有限时间区间内物理粒子与纯虚粒子的传播子和宽度
Propagators and widths of physical and purely virtual particles in a finite interval of time
AI总结：
该研究用相干态分析有限时间与紧致空间中物理及纯虚粒子的传播子，揭示有限τ下宽度、辐射修正、μ子过程及自能级数收敛性，并以单峰与双峰区分两类粒子。
摘要：
我们利用相干态，在有限时间区间τ和紧致空间流形Ω上研究物理粒子与纯虚粒子的自由传播子和缀饰传播子。在自由场极限下，传播子由整函数(e^z-1-z)/z^2描述，该函数在实轴上的形状类似于Breit-Wigner函数，其有效宽度约为1/τ。其实部为正，与幺正性一致；在纳入辐射修正后仍保持为正，因为这些修正会把该函数移入物理半平面。我们考察了限制于有限τ对不稳定粒子与共振之区分问题的影响，并表明μ子观测来自正确的物理过程，这与τ=∞时发生的情况不同。我们还研究了纯虚粒子的情形，并表明如果τ足够小，则存在一种情形，使自能的几何级数始终收敛。缀饰传播子的图像显示出可检验的差异：物理粒子具有通常的单峰特征，而纯虚粒子则具有双峰特征。
英文摘要：
We study the free and dressed propagators of physical and purely virtual particles in a finite interval of time $τ$ and on a compact space manifold $Ω$, using coherent states. In the free-field limit, the propagators are described by the entire function $(e^{z}-1-z)/z^{2}$, whose shape on the real axis is similar to the one of a Breit-Wigner function, with an effective width around $1/τ$. The real part is positive, in agreement with unitarity, and remains so after including the radiative corrections, which shift the function into the physical half plane. We investigate the effects of the restriction to finite $τ$ on the problem of unstable particles vs resonances, and show that the muon observation emerges from the right physical process, differently from what happens at $τ=\infty $. We also study the case of purely virtual particles, and show that, if $τ$ is small enough, there exists a situation where the geometric series of the self-energies is always convergent. The plots of the dressed propagators show testable differences: while physical particles are characterized by the usual, single peak, purely virtual particles are characterized by twin peaks.
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