9,984 research outputs found

### Non-Abelian Stokes Theorem and Quark Confinement in SU(3) Yang-Mills Gauge Theory

We derive a new version of SU(3) non-Abelian Stokes theorem by making use of
the coherent state representation on the coset space $SU(3)/(U(1)\times
U(1))=F_2$, the flag space. Then we outline a derivation of the area law of the
Wilson loop in SU(3) Yang-Mills theory in the maximal Abelian gauge (The
detailed exposition will be given in a forthcoming article). This derivation is
performed by combining the non-Abelian Stokes theorem with the reformulation of
the Yang-Mills theory as a perturbative deformation of a topological field
theory recently proposed by one of the authors. Within this framework, we show
that the fundamental quark is confined even if $G=SU(3)$ is broken by partial
gauge fixing into $H=U(2)$ just as $G$ is broken to $H=U(1) \times U(1)$. An
origin of the area law is related to the geometric phase of the Wilczek-Zee
holonomy for U(2). Abelian dominance is an immediate byproduct of these results
and magnetic monopole plays the dominant role in this derivation.Comment: 14 pages, Latex, no figures, version accepted for publication in Mod.
Phys. Lett. A (some comments are added in the final parts

### Magnetic condensation, Abelian dominance, and instability of Savvidy vacuum in Yang-Mills theory

We propose a novel type of color magnetic condensation originating from
magnetic monopoles so that it provides the mass of off-diagonal gluons in the
Yang-Mills theory.
This dynamical mass generation enables us to explain the infrared Abelian
dominance and monopole dominance by way of a non-Abelian Stokes theorem, which
supports the dual superconductivity picture of quark confinement. Moreover, we
show that the instability of Savvidy vacuum disappears by sufficiently large
color magnetic condensation.Comment: 6 pages, 1 figure; a contribution to the 8th workshop on
non-perturbative QC

### Vacuum condensates, effective gluon mass and color confinement

We propose a new reformulation of Yang-Mills theory in which three- and
four-gluon self-interactions are eliminated at the price of introducing a
sufficient number of auxiliary fields. We discuss the validity of this
reformulation in the possible applications such as dynamical gluon mass
generation, color confinement and glueball mass calculation. We emphasize the
transverse-gluon pair condensation as the basic mechanism for dynamical mass
generation. The confinement is realized as a consequence of a fact that the
auxiliary fields become dynamical in the sense that they acquire the kinetic
term due to quantum corrections.Comment: 12 pages, 5 figures, invited talk given at International Symposium on
Color Confinement and Hadrons in Quantum Chromodynamics - Confinement 2003,
Wako, Japan, 21-24 Jul 2003, a reference correcte

### Implications of Analyticity to Mass Gap, Color Confinement and Infrared Fixed Point in Yang--Mills theory

Analyticity of gluon and Faddeev--Popov ghost propagators and their form
factors on the complex momentum-squared plane is exploited to continue
analytically the ultraviolet asymptotic form calculable by perturbation theory
into the infrared non-perturbative solution. We require the non-perturbative
multiplicative renormalizability to write down the renormalization group
equation. These requirements enable one to settle the value of the exponent
characterizing the infrared asymptotic solution with power behavior which was
originally predicted by Gribov and has recently been found as approximate
solutions of the coupled truncated Schwinger--Dyson equations. For this
purpose, we have obtained all the possible superconvergence relations for the
propagators and form factors in both the generalized Lorentz gauge and the
modified Maximal Abelian gauge. We show that the transverse gluon propagators
are suppressed in the infrared region to be of the massive type irrespective of
the gauge parameter, in agreement with the recent result of numerical
simulations on a lattice. However, this method alone is not sufficient to
specify some of the ghost propagators which play the crucial role in color
confinement. Combining the above result with the renormalization group equation
again, we find an infrared enhanced asymptotic solution for the ghost
propagator. The coupled solutions fulfill the color confinement criterion due
to Kugo and Ojima and also Nishijima, at least, in the Lorentz--Landau gauge.
We also point out that the solution in compatible with color confinement leads
to the existence of the infrared fixed point in pure Yang--Mills theory without
dynamical quarks. Finally, the Maximal Abelian gauge is also examined in
connection with quark confinement.Comment: 60 pages, 11 figure

### Finite-Temperature and -Density QED: Schwinger-Dyson Equation in the Real-Time Formalism

Based on the real-time formalism, especially, on Thermo Field Dynamics, we
derive the Schwinger-Dyson gap equation for the fermion propagator in QED and
Four-Fermion model at finite-temperature and -density. We discuss some
advantage of the real-time formalism in solving the self-consistent gap
equation, in comparison with the ordinary imaginary-time formalism. Once we
specify the vertex function, we can write down the SD equation with only
continuous variables without performing the discrete sum over Matsubara
frequencies which cannot be performed in advance without further approximation
in the imaginary-time formalism. By solving the SD equation obtained in this
way, we find the chiral-symmetry restoring transition at finite-temperature and
present the associated phase diagram of strong coupling QED.
In solving the SD equation, we consider two approximations:
instantaneous-exchange and $p_0$-independent ones. The former has a direct
correspondence in the imaginary time formalism, while the latter is a new
approximation beyond the former, since the latter is able to incorporate new
thermal effects which has been overlooked in the ordinary imaginary-time
solution. However both approximations are shown to give qualitatively the same
results on the finite-temperature phase transition.Comment: 28 pages+15 figures (figures: not included, available upon request

### 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

### 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.

### Yang-Mills theory constructed from Cho--Faddeev--Niemi decomposition

We give a new way of looking at the Cho--Faddeev--Niemi (CFN) decomposition
of the Yang-Mills theory to answer how the enlarged local gauge symmetry
respected by the CFN variables is restricted to obtain another Yang-Mills
theory with the same local and global gauge symmetries as the original
Yang-Mills theory. This may shed new light on the fundamental issue of the
discrepancy between two theories for independent degrees of freedom and the
role of the Maximal Abelian gauge in Yang-Mills theory. As a byproduct, this
consideration gives new insight into the meaning of the gauge invariance and
the observables, e.g., a gauge-invariant mass term and vacuum condensates of
mass dimension two. We point out the implications for the Skyrme--Faddeev
model.Comment: 17pages, 1 figure; English improved; a version appeared in Prog.
Theor. Phy

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