arXiv subjects
Publications and source records attributed to B. Alles.
We present a measurement of the topological susceptibility in SU(3) Yang-Mills theory through the deconfinement phase transition. An improved operator is used for the topological charge density. A drop by an order of magnitude is observed from the confined to the deconfined phase.
The coherent state path integral formulation of certain many particle systems allows for their non perturbative study by the techniques of lattice field theory. In this paper we exploit this strategy by simulating the explicit example of the diffusion controlled reaction $A+A\to 0$. Our results are consistent with some renormalization group-based predictions thus clarifying the continuum limit of the action of the problem.
The renormalization constants present in the lattice evaluation of the topological susceptibility can be non-perturbatively calculated by using the so-called heating method. We test this method for the $O(3)$ non-linear $σ$-model in two dimensions. We work in a regime where perturbative calculations are exact and useful to check the values obtained from the heating method. The result of the test is positive and it clarifies some features concerning the method. Our procedure also allows a rather accurate determination of the first perturbative coefficients.
The O(n) non-linear $σ$-model is simulated on 2-dimensional regular and random lattices. We use two different levels of randomness in the construction of the random lattices and give a detailed explanation of the geometry of such lattices. In the simulations, we calculate the mass gap for $n=3, 4$ and 8, analysing the asymptotic scaling of the data and computing the ratio of Lambda parameters $Λ_{\rm random}/Λ_{\rm regular}$. These ratios are in agreement with previous semi-analytical calculations. We also numerically calculate the topological susceptibility by using the cooling method.
We study the renormalization group behaviour of the topological charge density in full QCD on the lattice. We propose a way of extracting the necessary renormalization functions from Monte Carlo simulations.
A semi-analytic method to compute the first coefficients of the renormalization group functions on a random lattice is introduced. It is used to show that the two-dimensional $O(N)$ non-linear $σ$-model regularized on a random lattice has the correct continuum limit. A degree $κ$ of ``randomness'' in the lattice is introduced and an estimate of the ratio $Λ_{random}/Λ_{regular}$ for two rather opposite values of $κ$ in the $σ$-model is also given. This ratio turns out to depend on $κ$.
The continuum limit and scaling properties of an asymptotically free field theory regularized on a random lattice are compared with those on a regular square lattice. We work on random lattices parametrized by a degree of ``randomness'' $κ$. We show that the continuum limit exists and different $κ$ are related by a finite renormalization.
We present preliminary results on the proton spin structure function at zero momentum, in the quenched approximation. Our calculation makes use of a nonperturbative means of determining the multiplicative renormalization of the topological charge density.
We present some new three-loop results in lattice gauge theories, for the Free Energy and for the Topological Susceptibility. These results are an outcome of a scheme which we are developing (using a symbolic manipulation language), for the analytic computation of renormalization functions on the lattice.
If a new $Z'$ is discovered with a mass $\sim 1 \ TeV$ at LHC/SSC, its (rare) decays into two charged leptons plus missing transverse energy will probe the $Z'$ coupling to the lepton doublet $(ν,e)_L$ and to $W^+W^-$, allowing further discrimination among extended electroweak models.