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- W4309133107 abstract "Let $mathfrak{g}$ be the Lie Algebra of a compact semi-simple gauge group. For a $mathfrak{g}$-valued 1-form $A$, consider the Yang-Mills action begin{equation} S_{{rm YM}}(A) = int_{mathbb{R}^4} left|dA + A wedge A right|^2 domega nonumber end{equation} using the standard metric on $Tmathbb{R}^4$. We want to make sense of the following path integral, begin{equation} {rm Tr} int_{A in mathcal{A}_{mathbb{R}^4, mathfrak{g}} /mathcal{G}} exp left[ cint_{S} dAright] e^{-frac{1}{2}S_{{rm YM}}(A)} DA, nonumber end{equation} whereby $DA$ is some Lebesgue type of measure on the space of $mathfrak{g}$-valued 1-forms, modulo gauge transformations $mathcal{A}_{mathbb{R}^4, mathfrak{g}} /mathcal{G}$. Here, $S$ is some compact flat rectangular surface. Using an Abstract Wiener space, we can define a Yang-Mills path integral rigorously, for a compact semi-simple gauge group. Subsequently, we will then derive the Wilson area law formula from the definition, using renormalization techniques and asymptotic freedom. One of the most important applications of the Area Law formula will be to explain why the potential measured between a quark and antiquark is a linear potential." @default.
- W4309133107 created "2022-11-23" @default.
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- W4309133107 date "2022-11-13" @default.
- W4309133107 modified "2023-10-09" @default.
- W4309133107 title "Wilson Area Law formula on $mathbb{R}^4$" @default.
- W4309133107 doi "https://doi.org/10.48550/arxiv.2211.07064" @default.
- W4309133107 hasPublicationYear "2022" @default.
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