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Atomic Nuclear Physics

Optical physics solutions to the problems by Lipson S.

By Lipson S.

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The closest one can get to the LF gauge is In this gauge one can now investigate the problem of incomplete gauge fixing. The gauge still leaves the freedom of -independent gauge transformations where if we restrict ourselves to periodic In such an incompletely gauge fixed situation, not all degrees of freedom are physical and approximations may result in inconsistencies. 39), which is a constraint on the physical Hilbert space. 39) is violated. A more thorough discussion on this subject and possible caveats can be found in Refs.

29), this implies that it may be possible to determine the coupling constants in the effective LF hamiltonian self-consistently. Similar results may be derived for Yukawa theories. 16), which are also accessible in a LF calculation. Extracting vacuum condensates from a canonical LF calculation via sum rules has, for example, been done in Ref. 73 for the quark condensate in The numerical result for was confirmed later in Ref. 23 in an equal time framework. A finite quark mass calculation, based on LF wave functions and sum rule techniques, was first conducted in Refs.

16) can even be expressed in terms of a local Unfortunately, this is not possible for the term containing the fermionic spectral density, which would read Note that in order to obtain the full counterterm necessary to establish agreement between a covariant calculation and a canonical LF calculation, one still has to add the one-loop counterterm — but this should be obvious and can be easily done. Similar statements hold for fermion loops in the boson self-energy. , no space–time symmetries can be used to fine-tune the counterterm.

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