论文标题
在非铁质标量量子场理论中的离散时空对称性和粒子混合
Discrete spacetime symmetries and particle mixing in non-Hermitian scalar quantum field theories
论文作者
论文摘要
我们讨论了带有PT对称性的游离非铁量量子量子场理论中的第二个量化，离散的对称转换和内部产物，重点是具有反动物质量混合的两个复杂标量场的原型模型。而内部产品的定义对于赫米尔顿人所描述的理论是独一无二的，但它的表述对于非热汉密尔顿人来说并不是独一无二的。相对于常规狄拉克内部产品，能量本征不是正交的，因此我们必须考虑其他离散转换以定义正定规范。我们阐明了规范结合的操作员之间的关系，并引入了先前针对量子力学系统引入的其他离散对称C'，并表明C'PT Inner产品确实产生了一个正定标准的标准，因此适合定义具有PT Symetry pt symetry的Fock空间，以pt symetry eigenstates中的pt Symetry。我们还讨论了PT-对称非亚米特标量量子场理论和遗传学理论之间的相似性转换，表明它们在存在相互作用的情况下需要进行修改。为了说明我们的讨论，我们比较了赫尔米尔理论中的粒子混合，以及与PT对称的相应的非热模型中的混合，显示后者如何保持单位性并在标量和伪内玻色之间表现出混合。
We discuss second quantization, discrete symmetry transformations and inner products in free non-Hermitian scalar quantum field theories with PT symmetry, focusing on a prototype model of two complex scalar fields with anti-Hermitian mass mixing. Whereas the definition of the inner product is unique for theories described by Hermitian Hamiltonians, its formulation is not unique for non-Hermitian Hamiltonians. Energy eigenstates are not orthogonal with respect to the conventional Dirac inner product, so we must consider additional discrete transformations to define a positive-definite norm. We clarify the relationship between canonical-conjugate operators and introduce the additional discrete symmetry C', previously introduced for quantum-mechanical systems, and show that the C'PT inner product does yield a positive-definite norm, and hence is appropriate for defining the Fock space in non-Hermitian models with PT symmetry in terms of energy eigenstates. We also discuss similarity transformations between PT-symmetric non-Hermitian scalar quantum field theories and Hermitian theories, showing that they would require modification in the presence of interactions. As an illustration of our discussion, we compare particle mixing in a Hermitian theory and in the corresponding non-Hermitian model with PT symmetry, showing how the latter maintains unitarity and exhibits mixing between scalar and pseudoscalar bosons.
