论文标题
适用于配置空间中的Tachyon表示形式的适当标量产品
A proper scalar product for tachyon representations in configuration space
论文作者
论文摘要
我们为标量字段提出了一种新的内部产品，该产品是$ M^2 <0 $的Klein-Gordon方程解决方案。该内部产物是非本地的，具有包括第二种贝塞尔功能的整体内核，并且相关的规范在振荡溶液的子空间中被证明是积极的，而不是常规的溶液。庞加莱的转换是在这个子空间上实施的，这是适当正面庞加莱集团的单一且不可还原代表的支持。我们还提供了统一的配置和动量空间之间的新傅立叶变换，并将投影恢复到表示空间。这种新场景提出了对相应量子场理论的修订。
We propose a new inner product for scalar fields that are solutions of the Klein-Gordon equation with $m^2<0$. This inner product is non-local, bearing an integral kernel including Bessel functions of the second kind, and the associated norm proves to be positive definite in the subspace of oscillatory solutions, as opposed to the conventional one. Poincaré transformations are unitarily implemented on this subspace, which is the support of a unitary and irreducible representation of the proper orthochronous Poincaré group. We also provide a new Fourier Transform between configuration and momentum spaces which is unitary, and recover the projection onto the representation space. This new scenario suggests a revision of the corresponding quantum field theory.
