论文标题
Coleman-Weinberg的潜力$ P $ -ADIC FIELD理论
Coleman-Weinberg potential in $p$-adic field theory
论文作者
论文摘要
在本文中，我们研究了$ λϕ^4 $标量字段理论在p-adic数字的未扩展上定义的$ {\ mathbb q} _ {p^n} $。对于不同的``时空''尺寸$ n $，我们计算一环量子校正以发挥有效的潜力。出乎意料的是，尽管非近距离的几何形状具有异常的特性，但P-Adic场理论的Coleman-Weinberg潜力的结构与其真实堂兄的结构非常相似。我们还研究了有效潜力的两个正式限制，$ p \ rightarrow 1 $和$ p \ rightarrow \ infty $。我们表明，$ p \ rightarrow 1 $限制允许从P-Adic有效潜力中重建实际领域理论的规范结果，并对这一事实提供解释。另一方面，在$ p \ rightarrow \ infty $限制中，该理论表现出非常奇特的行为，并具有有效潜力的新兴对数项，在真实理论中没有类似物。
In this paper, we study $λϕ^4$ scalar field theory defined on the unramified extension of p-adic numbers ${\mathbb Q}_{p^n}$. For different ``space-time'' dimensions $n$, we compute one-loop quantum corrections to the effective potential. Surprisingly, despite the unusual properties of non-Archimedean geometry, the Coleman-Weinberg potential of p-adic field theory has a structure very similar to that of its real cousin. We also study two formal limits of the effective potential, $p \rightarrow 1$ and $p \rightarrow \infty$. We show that the $p\rightarrow 1$ limit allows to reconstruct the canonical result for real field theory from the p-adic effective potential and provide an explanation of this fact. On the other hand, in the $p\rightarrow\infty$ limit, the theory exhibits very peculiar behavior with emerging logarithmic terms in the effective potential, which has no analog in real theories.
