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<p>In this work, we introduce an interesting method for determining the annihilation and creation operators in physical systems. This method is based on the Berezin integral mapping from the phase space of a system to the associated Hilbert subspace, and on the effect of the Thiemann complexifier on this mapping. Although the method is general, we apply it to two specific cases: a harmonic oscillator with phase space “<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10773_2025_6130_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="52" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb {C} \simeq \mathbb {R}^2\)</EquationSource> </InlineEquation>” , and a particle moving in a circle with phase space “<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10773_2025_6130_Article_IEq2.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="51" /> </InlineMediaObject> <EquationSource Format="TEX">\(S^{1}\times \mathbb {R}\)</EquationSource> </InlineEquation>”.</p>

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Annihilation and Creation Operators in the Berezin–Thiemann Quantization Framework

  • 期刊论文

  • 发表日期：

    2025年10月13日

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  • A. Rabeie

摘要

In this work, we introduce an interesting method for determining the annihilation and creation operators in physical systems. This method is based on the Berezin integral mapping from the phase space of a system to the associated Hilbert subspace, and on the effect of the Thiemann complexifier on this mapping. Although the method is general, we apply it to two specific cases: a harmonic oscillator with phase space “ \(\mathbb {C} \simeq \mathbb {R}^2\) ” , and a particle moving in a circle with phase space “ \(S^{1}\times \mathbb {R}\) ”.