Scholarlink

<p>The classification of elementary particles based on unitary irreducible representations of the Poincaré group has been a cornerstone of modern Quantum Field Theory (QFT). While the Standard Model (SM) does not inherently include Dark Matter (DM), any fundamental DM candidate should still conform to this classification or its extensions. Eugene P. Wigner introduced a class of nontrivial representations characterized by an additional discrete degree of freedom, known as the Wigner degeneracy. In this work, we systematically investigate the QFT of such Wigner multiplets, particularly focusing on the massive spin-1/2 fermion. We construct a theoretical framework where the two-fold Wigner spinor fields, <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_26370_Article_IEq1.gif" Format="GIF" Height="24" Rendition="HTML" Resolution="72" Type="Linedraw" Width="53" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <msub> <mi>ψ</mi> <mrow> <mo>±</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </msub> <mfenced close=")" open="("> <mi>x</mi> </mfenced> </math></EquationSource> <EquationSource Format="TEX">\( {\psi}_{\pm \frac{1}{2}}(x) \)</EquationSource> </InlineEquation>, form a doublet representation. We analyze their transformation properties under discrete symmetries (e.g., charge-conjugation <i>C</i>, spatial parity <i>P</i>, and time-reversal <i>T</i>), revealing novel mixing effects due to the Wigner degeneracy and an emergent accidental U(2) global symmetry. Furthermore, we explore the Yukawa interactions involving the Wigner doublets, showing that such interactions generally violate the <i>CPT</i> invariance. We also study gauge theories within the Wigner framework, where the physical Wigner doublet naturally leads to exotic phenomenological consequences beyond the SM, including phase transitions. These results provide new insights into the possible role of the Wigner-degenerate states in fundamental physics, particularly in the dark sector.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Wigner multiplets in QFT: dark sector and CPT-violating scenarios

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年6月5日

查看全文
  • Cheng-Yang Lee,
  • Ruifeng Leng,
  • Siyi Zhou

摘要

The classification of elementary particles based on unitary irreducible representations of the Poincaré group has been a cornerstone of modern Quantum Field Theory (QFT). While the Standard Model (SM) does not inherently include Dark Matter (DM), any fundamental DM candidate should still conform to this classification or its extensions. Eugene P. Wigner introduced a class of nontrivial representations characterized by an additional discrete degree of freedom, known as the Wigner degeneracy. In this work, we systematically investigate the QFT of such Wigner multiplets, particularly focusing on the massive spin-1/2 fermion. We construct a theoretical framework where the two-fold Wigner spinor fields, ψ ± 1 2 x \( {\psi}_{\pm \frac{1}{2}}(x) \) , form a doublet representation. We analyze their transformation properties under discrete symmetries (e.g., charge-conjugation C, spatial parity P, and time-reversal T), revealing novel mixing effects due to the Wigner degeneracy and an emergent accidental U(2) global symmetry. Furthermore, we explore the Yukawa interactions involving the Wigner doublets, showing that such interactions generally violate the CPT invariance. We also study gauge theories within the Wigner framework, where the physical Wigner doublet naturally leads to exotic phenomenological consequences beyond the SM, including phase transitions. These results provide new insights into the possible role of the Wigner-degenerate states in fundamental physics, particularly in the dark sector.