Momentum Gauge Fields and Non-Commutative Space-Time

• URL: http://arxiv.org/abs/2206.02638v2
• Date: Sat, 24 Dec 2022 00:20:14 GMT
• Title: Momentum Gauge Fields and Non-Commutative Space-Time
• Authors: E. Guendelman and D. Singleton
• Abstract summary: We present a gauge principle that starts with the momentum space representation of the position operator ($hat x_i = i hbar fracpartialpartial p_i$) 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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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