arXiv subjects
Publications and source records attributed to Gino N. J. Ananos.
In this work we use the lattice regularization method to study the behavior of the six point renormalized coupling constant defined at zero momentum for the three-dimensional $ϕ^4 $ theory in the intermediate and strong coupling domain. The result is in good agreement with the corresponding study in the Ising limit.
We study the behavior of the renormalized sextic coupling at the intermediate and strong coupling regime for the $ϕ^4 $ theory defined in $d=2$-dimension. We found a good agreement with the results obtained by the field-theoretical renormalization-group in the Ising limit. In this work we use the lattice regularization method.
The existence of anomalous symmetry-breaking solutions of the SO(2,1) commutator algebra is explicitly extended beyond the case of scale-invariant contact interactions. In particular, the failure of the conservation laws of the dilation and special conformal charges is displayed for the two-dimensional inverse square potential. As a consequence, this anomaly appears to be a generic feature of conformal quantum mechanics and not merely an artifact of contact interactions. Moreover, a renormalization procedure traces the emergence of this conformal anomaly to the ultraviolet sector of the theory, within which lies the apparent singularity.
The structure of the commutator algebra for conformal quantum mechanics is considered. Specifically, it is shown that the emergence of a dimensional scale by renormalization implies the existence of an anomaly or quantum-mechanical symmetry breaking, which is explicitly displayed at the level of the generators of the SO(2,1) conformal group. Correspondingly, the associated breakdown of the conservation of the dilation and special conformal charges is derived.