13,498 research outputs found
Transverse Ward-Takahashi Identity, Anomaly and Schwinger-Dyson Equation
Based on the path integral formalism, we rederive and extend the transverse
Ward-Takahashi identities (which were first derived by Yasushi Takahashi) for
the vector and the axial vector currents and simultaneously discuss the
possible anomaly for them. Subsequently, we propose a new scheme for writing
down and solving the Schwinger-Dyson equation in which the the transverse
Ward-Takahashi identity together with the usual (longitudinal) Ward-Takahashi
identity are applied to specify the fermion-boson vertex function. Especially,
in two dimensional Abelian gauge theory, we show that this scheme leads to the
exact and closed Schwinger-Dyson equation for the fermion propagator in the
chiral limit (when the bare fermion mass is zero) and that the Schwinger-Dyson
equation can be exactly solved.Comment: 22 pages, latex, no figure
On ghost condensation, mass generation and Abelian dominance in the Maximal Abelian Gauge
Recent work claimed that the off-diagonal gluons (and ghosts) in pure
Yang-Mills theories, with Maximal Abelian gauge fixing (MAG), attain a
dynamical mass through an off-diagonal ghost condensate. This condensation
takes place due to a quartic ghost interaction, unavoidably present in MAG for
renormalizability purposes. The off-diagonal mass can be seen as evidence for
Abelian dominance. We discuss why ghost condensation of the type discussed in
those works cannot be the reason for the off-diagonal mass and Abelian
dominance, since it results in a tachyonic mass. We also point out what the
full mechanism behind the generation of a real mass might look like.Comment: 7 pages; uses revtex
Spontaneous Chiral-Symmetry Breaking in Three-Dimensional QED with a Chern--Simons Term
In three-dimensional QED with a Chern--Simons term we study the phase
structure associated with chiral-symmetry breaking in the framework of the
Schwinger--Dyson equation. We give detailed analyses on the analytical and
numerical solutions for the Schwinger--Dyson equation of the fermion
propagator, where the nonlocal gauge-fixing procedure is adopted to avoid
wave-function renormalization for the fermion. In the absence of the
Chern--Simons term, there exists a finite critical number of four-component
fermion flavors, at which a continuous (infinite-order) chiral phase transition
takes place and below which the chiral symmetry is spontaneously broken. In the
presence of the Chern--Simons term, we find that the spontaneous
chiral-symmetry-breaking transition continues to exist, but the type of phase
transition turns into a discontinuous first-order transition. A simple
stability argument is given based on the effective potential, whose stationary
point gives the solution of the Schwinger-Dyson equation.Comment: 34 pages, revtex, with 9 postscriptfigures appended (uuencoded
Self-interaction effects on screening in three-dimensional QED
We have shown that self interaction effects in massive quantum
electrodynamics can lead to the formation of bound states of quark antiquark
pairs. A current-current fermion coupling term is introduced, which induces a
well in the potential energy profile. Explicit expressions of the effective
potential and renormalized parameters are provided
Renormalizing a BRST-invariant composite operator of mass dimension 2 in Yang-Mills theory
We discuss the renormalization of a BRST and anti-BRST invariant composite
operator of mass dimension 2 in Yang-Mills theory with the general BRST and
anti-BRST invariant gauge fixing term of the Lorentz type. The interest of this
study stems from a recent claim that the non-vanishing vacuum condensate of the
composite operator in question can be an origin of mass gap and quark
confinement in any manifestly covariant gauge, as proposed by one of the
authors. First, we obtain the renormalization group flow of the Yang-Mills
theory. Next, we show the multiplicative renormalizability of the composite
operator and that the BRST and anti-BRST invariance of the bare composite
operator is preserved under the renormalization. Third, we perform the operator
product expansion of the gluon and ghost propagators and obtain the Wilson
coefficient corresponding to the vacuum condensate of mass dimension 2.
Finally, we discuss the connection of this work with the previous works and
argue the physical implications of the obtained results.Comment: 49 pages, 35 eps-files, A number of typographic errors are corrected.
