Dario Zappala

Noncommutative gravitational quantum well

We study noncommutative geometry at the quantum mechanics level by means of a model where noncommutativity of both configuration and momentum spaces is considered. We analyze how this model affects the problem of the two-dimensional gravitational quantum well and use the latest experimental results for the two lowest energy states of neutrons in the Earths gravitational field to establish an upper bound on the fundamental momentum scale introduced by noncommutativity, namely, {radical}({eta}) < or approx. 1 meV/c, a value that can be improved in the future by up to 3 orders of magnitude. We show that the configuration space noncommutativity has, in leading order, no effect on the problem. We also analyze some features introduced by the model, especially a correction to the presently accepted value of Plancks constant to 1 part in 10{sup 24}.

Ising exponents from the functional renormalisation group

We study the 3d Ising universality class using the functional renormalization group. With the help of background fields and a derivative expansion up to fourth order we compute the leading index, the subleading symmetric and antisymmetric corrections to scaling, the anomalous dimension, the scaling solution, and the eigenperturbations at criticality. We also study the cross correlations of scaling exponents, their dependence on dimensionality, and the numerical convergence of the derivative expansion. Collecting all available data from functional renormalization group studies to date, we estimate that systematic errors are in good agreement with findings from Monte Carlo simulations, ϵ-expansion techniques, and resummed perturbation theory.

Nonuniform symmetry breaking in noncommutative λ Φ 4 theory

Spontaneous symmetry breaking in noncommutative cutoff

Towards an accurate determination of the critical exponents with the renormalization group flow equations

\ensuremath{\lambda}{\ensuremath{\Phi}}^{4}

Scaling of variables and the relation between noncommutative parameters in noncommutative quantum mechanics

theory has been analyzed by using the formalism of the effective action for composite operators in the Hartree-Fock approximation. It turns out that there is no phase transition to a constant vacuum expectation of the field and the broken phase corresponds to a nonuniform background. By considering

Proper time regulator and renormalization group flow

〈\ensuremath{\varphi}(x)〉=A\mathrm{cos}(\stackrel{\ensuremath{\rightarrow}}{Q}\ensuremath{\cdot}\stackrel{\ensuremath{\rightarrow}}{x})

Improving the renormalization group approach to the quantum mechanical double well potential

the generated mass gap depends on the angles among the momenta

Quark matter in neutron stars within the Nambu-Jona-Lasinio model and confinement

\stackrel{\ensuremath{\rightarrow}}{k}

Vacuum instability as the origin of asymptotic freedom

and

Constraining and applying a generic high-density equation of state

\stackrel{\ensuremath{\rightarrow}}{Q}