Bremsstrahlung radiation as a coherent state in thermal QED

Abstract

Based on fully finite temperature field theory we investigate the radiation probability in the bremsstrahlung process in thermal QED. It turns out that the infrared divergences resulting from the emission and absorption of the real photons are canceled by the virtual photon exchange processes at finite temperature. The full quantum calculation results for soft photons radiation coincide completely with that obtained in the semi-classical approximation. In the framework of Thermofield Dynamics it is shown that the bremsstrahlung radiation in thermal QED is a coherent state, the quasiclassical behavior of the coherent state leads to above coincidence.

Cyclazines‐Structure and Aromaticity or Antiaromaticity on the Magnetic Criterion

“…Also various aza‐analogues of N[2.2.3] were classified accordingly (e. g. Figure S1–Supporting Information) [17,57–59] and the complex 1 H and 13 C NMR spectra completely assigned by Castle et al [60,61] . The same for the anti‐aromatic antipode, N[3.3.3] : Synthesized already in 1969 and the paratropic ring current of the 12π‐perimeter was identified by the high shielding degree of proton resonances, [8,62] and later by a NICS zz scan [16,63] . The remaining cyclazines containing only five‐ and six‐membered ring moieties can establish the peripheral ring current only as charged species.…”

“…The present information on the magnetic criterion is literature relevant in that N[2.3.4] [67] and N[2.3.3]S [63] are not completely but only partly anti‐aromatic; there are two ring currents of different direction within the same molecule and only the dominating one is paratropic.…”