A numerical approach to harmonic noncommutative spectral field theory. (English) Zbl 1247.81546
Summary: We present a first numerical investigation of a noncommutative 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 can be quite different from the original spectral model.
MSC:
| 81T75 | Noncommutative geometry methods in quantum field theory |
| 81T80 | Simulation and numerical modelling (quantum field theory) (MSC2010) |
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
| 65C05 | Monte Carlo methods |
| 82B30 | Statistical thermodynamics |
| 82B26 | Phase transitions (general) in equilibrium statistical mechanics |
| 53D17 | Poisson manifolds; Poisson groupoids and algebroids |
| 81V25 | Other elementary particle theory in quantum theory |
Keywords:
noncommutative geometry; spectral action; noncommutative quantum field theory; Yang-Mills-Higgs models; numerical simulation; phase transitionsReferences:
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