It is usually assumed that the infrared divergences that occur for virtual photons in Feynman diagrams cancel against the corresponding divergences in phase space integrals for the emission of real soft photons. If this were the case then why do the corresponding phase space integrals for the absorption of real soft photons not diverge too, as one might expect on grounds of time-reversal symmetry, and if so what cancels these divergences? We show that this apparent time asymmetry is an artifact of the way that the diagrams are calculated, and we introduce a procedure for such calculations that is manifestly time symmetric. Moreover, we show that it is not mathematically meaningful to distinguish arbitrarily soft massless particles of positive and negative energy.
Usually, the Bloch-Nordsieck theorem is expected to be violated in weak interactions, as the corresponding asymptotic states are not weak singlets. However, a manifest gauge-invariant approach replaces the asymptotic states with composite states, and thereby restores the Bloch- Nordsieck theorem. The Froehlich-Morchio-Strocchi mechanism ensures that this is in agreement with existing phenomenology. We outline the necessary steps of this construction.
We studied different levels of resummations of the exactly solvable Bloch-Nordsieck model in order to be able to compare the approximations with an exact result. We studied one-loop perturbation theory, 2PI resummation and Schwinger-Dyson equations truncated in a way to maintain Ward-identities. At all levels we carefully performed renormalization. We found that although the 2PI resummation does not exhibit infrared sensitivity at the mass shell (the one-loop perturbation theory does), but it is still far from the exact solution. The method of truncated Schwinger-Dyson equations, however, is e…
We discuss the infrared structure of processes with massive quarks in the initial state. It is well known that, starting from next-to-next-to-leading order in perturbative QCD, such processes exhibit a violation of the Bloch-Nordsieck theorem, in that the sum of real and virtual contributions to partonic cross sections contains uncanceled infrared singularities. The main purpose of this paper is to present a simple physical argument that elucidates the origin of these singularities and simplifies the derivation of infrared-singular contributions to heavy-quark initiated cross sections.
Lifetimes of quasiparticles and collective excitations in hot QED plasmas
用微扰法计算高温QED等离子体中费米子激发寿命时，会遇到屏蔽修正不能消除的红外发散。造成这些发散的物理过程是涉及长波长、准静态、磁性光子交换的碰撞，这些光子不受等离子体效应的屏蔽。在有限温度下，基于推广的Bloch-Nordsieck模型，可以在非微扰的假设下计算主导发散。由此得到的费米子传播子的表达式没有红外问题，并且在很长时间内表现出{ \it非指数}阻尼：$S_R(t)\sim \exp\{-αT t \lnω_pt\}$，其中$ω_p=eT/3$是等离子体频率，$α=e^2/4π$。
在微扰理论中对超相对论等离子体的研究中，红外发散是一个很大的问题，屏蔽修正不能消除红外发散。它们影响，特别是，计算的寿命的基本激发，从而怀疑准粒子图片的有效性。我们表明，至少对于阿贝尔等离子体，阻尼率的红外问题可以通过基于布洛赫-Nordsieck近似的非微扰处理来解决。由此得到的费米子传播子的表达式没有发散，并且在很长时间内表现出{ \it非指数}阻尼：$S_R(t)\sim \exp\{-αT t \lnω_pt\}$，其中$ω_p=gT/3$是等离子体频率，$α=g^2/4π$。
超相对论等离子体中带电激发寿命的微扰计算受到屏蔽修正不能消除的红外发散的困扰。造成这些发散的物理过程是涉及长波长、准静态、磁胶子（或光子）交换的碰撞，这些胶子不受等离子体效应的屏蔽。在QED中，领先的分歧可以在有限温度下基于Bloch-Nordsieck模型的推广的非微扰近似中进行计算。由此得到的费米子传播子的表达式没有红外问题，并且在很长时间内表现出"非指数“阻尼：$S_R(t)\sim exp {-αT t lnω_pt}$，其中$ω_p=eT/3$是等离子体频率，$α=e^2/4π$。
