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Relativistic Quantum Dynamics 
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#19
Feb2411, 04:27 PM

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The dressed particle approach can be regarded as a generalization of the above derivation to higher orders of the perturbation theory. Eugene. 


#20
Feb2511, 02:16 AM

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Eugene. 


#21
Feb2511, 03:39 AM

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#22
Feb2511, 03:48 AM

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Eugene. 


#23
Feb2511, 05:12 AM

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The mean number of photons in the photon state accompanying a free electron is infinite. Since one can show (and Bob_for_short was always eager to point this out, in his own language) that the overlap of this photon state with an arbitrary Nphoton state is exactly zero for any N, the state of the photon cloud cannot be a Fock state. 


#24
Feb2511, 05:36 AM

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But it is impossible to discuss this with someone who ignores all field theoretical insight. But even if you argue that on the level of perturbation theory, this argument is adequate, it doesn't change may main point: That for the _calculation_ of radiation corrections to Smatrix entries your formalism is utterly unsuitable, and you need to refer to Weinberg's calculations. By the way, in 10.1 you say (p.351 top): ''The physical vacuum in QED is not just an empty state without particles. It is more like a boiling “soup” of particles, antiparticles, and photons.'' This is incorrect. It would be a boiling soup of bare particles, but these are eliminated by renormalization. The renormalized vacuum is completely empty and inert. 


#25
Feb2511, 05:57 AM

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Of course, form factors may be probed by means of scattering experiments, but this is a different matter. But trivial form factors are synonymous with point particles. See the entry ''Are electrons pointlike/structureless?'' of Chapter B2 of my theoretical physics FAQ at http://www.mat.univie.ac.at/~neum/ph...html#pointlike 


#26
Feb2511, 05:59 AM

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#27
Feb2511, 06:14 AM

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#28
Feb2511, 08:51 AM

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On top of p.133 of your book, I found the remark that ''the photon is not a true elementary particle as it is not described by an irreducible representation of the PoincarŽe group. We will see in subsection 5.3.3 that a photon is described by a reducible representation of the PoincarŽe group which is a direct sum of two irreducible representations with helicities +1 and 1.''
In your terminology (that only considers irreducible representations of the connected part of the Poincare group), the lefthanded photon is elementary, and the righthanded photon is its antiparticle. Thus photons are elementary even according to this rule  just not all of them. 


#29
Feb2511, 12:53 PM

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Eugene. 


#30
Feb2511, 01:16 PM

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#31
Feb2511, 01:17 PM

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Eugene. 


#32
Feb2511, 01:48 PM

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See, e.g., (2.21) in http://arxiv.org/pdf/quantph/9907069 for a nonselfadjoint momentum operator; physically more relevant examples and the HY theorem itself are discussed in Vol.3 of the math physics treatise by Thirring. 


#33
Feb2511, 01:55 PM

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Instead of Maxwell equations, I suggest to use the DarwinBreit Hamiltonian derived in subsection 12.1.1. In chapter 12 I discuss a number of electromagnetic effects and how they can be explained/described using this Hamiltonian. If you know some other effect, where this Hamiltonian fails, then it would be a real problem for my approach. Do you know such an effect? Eugene. 


#34
Feb2511, 02:01 PM

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Eugene. 


#35
Feb2511, 02:08 PM

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Eugene. 


#36
Feb2511, 02:11 PM

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Eugene. 


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