GENERAL-SOLUTIONS FOR TUNNELING OF SCALAR FIELDS WITH QUARTIC POTENTIALS
GENERAL-SOLUTIONS FOR TUNNELING OF SCALAR FIELDS WITH QUARTIC POTENTIALS
复制标题
DOI：
10.1103/physrevd.48.2800
复制
发表时间：
1993-09-15
影响因子：
5
通讯作者：
ADAMS, FC
中科院分区：
文献类型：
--
作者：
ADAMS, FC
对于具有四次势V（phi）的单个标量场phi的理论，我们找到了四维和三维中欧几里得作用的半解析表达式。四维的作用决定了零温度下从假真空态到真真空态的量子隧穿速率;类似地，三维的作用决定了有限温度理论的热隧穿速率。我们表明，对于所有的四次电位的行动可以从一个参数家庭的瞬子解决方案对应的一个参数家庭的微分方程。我们找到解决方案的数值和多项式拟合公式，以获得表达式的欧几里德行动。这些结果允许一个计算隧道速率的整个可能范围内的四次电位，从薄壁（近退化）限制到相反的限制消失的势垒高度。我们也提出了一个类似的计算包含phi 4lnphi 2条款，这是在一个循环近似的有效电位在电弱理论中出现的电位。
For the theory of a single scalar field phi with a quartic potential V(phi), we find semianalytic expressions for the Euclidean action in both four and three dimensions. The action in four dimensions determines the quantum tunneling rate at zero temperature from a false vacuum state to the true vacuum state; similarly, the action in three dimensions determines the thermal tunneling rate for a finite temperature theory. We show that for all quartic potentials the action can be obtained from a one-parameter family of instanton solutions corresponding to a one-parameter family of differential equations. We find the solutions numerically and use polynomial fitting formulas to obtain expressions for the Euclidean action. These results allow one to calculate tunneling rates for the entire possible range of quartic potentials, from the thin-wall (nearly degenerate) limit to the opposite limit of vanishing barrier height. We also present a similar calculation for potentials containing phi4lnphi2 terms, which arise in the one-loop approximation to the effective potential in electroweak theory.