Related papers: Integrals over SU(N)
Let $\gamma$ denote imaginary parts of complex zeros of the Riemann zeta-function $\zeta(s)$. Certain sums over the $\gamma$'s are evaluated, by using the function $G(s) = \sum_{\gamma>0}\gamma^{-s}$ and other techniques. Some integrals…
We discuss factorization of the hypergeometric-type difference equations on the uniform lattices and show how one can construct a dynamical algebra, which corresponds to each of these equations. Some examples are exhibited, in particular,…
For pure SU(2) lattice gauge theory at finite T, by the help of the cooling method, we search for classical (approximate) solutions having non-trivial holonomy at the spatial boundary. We identify various typical objects and provide their…
Equations over linearly ordered semilattices are studied. For any equation $t(X)=s(X)$ we find irreducible components of its solution set and compute the average number of irreducible components of all equations in $n$ variables.
The Hultman numbers enumerate permutations whose cycle graph has a given number of alternating cycles (they are relevant to the Bafna-Pevzner approach to genome comparison and genome rearrangements). We give two new interpretations of the…
The properties of SU(1,1) SU(2),SU(2,1) and SU(3) have often been used in quantum optics. In this paper we demonstrate the use of these symmetries. The group properties of SU(1,1) SU(2), and SU(2,1) are used to find the transition…
We revise the $SU(N_c)$, $N_c=3,4,6$, lattice data on pure gauge theories at finite temperature by means of a quasi-particle approach. In particular we focus on the relation between the quasi-particle effective mass and the order of the…
The total perturbative contribution to the free-energy of hot SU(3) gauge theory is argued to lie significantly higher than the full result obtained by lattice simulations. This then suggests the existence of large non-perturbative…
A method is presented for calculating the Lie point symmetries of a scalar difference equation on a two-dimensional lattice. The symmetry transformations act on the equations and on the lattice. They take solutions into solutions and can be…
We extend the definition of L\"uscher's lattice topological charge to the case of $4$d $SU(N)$ gauge fields coupled with $\mathbb{Z}_N$ $2$-form gauge fields. This result is achieved while maintaining the locality, the $SU(N)$ gauge…
We develop a formula for tautological integrals over geometric subsets of the Hilbert scheme of points on complex manifolds. As an illustration of the theory, we derive a new iterated residue formula for the number of nodal curves in…
We calculate the free energy of SU(N) gauge theories on the lattice, to three loops. Our result, combined with Monte Carlo data for the average plaquette, gives a more precise estimate of the gluonic condensate.
Lattice QCD calculations have been conducted using large-scale classical computers based on the Lagrangian formalism of field theory for the past 40 years. On the other hand, the advent of quantum computers has brought increasing attention…
The definition and computation of the topological susceptibility in non-abelian gauge theories is complicated by the presence of non-integrable short-distance singularities. Recently, alternative representations of the susceptibility were…
We construct the generator of hamiltonian gauge symmetries in a 2+1 dimensional massive theory of gravity, proposed recently, through a systematic off-shell algorithm. Using a field dependant map among gauge parameters we show that the…
We study a five-dimensional pure SU(2) gauge theory formulated on the orbifold and discretized on the lattice by means of Monte Carlo simulations. The gauge symmetry is explicitly broken to U(1) at the orbifold boundaries. The action is the…
We give an introduction to the calculation of path integrals on a lattice, with the quantum harmonic oscillator as an example. In addition to providing an explicit computational setup and corresponding pseudocode, we pay particular…
The adjoint SU(2) lattice gauge theory in 3+1 dimensions with the Wilson plaquette action modified by a Z(2) monopole suppression term is reinvestigated with special emphasis on the existence of a finite-temperature phase transition…
In this note, I revisit integrals over $\SU(N)$ of the form $ \int DU\, U_{i_1j_1}\cdots U_{i_pj_p}\Ud_{k_1l_1}\cdots \Ud_{k_nl_n}$. While the case $p=n$ is well known, it seems that explicit expressions for $p=n+N$ had not appeared in the…
We develop a method for calculating the Lyapunov characteristic exponents of lattice gauge theories. The complete Lyapunov spectrum of SU(2) gauge theory is obtained and Kolmogorov-Sinai entropy is calculated. Rapid convergence with lattice…