The Heisenberg Uncertainty Principle and Its Higher-Dimensional Analogues Through Wigdersons’ Method

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发表日期：

2025年3月11日

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Yiyu Tang

摘要

This article investigates whether the method discovered recently by Avi Wigderson and Yuval Wigderson can be used to prove the Heisenberg Uncertainty Principle in higher-dimensional spaces $\mathbb {R}^d$ $R^{d}$ , and to accurately determine how the constant depends on the dimension d. Our first result is an affirmative answer to this question. Building upon this, we also obtain new uncertainty principles from Wigdersons’ method, showing that the method’s effectiveness not only in deriving the Heisenberg Uncertainty Principle in $\mathbb {R}^d$ $R^{d}$ but also in deriving several of its extensions. Finally, we give some comments on the generalization of our theorems to other operators.