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arXiv · 0704.1355

Lowest Landau Level of Relativistic Field Theories in a Strong Background Field

Xavier Calmet·Martin Kober
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Abstract

We consider gauge theories in a strong external magnetic like field. This situation can appear either in conventional four-dimensional theories, but also naturally in extra-dimensional theories and especially in brane world models. We show that in the lowest Landau level approximation, some of the coordinates become non-commutative. We find physical reasons to formal problems with non-commutative gauge theories such as the issue with SU(N) gauge symmetries. Our construction is applied to a minimal extension of the standard model. It is shown that the Higgs sector might be non-commutative whereas the remaining sectors of the standard model remain commutative. Signatures of this model at the LHC are discussed. We then discuss an application to a dark matter sector coupled to the Higgs sector of the standard model and show that here again, dark matter could be non-commutative, the standard model fields remaining commutative.

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Xavier Calmet, Martin Kober. 2007-09-15. Lowest Landau Level of Relativistic Field Theories in a Strong Background Field. https://arxiv.org/abs/0704.1355

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