QuantumPhysics.dvi

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This gives the molecule an electric dipole moment. An electric chargeqinserted into water vapor,
will experience screening. A positive chargeq >0 located at a pointPwill preferentially orient the
water molecules so that their negative ends (the Oxygen) point towards the pointP, while their
positive ends point away fromP. The collective effect produced by the systematic orientations of
the water molecules results in the screening of the chargeq, so that the effective charge observed
some distance away fromqwill be smaller thanq.


Now introduce the electric chargeqin thevacuum. At first sight, it will seem that there is
no material available to screen this charge, since naively the vacuum is empty. In fact, we know
already from the Casimir effect that vacuum fluctuations of thequantum electro-magnetic field
induces physically observable effects. Here, it is the vacuumfluctuations of the Dirac field of the
electron and positron that will produce a measurable effect. We begin by describing the effect
qualitatively first, and we will compute it in full in the subsequent subsections.


Qualitatively, the origin of vacuum polarization lies in the fact that vacuum fluctuations of the
Dirac field amount to the creation of virtual pairs of an electron and a positron. These particles
are virtual in the sense that there is not enough energy available to make them materialize as real
physical electron and positron. By the energy-time uncertainty relation, these particles can exist
only for a very short time, after which they must annihilate one another. But during their short
life-time, the pair forms a small electric dipole. And this (virtual) dipole has a screening effect on
the electric charge which is completely analogous to the effect produced by a real electric dipole
like water. As a result, if a chargeqis introduced at a pointP in the Dirac vacuum, then the
effective charge felt must decrease with distance away fromP.


Is it possible to have the opposite effect? Namely, could the effective charge increase as the
distance increases? Not in electro-dynamics. In non-Abelian gauge theories (Yang-Mills theories)
however, this is possible, and in fact generic within certain ranges of parameters, and this effect is
equivalent to the property of asymptotic freedom.

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