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arXiv · 2206.02638

Momentum Gauge Fields and Non-Commutative Space-Time

E. Guendelman·D. Singleton
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Abstract

In this work we present a gauge principle that starts with the momentum space representation of the position operator (${\hat x}_i = i \hbar \frac{\partial}{\partial p_i}$) rather than starting with the position space representation of the momentum operator (${\hat p}_i = -i \hbar \frac{\partial}{\partial x_i}$). We discuss some simple examples with this new type of gauge theory: (i) analog solutions from ordinary gauge theory in this momentum gauge theory, (ii) Landau levels using momentum gauge fields, (iii) the emergence of non-commutative space-times from the momentum gauge fields. We find that the non-commutative space-time parameter can be momentum dependent, and one can construct a model where space-time is commutative at low momentum but becomes non-commutative at high momentum.

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E. Guendelman, D. Singleton. 2022-06-06. Momentum Gauge Fields and Non-Commutative Space-Time. https://doi.org/10.3390/sym15010126

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