https://doi.org/10.1140/epjc/s10052-020-08618-z
Regular Article – Theoretical Physics
Spectral action in matrix form
1
Physics Department, American University of Beirut, Beirut, Lebanon
2
Laboratoire de Physique-ENS-CNRS, PSL Research University and Sorbonne Universités, 24 rue Lhomond, 75231, Paris Cedex 05, France
3
Institute for Mathematics, Astrophysics and Particle Physics, Radboud University Nijmegen, Heyendaalseweg 135, 6525 AJ, Nijmegen, The Netherlands
Received:
2
October
2020
Accepted:
28
October
2020
Published online:
11
November
2020
Quantization of the noncommutative geometric spectral action has so far been performed on the final component form of the action where all traces over the Dirac matrices and symmetry algebra are carried out. In this work, in order to preserve the noncommutative geometric structure of the formalism, we derive the quantization rules for propagators and vertices in matrix form. We show that the results in the case of a product of a four-dimensional Euclidean manifold by a finite space, could be cast in the form of that of a Yang–Mills theory. We illustrate the procedure for the toy electroweak model.
© The Author(s) 2020
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