论文标题
在有限温度下，在压缩空间上的标量场的有效潜力的非分析项
Non-analytic Term in Effective Potential at Finite Temperature for Scalar Field on Compactified Space
论文作者
论文摘要
我们研究了非分析术语，该术语不能以任何依赖场质量平方的积极整数的形式编写，在有限温度下以一环近似为有效的潜在潜力，用于$ d $ d $ d $二维时空的真实标量场，$s_τ^1 \ $s_τ^1 \ times r^{d-（p+1）}} \ time time time time \ prod \ prod \ prod_} $}通过使用第二种修改的Bessel函数的积分表示，可以将有效电位重铸为复杂平面中的积分形式，并为多种模式求和而进行分析扩展。阐明了模式总结的极点结构，所有非分析项均由残基定理获得。我们发现，当欧几里得空间的尺寸为$ d-（p+1）$时，有效电位具有非分析术语。对于$ d $和$ p $的给定值，似乎只有一个非分析术语，而非分析术语存在。
We study non-analytic terms, which cannot be written in the form of any positive integer power of field-dependent mass squared, in effective potential at finite temperature in one-loop approximation for a real scalar field on the $D$-dimensional space-time, $S_τ^1\times R^{D-(p+1)}\times\prod_{i=1}^pS_i^1$. The effective potential can be recast into the integral form in the complex plane by using the integral representation for the modified Bessel function of the second kind and the analytical extension for multiple mode summations. The pole structure of the mode summations is clarified and all the non-analytic terms are obtained by the residue theorem. We find that the effective potential has a non-analytic term when the dimension of the flat Euclidean space, $D-(p+1)$ is odd. There appears only one non-analytic term for the given values of $D$ and $p$, for which the non-analytic term exists.
