meopemuk
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@LittleSchwinger: Thank you for the kind words about my work.
1. This is the Lagrangian before renormalization. At page 295 the authors expressed a belief that renormalization can be added to their finite-time description. But I doubt that it can be done, because the whole point of renormalization is to fix time evolution in the infinite time interval (a.k.a. the S-matrix) by adding infinite counterterms to the Hamiltonian, thus destroying the possibility to obtain a realistic time evolution at finite time intervals.
2. This Lagrangian/Hamiltonian is formulated in the "bare" particle representation. But time evolution of bare particles (even if they are alone) is meaningless, because they are not eigenstates of the total mass operator. If you start with a single bare electron at time t=0, then at the next time instant the electron will "dress" itself with a coat of virtual photons. Real life electrons don't do that.
The "dressed particle" theory fixes both these problems. It rewrites the Hamiltonian of the renormalized QED in terms of physical or dressed particles (e.g., the bare electron plus its virtual coat). The new Hamiltonian appears to be finite and can be used as the generator of time evolution for physical multiparticle states. The S-matrix obtained with this Hamiltonian coincides with the S-matrix of renormalized QED in all perturbation orders.
Eugene
The authors of this work used the "standard" Lagrangian of QED in equation right after eq. (2.56). I have two major issues with their approach:Demystifier said:Title: Quantum Field Theory with Finite Time Interval: Application to QED
1. This is the Lagrangian before renormalization. At page 295 the authors expressed a belief that renormalization can be added to their finite-time description. But I doubt that it can be done, because the whole point of renormalization is to fix time evolution in the infinite time interval (a.k.a. the S-matrix) by adding infinite counterterms to the Hamiltonian, thus destroying the possibility to obtain a realistic time evolution at finite time intervals.
2. This Lagrangian/Hamiltonian is formulated in the "bare" particle representation. But time evolution of bare particles (even if they are alone) is meaningless, because they are not eigenstates of the total mass operator. If you start with a single bare electron at time t=0, then at the next time instant the electron will "dress" itself with a coat of virtual photons. Real life electrons don't do that.
The "dressed particle" theory fixes both these problems. It rewrites the Hamiltonian of the renormalized QED in terms of physical or dressed particles (e.g., the bare electron plus its virtual coat). The new Hamiltonian appears to be finite and can be used as the generator of time evolution for physical multiparticle states. The S-matrix obtained with this Hamiltonian coincides with the S-matrix of renormalized QED in all perturbation orders.
Eugene