Ordinary versus PT-symmetric $\phi^3$ quantum field theory
Ordinary versus PT-symmetric $\phi^3$ quantum field theory
复制标题
普通量子场论与 PT 对称 $phi^3$ 量子场论
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
Emanuele Messina
中科院分区：
文献类型：
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作者：
C. Bender;V. Branchina;Emanuele Messina
一个量子力学理论是PT对称的，如果它是由一个与PT交换的哈密顿量描述的，其中算子P执行空间反射，算子T执行时间反转。一个PT对称的哈密顿函数通常有一个不间断PT对称的参数区域，其中的能量特征值都是实数。也可能存在一个PT对称破缺的区域，其中一些特征值是复的。这些区域被在实验室实验中反复观察到的相变分开。本文主要讨论pt对称igΦ³量子场论的性质。这个量子场论是由哈密顿H=p²+ix³描述的pt对称量子力学理论的类比，其特征值已被严格地证明为全实数。本文比较了传统厄米量子场论gΦ³量子场论与pt对称igΦ³量子场论的重整化群性质。结果表明，虽然d=6维的传统gΦ³理论是渐近自由的，但igΦ³理论类似于d=4维的gΦ⁴理论；它是能量稳定的，扰动可重整的，平凡的。
A quantum-mechanical theory is PT-symmetric if it is described by a Hamiltonian that commutes with PT, where the operator P performs space reflection and the operator T performs time reversal. A PT-symmetric Hamiltonian often has a parametric region of unbroken PT symmetry in which the energy eigenvalues are all real. There may also be a region of broken PT symmetry in which some of the eigenvalues are complex. These regions are separated by a phase transition that has been repeatedly observed in laboratory experiments. This paper focuses on the properties of a PT-symmetric igΦ³ quantum field theory. This quantum field theory is the analog of the PT-symmetric quantum-mechanical theory described by the Hamiltonian H=p²+ix³, whose eigenvalues have been rigorously shown to be all real. This paper compares the renormalization group properties of a conventional Hermitian gΦ³ quantum field theory with those of the PT-symmetric igΦ³ quantum field theory. It is shown that while the conventional gΦ³ theory in d=6 dimensions is asymptotically free, the igΦ³ theory is like a gΦ⁴ theory in d=4 dimensions; it is energetically stable, perturbatively renormalizable, and trivial.
影响因子：
8.6
作者：
Bittner, S.;Dietz, B.;Schaefer, F.
通讯作者：
Schaefer, F.