有效势中的规范选择、红外陷阱与热效应
Gauge Choices, Infrared Pitfalls, and Thermal Effects in Effective Potentials
AI总结：
针对有效势的规范依赖性与红外发散问题，研究通过费米规范下的乘性反常结合热核技术，同时改善了有效势的规范独立性与红外行为，且可推广至有限温度情形。
摘要：
有效势的计算对暴胀、真空稳定性、相变等一系列唯象学应用至关重要，但其存在规范依赖性的缺陷。此外，在自发对称性破缺的理论中，当戈德斯通质量趋于零时，有效势会出现红外（IR）发散。我们通过计算单圈阶有效势时考虑费米规范中椭圆算子非因子化产生的乘性反常，证明其规范独立性和红外行为均同时优于朗道规范计算的相应结果。利用热核技术的方法可直接清晰地复现后者，从而为从一开始就反映反常相关的抵消提供了捷径。我们的结果可推广到有限温度下有效势的处理，特别是热核方法将规范独立性拓展到质量与温度展开的任意阶。
英文摘要：
The evaluation of effective potentials is critical for a range of phenomenological applications, including inflation, vacuum stability, and phase transitions. A drawback arises from the gauge-dependence of the effective potential. Furthermore, in theories with spontaneous symmetry breaking, the effective potential exhibits infrared (IR) divergences in the limit of vanishing Goldstone masses. By considering the multiplicative anomaly that arises due to non-factorisation of elliptic operators in the Fermi gauge when computing the effective potential at one-loop order, we demonstrate that its gauge independence and IR behaviour are improved to the corresponding findings of Landau gauge calculations simultaneously. The latter are straightforwardly and transparently reproduced using an approach that employs the Heat Kernel technique, thereby providing a shortcut to reflect anomaly-related cancellations from the outset. Our findings generalise to the treatment of the effective potential at finite temperature. In particular, the Heat Kernel extends gauge independence to any value of the expansion in mass over temperature.
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