arXiv 0710.12562007-10-05hep-th

复化路径积分与量子场论的位相

Complexified Path Integrals and the Phases of Quantum Field Theory

Gerald Guralnik, Zachary Guralnik

备注：: 15 pages, 9 figures (newer version has better images)
发表信息：: Annals Phys.325:2486-2498,2010
DOI：: 10.1016/j.aop.2010.06.001

摘要：

定义量子场论的路径积分是由施温格作用原理产生的一组泛函微分方程的特解。事实上，这些方程有大量的额外的解决方案，这是描述的积分复杂的path.We讨论的额外的解决方案，虽然通常被忽视，可能是物理与已知的例子，包括自发对称性破缺和θ真空的属性。我们表明，考虑全套的解决方案产生的描述相变的量子场论补充通常的描述李杨零的积累。特别是，我们认为，非解析性由于李杨零的积累与斯托克斯现象和崩溃的解决方案集在各种限制，包括但不限于，热力学限制。一个精确的演示这种关系的零维模型。最后，零维多项式的行动，我们证明了博雷尔重申的摄动展开，与几个选择的奇异性避免轮廓在复杂的博雷尔平面，产量不等的解决方案的行动原则方程。

英文摘要：

The path integral by which quantum field theories are defined is a particular solution of a set of functional differential equations arising from the Schwinger action principle. In fact these equations have a multitude of additional solutions which are described by integrals over a complexified path. We discuss properties of the additional solutions which, although generally disregarded, may be physical with known examples including spontaneous symmetry breaking and theta vacua. We show that a consideration of the full set of solutions yields a description of phase transitions in quantum field theories which complements the usual description in terms of the accumulation of Lee-Yang zeroes. In particular we argue that non-analyticity due to the accumulation of Lee-Yang zeros is related to Stokes phenomena and the collapse of the solution set in various limits including but not restricted to, the thermodynamic limit. A precise demonstration of this relation is given in terms of a zero dimensional model. Finally, for zero dimensional polynomial actions, we prove that Borel resummation of perturbative expansions, with several choices of singularity avoiding contours in the complex Borel plane, yield inequivalent solutions of the action principle equations.

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