Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2007-09-02
Physics
High Energy Physics
High Energy Physics - Theory
LaTeX, 23 pages. Preface added which explains the mathematical achievements since v1; these are presented in arXiv:1108.2184.
Scientific paper
Observing that the Hamiltonian of the renormalisable scalar field theory on 4-dimensional Moyal space A is the square of a Dirac operator D of spectral dimension 8, we complete (A,D) to a compact 8-dimensional spectral triple. We add another Connes-Lott copy and compute the spectral action of the corresponding U(1)-Yang-Mills-Higgs model. We find that in the Higgs potential the square \phi^2 of the Higgs field is shifted to \phi * \phi + const X_\mu * X^\mu, where X_\mu is the covariant coordinate. The classical field equations of our model imply that the vacuum is no longer given by a constant Higgs field, but both the Higgs and gauge fields receive non-constant vacuum expectation values.
Grosse Harald
Wulkenhaar Raimar
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