group properties of eigenfunctions of Dirac operator on the Riemann sphere $S^2$. The eigenvalues $\lambda$ are nonzero integers. The eigenfunctions are two-component spinors that belong to…
A well-defined chirally split functional integrating the 2D chirally split diffeomorphism anomaly is exhibited on an arbitrary compact Riemann surface without boundary. The construction requires both the use of the Beltrami parametrisation…
With a view towards higher-spin applications, we study the partition function of a free complex fermion in 2d CFT, restricted to the neutral (zero fermion number) sector. This restriction leads to a partial theta function with a…
Let $G$ be a non-compact connected semisimple real Lie group with finite center. Suppose $L$ is a non-compact connected closed subgroup of $G$ acting transitively on a symmetric space $G/H$ such that $L\cap H$ is compact. We study the…
Emil Artin defined a zeta function for algebraic curves over finite fields and made a conjecture about them analogous to the famous Riemann hypothesis. This and other conjectures about these zeta functions would come to be called the Weil…
Let $\sigma$ denote an endomorphism of a smooth algebraic group $G$ over the algebraic closure of a finite field, and assume all iterates of $\sigma$ have finitely many fixed points. Steinberg gave a formula for the number of fixed points…
Based on the relation to random matrix theory, exact expressions for all microscopic spectral correlators of the Dirac operator can be computed from finite-volume partition functions. This is illustrated for the case of $SU(N_c)$ gauge…
We discuss the dynamics of the Dirac fermions in the general strong gravitational and electromagnetic fields. We derive the general Hermitian Dirac Hamiltonian and transform it to the Foldy-Wouthuysen representation for the spatially…
We address in this work the question of the discretization of two-dimensional periodic Dirac Hamiltonians. Standard finite differences methods on rectangular grids are plagued with the so-called Fermion doubling problem, which creates…
In this paper we show how to construct a Dirac operator on a lattice in complete analogy with the continuum. In fact we consider a more general problem, that is, the Dirac operator over an abelian finite group (for which a lattice is a…
The goal of this paper is to exhibit a deep relation between the partition function of the Ising model on a planar trivalent graph and the generating series of the spin network evaluations on the same graph. We provide respectively a…
We study the problem of approximating the partition function of the ferromagnetic Ising model in graphs and hypergraphs. Our first result is a deterministic approximation scheme (an FPTAS) for the partition function in bounded degree graphs…
We discuss the two-dimensional isotropic antiferromagnet in the framework of gauge invariance. Gauge invariance is one of the most subtle useful concepts in theoretical physics, since it allows one to describe the time evolution of complex…
Proofs of two statements are provided in this paper. First, the authors prove that the formalism of the pseudo-Hermitian quantum mechanics allows describing the Dirac particles motion in arbitrary stationary gravitational fields. Second, it…
Our previous results on the nonperturbative calculations of the mean current and of the energy-momentum tensor in QED with the T-constant electric field are generalized to arbitrary dimensions. The renormalized mean values are found; the…
We consider quantum rings realized in materials where the dynamics of charge carriers mimics that of two-dimensional (2D) Dirac electrons. A general theoretical description of the ring-subband structure is developed that applies to a range…
The Dirac delta function and the Feynman propagator of the harmonic oscillator are found by a simple calculation using Fock Bargmann space and the generating function of the harmonic oscillator. With help of the Schwinger generating…
Lattice formulation of a fermionic field theory defined on a randomly triangulated compact manifold is discussed, with emphasis on the topological problem of defining spin structures on the manifold. An explicit construction is presented…
We continue to investigate the physical interpretation of the Riemann zeta function as a FZZT brane partition function associated with a matrix/gravity correspondence begun in arxiv:0708.0645. We derive the master matrix of the $(2,1)$…