关于$ϕ^4$ -周期和$c_2$不变量的图论的进一步研究
Further investigations into the graph theory of $ϕ^4$-periods and the $c_2$ invariant
摘要：
费曼周期是标量费曼积分的一个特殊留数，它在物理和数论上都很有趣。费曼图的图论可以解释费曼周期的两种方法是通过周期不变量的图运算和预测费曼周期的其他图量，一个值得注意的例子是$c_2$不变量。我们在这两个方向的结果和计算，证明了一个新的时期的身份和计算其后果高达11个循环的$ϕ^4$理论，证明了一个$c_2$不变的身份，并给出结果的计算调查$c_2$不变量在11个循环。
英文摘要：
A Feynman period is a particular residue of a scalar Feynman integral which is both physically and number theoretically interesting. Two ways in which the graph theory of the underlying Feynman graph can illuminate the Feynman period are via graph operations which are period invariant and other graph quantities which predict aspects of the Feynman period, one notable example is known as the $c_2$ invariant. We give results and computations in both these directions, proving a new period identity and computing its consequences up to 11 loops in $ϕ^4$-theory, proving a $c_2$ invariant identity, and giving the results of a computational investigation of $c_2$ invariants at 11 loops.
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