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Abstract <p> We construct a Bargmann-type isomorphism defined by the one-particle part <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11232_2025_2623_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(H\)</EquationSource> </InlineEquation> of the Fock space <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11232_2025_2623_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="39" /> </InlineMediaObject> <EquationSource Format="TEX">\(\Gamma(H)\)</EquationSource> </InlineEquation> for an infinite-dimensional space <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11232_2025_2623_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(H\)</EquationSource> </InlineEquation> with involution. The formulas obtained also make sense in the case <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11232_2025_2623_Article_IEq4.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="88" /> </InlineMediaObject> <EquationSource Format="TEX">\(\dim H&lt;\infty\)</EquationSource> </InlineEquation> and are closely related to the Segal–Bargmann space. Central to the construction is the notion of a shift-invariant distribution in the case of an infinite-dimensional domain of test functions. </p>

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Explicit Bargmann-type isomorphism between Berezin and Smolyanov representations of bosonic Fock spaces

  • 期刊论文

  • 发表日期：

    2025年4月25日

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  • N. N. Shamarov,
  • M. V. Shamolin

摘要

Abstract

We construct a Bargmann-type isomorphism defined by the one-particle part \(H\) of the Fock space \(\Gamma(H)\) for an infinite-dimensional space \(H\) with involution. The formulas obtained also make sense in the case \(\dim H<\infty\) and are closely related to the Segal–Bargmann space. Central to the construction is the notion of a shift-invariant distribution in the case of an infinite-dimensional domain of test functions.