非谐振子的无条件Wiener测度泛函积分
The functional integral with unconditional Wiener measure for anharmonic oscillator
摘要：
在这篇文章中，我们提出了计算的无条件Wiener测度泛函积分的一项的四阶指数的替代方法，在常规的微扰方法。与传统的微扰理论不同，我们将积分变量中的线性项展开为指数形式的幂级数。在这种情况下，我们可以利用抛物柱面函数来表示所讨论的积分。我们表明，在这种情况下，该系列的扩展是一致收敛的，我们发现在$N$维近似的维纳功能积分的递归关系。在连续极限下，我们发现广义Gelfand-Yaglom微分方程的有解解可得到所需的泛函积分（类似于标准Gelfand-Yaglom微分方程的线性谐振子的泛函积分）.
英文摘要：
In this article we propose the calculation of the unconditional Wiener measure functional integral with a term of the fourth order in the exponent by an alternative method as in the conventional perturbative approach. In contrast to the conventional perturbation theory, we expand into power series the term linear in the integration variable in the exponent. In such a case we can profit from the representation of the integral in question by the parabolic cylinder functions. We show that in such a case the series expansions are uniformly convergent and we find recurrence relations for the Wiener functional integral in the $N$ - dimensional approximation. In continuum limit we find that the generalized Gelfand - Yaglom differential equation with solution yields the desired functional integral (similarly as the standard Gelfand - Yaglom differential equation yields the functional integral for linear harmonic oscillator).
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