935 research outputs found
About the Dirac Equation with a potential
An elementary treatment of the Dirac Equation in the presence of a
three-dimensional spherically symmetric -potential is
presented. We show how to handle the matching conditions in the configuration
space, and discuss the occurrence of supercritical effects.Comment: 8 pages, 1 postscript figure, Latex, Revise
Inverse magnetic catalysis from the properties of the QCD coupling in a magnetic field
We compute the vacuum one-loop quark-gluon vertex correction at zero
temperature in the presence of a magnetic field. From the vertex function we
extract the effective quark-gluon coupling and show that it grows with
increasing magnetic field strength. The effect is due to a subtle competition
between the color charge associated to gluons and the color charge associated
to quarks, the former being larger than the latter. In contrast, at high
temperature the effective thermo-magnetic coupling results exclusively from the
contribution of the color charge associated to quarks. This produces a decrease
of the coupling with increasing field strength. We interpret the results in
terms of a geometrical effect whereby the magnetic field induces, on average, a
closer distance between the (electrically charged) quarks and antiquarks. At
high temperature, since the effective coupling is proportional only to the
color charge associated to quarks, such proximity with increasing field
strength makes the effective coupling decrease due to asymptotic freedom. In
turn, this leads to a decreasing quark condensate. In contrast, at zero
temperature both the effective strong coupling and the quark condensate
increase with increasing magnetic field. This is due to the color charge
associated to gluons dominating over that associated to quarks, with both
having the opposite sign. Thus, the gluons induce a kind of screening of the
quark color charge, in spite of the quark-antiquark proximity. The implications
of these results for the inverse magnetic catalysis phenomenon are discussed.Comment: Expanded discussion, references added. Version to appear in Phys.
Lett.
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