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On Wick Polynomials of Boson Fields in Locally Covariant Algebraic QFT

机译：在局部协助代数QFT中玻色田的烟囱多项式

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This work presents some results about Wick polynomials of a vector field renormalization in locally covariant algebraic quantum field theory in curved spacetime. General vector fields are pictured as sections of natural vector bundles over globally hyperbolic spacetimes and quantized through the known functorial machinery in terms of local -algebras. These quantized fields may be defined on spacetimes with given classical background fields, also sections of natural vector bundles, in addition to the Lorentzian metric. The mass and the coupling constants are in particular viewed as background fields. Wick powers of the quantized vector field are axiomatically defined imposing in particular local covariance, scaling properties, and smooth dependence on smooth perturbation of the background fields. A general classification theorem is established for finite renormalization terms (or counterterms) arising when comparing different solutions satisfying the defining axioms of Wick powers. The result is specialized to the case of general tensor fields. In particular, the case of a vector Klein-Gordon field and the case of a scalar field renormalized together with its derivatives are discussed as examples. In each case, a more precise statement about the structure of the counterterms is proved. The finite renormalization terms turn out to be finite-order polynomials tensorially and locally constructed with the backgrounds fields and their covariant derivatives whose coefficients are locally smooth functions of polynomial scalar invariants constructed from the so-called marginal subset of the background fields. The notion of local smooth dependence on polynomial scalar invariants is made precise in the text. Our main technical tools are based on the Peetre-Slovak theorem characterizing differential operators and on the classification of smooth invariants on representations of reductive Lie groups.
机译：这项工作提出了一些关于弯曲时空局部协助代数量子域理论的芯多项式的芯多项式。将一般矢量字段描绘成自然向量捆绑在全球双曲线套管上的分段，并通过已知的曲线机械量化在当地 - eAgbras方面。除了Lorentzian指标之外，可以在具有给定古典背景领域的空间中定义这些量化字段，以及自然向量束的部分。质量和耦合常数特别是被视为背景领域。量化矢量字段的芯功率在特定的本地协方差，缩放属性和对背景领域的平滑扰动的平滑依赖性的公正定义。在比较满足灯芯的定义公理的不同解决方案时，建立了用于有限重整化术语（或逆时针）的一般分类定理。结果是专门为一般张量字段的情况。特别地，讨论了载体Klein-Gordon场的情况和与其衍生物一起重整化的标量场的情况作为示例。在每种情况下，证明了关于对抗结构的更精确的陈述。有限的重整化术语转向是有限级多项式，其与背景领域及其协方衍生物构成，其系数是从背景领域的所谓边际子集构成的多项式标量不变的局部平滑函数。本地平滑依赖于多项式标量不变的概念在文本中精确完成。我们的主要技术工具基于Peetre-Slovak定理，表征差分运营商以及在还原谎言群体的表现中的平滑不变性的分类。

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  • 来源
    《Annales Henri Poincare》 |2019年第3期|共74页
  • 作者

    Khavkine Igor; Melati Alberto; Moretti Valter;

  • 作者单位

    Univ Milan Dipartimento Matemat Via Cesare Saldini 50 I-20133 Milan MI Italy;

    Univ Trento Dipartimento Fis Via Sommar 14 I-38123 Povo Trento Italy;

    Univ Trento Dipartimento Fis Via Sommar 14 I-38123 Povo Trento Italy;

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  • 正文语种 eng
  • 中图分类 理论物理学;
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