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I am wondering if it makes any sense to non-minimally (say, Pauli-like) couple an external gauge field with a non-relativistic scalar field: \begin{equation} p_\mu \rightarrow p_\mu - e A_\mu + \epsilon_{\mu \nu \rho}F^{\nu \rho} , \end{equation}

here $F^{\nu \rho}$ is the electromagnetic tensor, written for two spatial dimensions (note that I am not referring to the gravitational gauge field). Of course, one may calculate some observables in such a scenario, however, does there exist any experimental paradigm where such calculations can be verified? I presume that, if such couplings can be realized, many important effects related to the breaking of time-reversal symmetry can be realized without applying any magnetic field.

Quillo
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Jon Snow
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1 Answers1

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In my understanding, the Pauli interaction is not 'required' if one just invoke the gauge principle minimally. It is also nonrenormalizable by the way. There are mathematical arguments of why it should be forbidden, e.g. in hep-th/0005191. If that doesn't bother you, you can also try to check its phenomenological consequences, for example the anomalous magnetic dipole moment as in hep-th/9903179 and then compare it with the muon/electron g-2 experiments. Besides, there are studies on generating fractional spin in terms of Pauli interactions.

Kyle Kanos
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C. Sun
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