Scholarlink

<p>We present a constructive, gauge-invariant framework for non-Abelian Yang–Mills theory in four-dimensional Minkowski space, developed via an autonomous symbolic discovery engine called <span>NEXUS</span>. Starting from canonical quantization in the Weyl gauge, we synthesize a BRST-invariant Hamiltonian operator that preserves gauge symmetry, self-adjointness, and Osterwalder–Schrader reflection positivity. Through variational analysis on explicitly constructed trial functionals, we establish a non-zero lower bound between the vacuum and the first gauge-invariant excitation. This spectral gap aligns quantitatively with predictions from lattice QCD and supports the emergence of glueball-like excitations. The methodology integrates operator analysis, BRST cohomology, Euclidean reconstruction, and renormalization group stability, offering a formal framework for probing nonperturbative spectral structure in quantum gauge theories. Our approach highlights the potential of symbolic AI systems in deriving rigorous results within mathematical physics.</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

Variational and Operator-Theoretic Analysis of Spectral Gaps in Yang–Mills Hamiltonians

  • 期刊论文

  • 发表日期：

    2026年2月18日

查看全文
  • Mehardeep Singh

摘要

We present a constructive, gauge-invariant framework for non-Abelian Yang–Mills theory in four-dimensional Minkowski space, developed via an autonomous symbolic discovery engine called NEXUS. Starting from canonical quantization in the Weyl gauge, we synthesize a BRST-invariant Hamiltonian operator that preserves gauge symmetry, self-adjointness, and Osterwalder–Schrader reflection positivity. Through variational analysis on explicitly constructed trial functionals, we establish a non-zero lower bound between the vacuum and the first gauge-invariant excitation. This spectral gap aligns quantitatively with predictions from lattice QCD and supports the emergence of glueball-like excitations. The methodology integrates operator analysis, BRST cohomology, Euclidean reconstruction, and renormalization group stability, offering a formal framework for probing nonperturbative spectral structure in quantum gauge theories. Our approach highlights the potential of symbolic AI systems in deriving rigorous results within mathematical physics.