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<p>Using representation–theoretic techniques associated with the <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathfrak {su}(1,1)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="fraktur">su</mi> <mo stretchy="false">(</mo> <mn>1</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> symmetry algebra, we construct Perelomov coherent states for the Dunkl–Klein–Gordon equation in its canonical form, which is free of first–order Dunkl derivatives. Our analysis is restricted to the even–parity sector and to the regime where the curvature constant <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\( R \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>R</mi> </math></EquationSource> </InlineEquation> is much smaller than the system’s kinetic energy. The equation under consideration emerges from a matrix–operator framework based on Dirac gamma matrices and a universal length scale that encodes the curvature of space via the Dunkl operator, thereby circumventing the need for spin connections in the Dirac equation.</p>

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SU(1, 1) Coherent States for the Dunkl–Klein–Gordon Equation in its Canonical Form

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • M. Salazar–Ramírez,
  • J. A. Martínez–Nuño,
  • M. R. Cordero–López

摘要

Using representation–theoretic techniques associated with the \(\mathfrak {su}(1,1)\) su ( 1 , 1 ) symmetry algebra, we construct Perelomov coherent states for the Dunkl–Klein–Gordon equation in its canonical form, which is free of first–order Dunkl derivatives. Our analysis is restricted to the even–parity sector and to the regime where the curvature constant \( R \) R is much smaller than the system’s kinetic energy. The equation under consideration emerges from a matrix–operator framework based on Dirac gamma matrices and a universal length scale that encodes the curvature of space via the Dunkl operator, thereby circumventing the need for spin connections in the Dirac equation.