3,529 research outputs found
Short Range Interactions in the Hydrogen Atom
In calculating the energy corrections to the hydrogen levels we can identify
two different types of modifications of the Coulomb potential , with one
of them being the standard quantum electrodynamics corrections, ,
satisfying over the whole range of
the radial variable . The other possible addition to is a potential
arising due to the finite size of the atomic nucleus and as a matter of fact,
can be larger than in a very short range. We focus here on the latter
and show that the electric potential of the proton displays some undesirable
features. Among others, the energy content of the electric field associated
with this potential is very close to the threshold of pair production.
We contrast this large electric field of the Maxwell theory with one emerging
from the non-linear Euler-Heisenberg theory and show how in this theory the
short range electric field becomes smaller and is well below the pair
production threshold
On Gauge Invariance and Minimal Coupling
The principle of minimal coupling has been used in the study of Higgs boson
interactions to argue that certain higher dimensional operators in the
low-energy effective theory generalization of the Standard Model are suppressed
by loop factors, and thus smaller than others. It also has been extensively
used to analyze beyond-the-standard-model theories. We show that in field
theory, and even in quantum mechanics, the concept of minimal coupling is
ill-defined and inapplicable as a general principle, and give many pedagogical
examples which illustrate this fact. We also clarify some related
misconceptions about the dynamics of strongly coupled gauge theories. Many
arguments in the literature on Higgs boson interactions that use minimal
coupling, particularly in pseudo-Goldstone Higgs theories, are inherently
flawed.Comment: 25 pp, 2 figures v2: refs added, JHEP version, conclusions unchange
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