小波基量子场论中规范不变性的一个注记
A remark on gauge invariance in wavelet-based quantum field theory
摘要：
小波变换作为规范化规范理论的一种工具，自（Federbush，Progr. Theor. Phys.94，1135，1995），其中提出了借助于小波变换的场的积分表示：$$A_μ(x) = \frac{1}{C_ψ} \int_{\R_+ \times\R^d} \frac{1}{a^d} g \left(\frac{x-b}{a} \right) A_{μa}(b) \frac{dad^db}{a},$$，其中$A_{μa}(b)$被理解为在点$b\in \R^d$处测量的场$A_μ$，其分辨率为$a\in\R_+$。本文考虑规范场的小波理论，给出了尺度依赖场的规范变换的一个对应形式：$A_{μa}(x)\to A_{μa}(x)+\d_μf_a(x)$，并导出了它们的Ward-Takahashi恒等式。
英文摘要：
Wavelet transform has been attracting attention as a tool for regularization of gauge theories since the first paper of (Federbush, Progr. Theor. Phys. 94, 1135, 1995), where the integral representation of the fields by means of the wavelet transform was suggested: $$A_μ(x) = \frac{1}{C_ψ} \int_{\R_+ \times\R^d} \frac{1}{a^d} g \left(\frac{x-b}{a} \right) A_{μa}(b) \frac{dad^db}{a},$$ with $A_{μa}(b)$ being understood as the fields $A_μ$ measured at point $b\in \R^d$ with resolution $a\in\R_+$. In present paper we consider a wavelet-based theory of gauge fields, provide a counterpart of the gauge transform for the scale-dependent fields: $A_{μa}(x)\to A_{μa}(x)+\d_μf_a(x)$, and derive the Ward-Takahashi identities for them.
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