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<p>In this paper, we systematically investigate the Heisenberg-Pauli-Weyl uncertainty principle for free metaplectic transformation, as well as metaplectic operators. Specifically, we obtain two different types of the uncertainty principle for free metaplectic transformations in terms of the so-called phase derivative, one of which can be generalized to the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L^p\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mi>p</mi> </msup> </math></EquationSource> </InlineEquation>-case with <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(1\le p\le 2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>1</mn> <mo>≤</mo> <mi>p</mi> <mo>≤</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>. The obtained results are valid not only for free metaplectic transformations but also for general metaplectic operators. In particular, we point out that our results are closely related to those given in [<CitationRef CitationID="CR11">11</CitationRef>], and the relationship should be new and not exactly given in the existing literature.</p>

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Uncertainty Principles for Free Metaplectic Transformation and Associated Metaplectic Operators

  • 期刊论文

  • 发表日期：

    2026年5月5日

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  • Ping Liang,
  • Pei Dang,
  • Weixiong Mai

摘要

In this paper, we systematically investigate the Heisenberg-Pauli-Weyl uncertainty principle for free metaplectic transformation, as well as metaplectic operators. Specifically, we obtain two different types of the uncertainty principle for free metaplectic transformations in terms of the so-called phase derivative, one of which can be generalized to the \(L^p\) L p -case with \(1\le p\le 2\) 1 ≤ p ≤ 2 . The obtained results are valid not only for free metaplectic transformations but also for general metaplectic operators. In particular, we point out that our results are closely related to those given in [11], and the relationship should be new and not exactly given in the existing literature.