arXiv subjects
Publications and source records attributed to A. Tsapalis.
Gauge-invariant equal-time correlation functions are calculated in lattice QCD within the quenched approximation and with two dynamical quark species. These correlators provide information on the shape and multipole moments of the pion, the rho, the nucleon and the $Δ$.
Using state of the art lattice techniques we investigate the static baryon potential. We employ the multi-hit procedure for the time links and a variational approach to determine the ground state with sufficient accuracy that, for distances up to $\sim 1.2$ fm, we can distinguish the $Y$- and $Δ$- Ansätze for the baryonic Wilson area law. Our analysis shows that the $Δ$-Ansatz is favoured. This result is also supported by the gauge-invariant nucleon wave function which we measure for the first time.
We present results for the static three- and four-quark potentials in SU(3) and SU(4) respectively. Using a variational approach, combined with multi-hit for the time-like links, we determine the ground state of the baryonic string with sufficient accuracy to test the $Y-$ and $Δ-$ ansätze for the baryonic Wilson area law. Our results favor the $Δ$ ansatz, where the potential is the sum of two-body terms.
We present results on the static three- and four-quark potentials in SU(3) and SU(4) respectively within quenched lattice QCD. We use an analytic multi-hit procedure for the time links and a variational approach to determine the ground state. The three- and four-quark potentials extracted are consistent with a sum of two-body potentials, possibly with a weak many-body component. The results give support to the $Δ$ ansatz for the baryonic area law.
We demonstrate how correlation functions for non-diagonal operators can be measured with the loop-cluster algorithm for quantum spin models. We introduce the U(1) quantum link model and present the construction of a cluster algorithm for the model. We further show how an improved estimator for Wilson loops can be realized with the flux-cluster algorithm.
A new non-perturbative approach to quantum field theory --- D-theory --- is proposed, in which continuous classical fields are replaced by discrete quantized variables which undergo dimensional reduction. The 2-d classical O(3) model emerges from the (2+1)-d quantum Heisenberg model formulated in terms of quantum spins. Dimensional reduction is demonstrated explicitly by simulating correlation lengths up to 350,000 lattice spacings using a loop cluster algorithm. In the framework of D-theory, gauge theories are formulated in terms of quantum links --- the gauge analogs of quantum spins. Quantum links are parallel transporter matrices whose elements are non-commuting operators. They can be expressed as bilinears of anticommuting fermion constituents. In quantum link models dimensional reduction to four dimensions occurs, due to the presence of a 5-d Coulomb phase, whose existence is confirmed by detailed simulations using standard lattice gauge theory. Using Shamir's variant of Kaplan's fermion proposal, in quantum link QCD quarks appear as edge states of a 5-d slab. This naturally protects their chiral symmetries without fine-tuning. The first efficient cluster algorithm for a gauge theory with a continuous gauge group is formulated for the U(1) quantum link model. Improved estimators for Wilson loops are constructed, and dimensional reduction to ordinary lattice QED is verified numerically.