Abstract Wiener measure using abelian Yang-Mills action on R4\mathbb{R}^4

Let $\mathfrak{g}$ be the Lie algebra of a compact Lie 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 \nonumber \end{equation} using the standard metric on $T\mathbb{R}^4$. When we consider the Lie group $U(1)$, the Lie algebra $\mathfrak{g}$ is isomorphic to $\mathbb{R} \otimes i$, thus $A \wedge A = 0$. For some simple closed loop $C$, we want to make sense of the following path integral, \begin{equation} \frac{1}{Z}\ \int_{A \in \mathcal{A} /\mathcal{G}} \exp \left[ \int_{C} A\right] e^{-\frac{1}{2}\int_{\mathbb{R}^4}|dA|^2}\ DA, \nonumber \end{equation} whereby $DA$ is some Lebesgue type of measure on the space of $\mathfrak{g}$-valued 1-forms, modulo gauge transformations, $\mathcal{A} /\mathcal{G}$, and $Z$ is some partition function. We will construct an Abstract Wiener space for which we can define the above Yang-Mills path integral rigorously, using renormalization techniques found in lattice gauge theory. We will further show that the Area Law formula do not hold in the abelian Yang-Mills theory

Eccrine spiradenoma: an uncommon breast tumour

Eccrine spiradenoma is a benign tumour of the sweat gland. Eccrine glands can be found almost everywhere but are mostly concentrated on the palms, soles and the axillae. Lesions involving the breast are rare. We present a case of a 13-years-old Malay girl with eccrine spiradenoma of the breast. The clinical presentation and histological features are being described