3 research outputs found
Construction of the Pauli-Villars-regulated Dirac vacuum in electromagnetic fields
Using the Pauli-Villars regularization and arguments from convex analysis, we
construct solutions to the classical time-independent Maxwell equations in
Dirac's vacuum, in the presence of small external electromagnetic sources. The
vacuum is not an empty space, but rather a quantum fluctuating medium which
behaves as a nonlinear polarizable material. Its behavior is described by a
Dirac equation involving infinitely many particles. The quantum corrections to
the usual Maxwell equations are nonlinear and nonlocal. Even if photons are
described by a purely classical electromagnetic field, the resulting vacuum
polarization coincides to first order with that of full Quantum
Electrodynamics.Comment: Final version to appear in Arch. Rat. Mech. Analysi
The Quark Propagator from the Dyson-Schwinger Equations: I. the Chiral Solution
Within the framework of the Dyson-Schwinger equations in the axial gauge, we
study the effect that non-perturbative glue has on the quark propagator. We
show that Ward-Takahashi identities, combined with the requirement of matching
perturbative QCD at high momentum transfer, guarantee the multiplicative
renormalisability of the answer. Technically, the matching with perturbation
theory is accomplished by the introduction of a transverse part to the
quark-gluon vertex. We show that this transverse vertex is crucial for chiral
symmetry breaking, and that massless solutions exist below a critical value of
the strong coupling constant. Using the gluon propagator that we previously
calculated, we obtain small corrections to the quark propagator, which keeps a
pole at the origin in the chiral phase.Comment: 21 pages, 6 figures; McGill/94-24, SHEP 93/94-26 We generalise our
results by showing that they are not sensitive to the specific choice that we
make for the transverse vertex. We illustrate that fact in two new figure