QFT和中微子振荡问题中的内插波包和复合波函数
Interpolating wave packets and composite wave functions in QFT and neutrino oscillation problem
摘要：
本文给出了真空中中微子味跃迁振幅的一个一致的构造性协变描述。为此，构造了一个特殊的广义相对论波包，并将其正确地推广到高自旋上。这个包被唯一地定义为“内插”波包，它通过相对论不变的“宽度”精确地内插在动量空间和坐标空间中的局部状态之间。波包是明确地确定的分析性质的怀特曼函数在复杂的坐标空间自然连接其最小化的性质。该波包给出了非相对论高斯波包的自然相对论推广，但它只包含能量符号为正（负）的粒子（反粒子）的协变态，并且在传播过程中不发生混合，其相对论不变宽度也不发生变化。为了用这些外部粒子的波包图解处理振荡，引入了中间中微子协变复合波函数的概念。它严格而自然地连接了两个振荡图像，为详细描述这一过程提供了一种有效的语言，并解决了因果关系和协变等时规定的问题。它是密切相关的中微子创建/检测顶点的重叠功能，阐明了协变意义的“极点集成”的程序。它们在窄包近似下的时空渐近行为自然与单包态的这种近似和振荡幅度的渐近行为一致。相应的重叠函数明确计算的两个包的例子π衰变顶点。分析了它与以往近似计算的对应和差异。
英文摘要：
A consistent constructive covariant description of neutrino flavour transition amplitude in vacuum is presented. To this end a special generalized relativistic wave packet is constructed with correct extension onto the higher spins. This packet is uniquely defined as an `interpolating' wave packet, which by means of relativistically invariant `width' accurately interpolates between the states localized in momentum space and in coordinate space. The wave packet is unambiguously determined by analytical properties of Wightman functions in complex coordinate space naturally connected with its minimization properties. The packet gives natural relativistic generalization of non relativistic Gaussian wave packet but it contains covariant states of particle (antiparticle) only with positive (negative) energy sign and propagates without their mixing and without changing of its relativistically invariant width. For the diagrammatic treatment of oscillation with the use of these wave packets for external particles, the notion of covariant composite wave function for intermediate neutrino is introduced. It strictly and naturally connects both oscillation pictures, giving an effective language for detailed description of this process, and resolves the problems with causality and with covariant equal time prescription for the intermediate neutrino picture. It is closely related to overlap function of neutrino creation/detection vertices, elucidating a covariant meaning of the `pole integration' procedure. Their space-time asymptotic behaviour in narrow-packets approximation naturally conforms with such approximation of one-packet state and with the asymptotic behaviour of oscillation amplitude. The respective overlap function is explicitly calculated for two-packet example of pion decay vertex. Its correspondence and difference with previous approximate calculations is analyzed.
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