关于费米子加倍缺失以及尼尔森 - 二宫定理为何不适用于非局部量子场论的探究
An inquiry into the Absence of Fermion Doubling and why the Nielsen-Ninomiya Theorem Does Not Apply to Nonlocal Quantum Field Theory
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中文总结 AI 辅助
探究非局部量子场论是否有费米子加倍问题，通过全纯函数算子可逆性证明特定条件下无额外费米子，给出费米子加倍准则及测试程序，区分相关情况，得出完整连续非局部理论中不存在费米子加倍的结论。
中文摘要 AI 辅助
在本文中，我们将研究非局部量子场论是否会遭受费米子加倍问题。我们发现对于非局部狄拉克理论，只要形状因子在每一点都不为零，就不会引入额外的费米子种类。该证明源于全纯函数算子的可逆性，这意味着非局部狄拉克算子与原始局部狄拉克算子具有完全相同的核和有限动量零点集。我们将此结果与适用于紧致布里渊区上局部晶格费米子的标准尼尔森 - 二宫定理区分开来。我们提供了费米子加倍的一般准则、真假加倍的测试以及数学和物理费米子加倍的测试程序。接着我们将此结果与可能引入虚假多项式零点的有限导数截断区分开来。最后我们得出结论，在完整的连续非局部理论中不存在费米子加倍。
英文摘要
In this paper we will examine if nonlocal quantum field theory will suffer from the fermion doubling pathology. We find that for a nonlocal Dirac theory, that no additional fermion species are introduced. This is provided that the form factor is nonvanishing at every point. The proof follows from the invertibility of the entire-function operator, which implies that the nonlocal Dirac operator has exactly the same kernel and finite-momentum zero set as the original local Dirac operator. We will distinguish this result from the standard Nielsen-Ninomiya theorem, which applies local lattice fermions on a compact Brillouin zone. We provide a general criterion for fermion doubling, a test for genuine and false doubling, and then a test procedure for mathematical and physical fermion doubling. We then will go on to distinguish this result from finite derivative truncations, which can introduce spurious polynomial zeros. We then conclude that fermion doubling is absent in the full continuum nonlocal theory.
