The Infrared Problem in QED: A Lesson from a Model with Coulomb Interaction and Realistic Photon Emission
The Infrared Problem in QED: A Lesson from a Model with Coulomb Interaction and Realistic Photon Emission
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QED 中的红外问题：库仑相互作用和真实光子发射模型的教训
DOI：
10.1007/s00023-016-0486-5
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
F. Strocchi
中科院分区：
文献类型：
--
作者：
G. Morchio;F. Strocchi
The scattering of photons and heavy classical Coulomb interacting particles, with realistic particle–photon interaction (without particle recoil) is studied adopting the Koopman formulation for the particles. The model is translation invariant and allows for a complete control of the Dollard strategy devised by Kulish–Faddeev and Rohrlich (KFR) for QED: in the adiabatic formulation, the Møller operators exist as strong limits and interpolate between the dynamics and a non-free asymptotic dynamics, which is a unitary group; the S-matrix is non-trivial and exhibits the factorization of all the infrared divergences. The implications of the KFR strategy on the open questions of the LSZ asymptotic limits in QED are derived in the field theory version of the model, with the charged particles described by second quantized fields: i) asymptotic limits of the charged fields, $${\Psi_{{\rm out}/{\rm in}}(x)}$$Ψout/in(x), are obtained as strong limits of modified LSZ formulas, with corrections given by a Coulomb phase operator and an exponential of the photon field; ii) free asymptotic electromagnetic fields, $${B_{{\rm out}/{\rm in}}(x)}$$Bout/in(x), are given by the massless LSZ formula, as in Buchholz approach; iii) the asymptotic field algebras are a semidirect product of the canonical algebras generated by $${B_{{\rm out}/{\rm in}}}$$Bout/in, $${\Psi_{{\rm out}/{\rm in}}}$$Ψout/in; iv) on the asymptotic spaces, the Hamiltonian is the sum of the free (commuting) Hamiltonians of $${B_{{\rm out}/{\rm in}}}$$Bout/in, $${\Psi_{{\rm out}/{\rm in}}}$$Ψout/in and the same holds for the generators of the space translations.
The scattering of photons and heavy classical Coulomb interacting particles, with realistic particle–photon interaction (without particle recoil) is studied adopting the Koopman formulation for the particles. The model is translation invariant and allows for a complete control of the Dollard strategy devised by Kulish–Faddeev and Rohrlich (KFR) for QED: in the adiabatic formulation, the Møller operators exist as strong limits and interpolate between the dynamics and a non-free asymptotic dynamics, which is a unitary group; the S-matrix is non-trivial and exhibits the factorization of all the infrared divergences. The implications of the KFR strategy on the open questions of the LSZ asymptotic limits in QED are derived in the field theory version of the model, with the charged particles described by second quantized fields: i) asymptotic limits of the charged fields, $${\Psi_{{\rm out}/{\rm in}}(x)}$$Ψout/in(x), are obtained as strong limits of modified LSZ formulas, with corrections given by a Coulomb phase operator and an exponential of the photon field; ii) free asymptotic electromagnetic fields, $${B_{{\rm out}/{\rm in}}(x)}$$Bout/in(x), are given by the massless LSZ formula, as in Buchholz approach; iii) the asymptotic field algebras are a semidirect product of the canonical algebras generated by $${B_{{\rm out}/{\rm in}}}$$Bout/in, $${\Psi_{{\rm out}/{\rm in}}}$$Ψout/in; iv) on the asymptotic spaces, the Hamiltonian is the sum of the free (commuting) Hamiltonians of $${B_{{\rm out}/{\rm in}}}$$Bout/in, $${\Psi_{{\rm out}/{\rm in}}}$$Ψout/in and the same holds for the generators of the space translations.