arXiv subjects

Bernardino Spisso

Publications and source records attributed to Bernardino Spisso.

4 recordsLinked to original sources

arXiv2012

Noncommutative Field Theory: Numerical Analysis with the Fuzzy Disc

The fuzzy disc is a discretization of the algebra of functions on the two dimensional disc using finite matrices which preserves the action of the rotation group. We define a $φ^4$ scalar field theory on it and analyze numerically for three different limits for the rank of the matrix going to infinity. The numerical simulations reveal three different phases: uniform and disordered phases already the present in the commutative scalar field theory and a nonuniform ordered phase as a noncommutative effects. We have computed the transition curves between phases and their scaling. This is in agreement with studies on the fuzzy sphere, although the speed of convergence for the disc seems to be better. We have performed also three the limits for the theory in the cases of the theory going to the commutative plane or commutative disc. In this case the theory behaves differently, showing the intimate relationship between the nonuniform phase and noncommutative geometry.

hep-th↗

arXiv2012

A numerical approach to harmonic non-commutative spectral field theory

We present a first numerical investigation of a non-commutative gauge theory defined via the spectral action for Moyal space with harmonic propagation. This action is approximated by finite matrices. Using Monte Carlo simulation we study various quantities such as the energy density, the specific heat density and some order parameters, varying the matrix size and the independent parameters of the model. We find a peak structure in the specific heat which might indicate possible phase transitions. However, there are mathematical arguments which show that the limit of infinite matrices is very different from the original spectral model.

math-ph↗

arXiv2011

First numerical approach to a Grosse-Wulkenhaar model

A numerical investigation of a non-commutative field theory defined via the spectral action principle is conducted. The construction of this triple relies on an 8-dimensional Clifford algebra. Following to the standard procedure of non-commutative geometry, the spectral action is computed for the product of the triple (A,H,D) with a matrix-valued spectral triple. Using Monte Carlo simulation we study various quantities such as the energy density, the specific heat density and some order parameters varying the matrix size and the independent parameters of the model.

hep-th↗

arXiv2011

A numerical approach to harmonic non-commutative spectral field theory

The object of this work is the numerical investigation of a non-commutative field theory defined via the spectral action principle. The Starting point is a spectral triple (A,H,D) referred to as harmonic. The construction of these data relies on an 8-dimensional Clifford algebra. The spectral action is computed for the product of the triple (A,H,D) with a matrix-valued spectral triple. Renormalization theory associates to the spectral action a probability measure. Its associated correlation functions define then a field theory. In the perturbative approach this measure is constructed as a formal power series. This requires explicit knowledge of the solutions of the Euler-Lagrange equations. For the model under consideration, it turns out impossible to obtain these solutions. An alternative approach consists in a discretization of all variables and a numerical investigation of the behavior of the correlation functions when the discretization becomes finer. Despite the complexity of the approximated spectral action, some reliable numerical results are obtained, showing that a numerical treatment of this kind of models in the Moyal matrix basis is possible.

math-ph↗