A paragraph is added in the beginning of section 5.3. Two equations (7.1) and
(7.2) are added. A version to be published in Phys. Rev.
Two-Band-Type Superconducting Instability in MgB2
Using the tight-binding method for the -bands in MgB, the Hubbard
on-site Coulomb interaction on two inequivalent boron -orbitals is
transformed into expressions in terms of -band operators. For scattering
processes relevant to the problemin which a wave vector {\bf q} is parallel to
, it is found to take a relatively simple form consisting of
intra-band Coulomb scattering, interband pair scattering etc. with large
constant coupling constants. This allows to get a simple expression for the
amplitude of interband pair scattering between two -bands, which diverges
if the interband polarization function in it becomes large enough.The latter
was approximately evaluated and found to be largely enhanced in the band
structure in MgB. These results lead to a divergent interband pair
scattering, meaning two-band-type superconducting instability with enhanced
. Adding a subsidiary BCS attractive interaction in each band into
consideration, a semi-quantitative gap equation is given, and and isotope
exponent are derived. The present instability is asserted to be the
origin of high in MgB.Comment: 4 pages, to be published in J. Phys. Soc. Jpn. vol. 70, No.
Zero Temperature Chiral Phase Transition in (2+1)-Dimensional QED with a Chern-Simons Term
We investigate the zero temperature chiral phase transition in
(2+1)-dimensional QED in the presence of a Chern-Simons term, changing the
number of fermion flavors. In the symmetric phase, there are no light degrees
of freedom even at the critical point. Unlike the case without a Chern-Simons
term, the phase transition is first-order.Comment: 7 pages, RevTeX, no figure
Regularization-independent study of renormalized non-perturbative quenched QED
A recently proposed regularization-independent method is used for the first
time to solve the renormalized fermion Schwinger-Dyson equation numerically in
quenched QED. The Curtis-Pennington vertex is used to illustrate the
technique and to facilitate comparison with previous calculations which used
the alternative regularization schemes of modified ultraviolet cut-off and
dimensional regularization. Our new results are in excellent numerical
agreement with these, and so we can now conclude with confidence that there is
no residual regularization dependence in these results. Moreover, from a
computational point of view the regularization independent method has enormous
advantages, since all integrals are absolutely convergent by construction, and
so do not mix small and arbitrarily large momentum scales. We analytically
predict power law behaviour in the asymptotic region, which is confirmed
numerically with high precision. The successful demonstration of this efficient
new technique opens the way for studies of unquenched QED to be undertaken in
the near future.Comment: 20 pages,5 figure
Dynamical mass generation of a two-component fermion in Maxwell-Chern-Simons QED_3: The lowest ladder approximation
Dynamical mass generation of a two-component fermion in with a
Chern-Simons term is investigated by solving the Schwinger-Dyson equation
formulated in the lowest ladder approximation. Dependence of the dynamical
fermion mass on a gauge-fixing parameter, a gauge coupling constant, and a
topological mass is examined by approximated analytical and also numerical
methods. The inclusion of the Chern-Simons term makes impossible to choose a
peculiar gauge in which a wave function renormalization is absent. The
numerical evaluation shows that the wave function renormalization is fairly
close to 1 in the Landau gauge. It means that this gauge is still a specific
gauge where the Ward-Takahashi identity is satisfied approximately. We also
find that the dynamical mass is almost constant if the topological mass is
larger than the coupling constant, while it decreases when the topological mass
is comparable to or smaller than the coupling constant and tends to the value
in without the Chern-Simons term.Comment: 22 pages, 9 figures, Version to appear in Phys. Rev.
Stability of the Magnetic Monopole Condensate in three- and four-colour QCD
It is argued that the ground state of three- and four-colour QCD contains a
monopole condensate, necessary for the dual Meissner effect to be the mechanism
of confinement, and support its stability on the grounds that it gives the
off-diagonal gluons an effective mass sufficient to remove the unstable ground
state mode.Comment: jhep.cls, typos corrected, references added, some content delete
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