117 research outputs found
Wilson Loop and the Treatment of Axial Gauge Poles
We consider the question of gauge invariance of the Wilson loop in the light
of a new treatment of axial gauge propagator proposed recently based on a
finite field-dependent BRS (FFBRS) transformation. We remark that as under the
FFBRS transformation the vacuum expectation value of a gauge invariant
observable remains unchanged, our prescription automatically satisfies the
Wilson loop criterion. Further, we give an argument for {\it direct}
verification of the invariance of Wilson loop to O(g^4) using the earlier work
by Cheng and Tsai. We also note that our prescription preserves the thermal
Wilson loop to O(g^2).Comment: 8 pages, LaTex; some typos related to equation (18) correcte
Correct Treatment of 1/(\eta\cdot k)^p Singularities in the Axial Gauge Propagator
The propagators in axial-type, light-cone and planar gauges contain
1/(\eta\cdot k)^p-type singularities. These singularities have generally been
treated by inventing prescriptions for them. In this work, we propose an
alternative procedure for treating these singularities in the path integral
formalism using the known way of treating the singularities in Lorentz gauges.
To this end, we use a finite field-dependent BRS transformation that
interpolates between Lorentz-type and the axial-type gauges. We arrive at the
-dependent tree propagator in the axial-type gauges. We examine the
singularity structure of the propagator and find that the axial gauge
propagator so constructed has {\it no} spurious poles (for real ). It
however has a complicated structure in a small region near . We
show how this complicated structure can effectively be replaced by a much
simpler propagator.Comment: 34 pages, LaTex, 2 ps figures; some comments on Wilson loop and two
references added; (this) revised version to appear in Int.J.Mod.Phys.
Gauge-Independent Off-Shell Fermion Self-Energies at Two Loops: The Cases of QED and QCD
We use the pinch technique formalism to construct the gauge-independent
off-shell two-loop fermion self-energy, both for Abelian (QED) and non-Abelian
(QCD) gauge theories. The new key observation is that all contributions
originating from the longitudinal parts of gauge boson propagators, by virtue
of the elementary tree-level Ward identities they trigger, give rise to
effective vertices, which do not exist in the original Lagrangian; all such
vertices cancel diagrammatically inside physical quantities, such as current
correlation functions or S-matrix elements. We present two different, but
complementary derivations: First, we explicitly track down the aforementioned
cancellations inside two-loop diagrams, resorting to nothing more than basic
algebraic manipulations. Second, we present an absorptive derivation,
exploiting the unitarity of the S-matrix, and the Ward identities imposed on
tree-level and one-loop physical amplitudes by gauge invariance, in the case of
QED, or by the underlying Becchi-Rouet-Stora symmetry, in the case of QCD. The
propagator-like sub-amplitude defined by means of this latter construction
corresponds precisely to the imaginary parts of the effective self-energy
obtained in the former case; the real part may be obtained from a (twice
subtracted) dispersion relation. As in the one-loop case, the final two-loop
fermion self-energy constructed using either method coincides with the
conventional fermion self-energy computed in the Feynman gauge.Comment: 30 pages; uses axodraw (axodraw.sty included in the src); final
version to appear in Phys. Rev.
Similarity Renormalization, Hamiltonian Flow Equations, and Dyson's Intermediate Representation
A general framework is presented for the renormalization of Hamiltonians via
a similarity transformation. Divergences in the similarity flow equations may
be handled with dimensional regularization in this approach, and the resulting
effective Hamiltonian is finite since states well-separated in energy are
uncoupled. Specific schemes developed several years ago by Glazek and Wilson
and contemporaneously by Wegner correspond to particular choices within this
framework, and the relative merits of such choices are discussed from this
vantage point. It is shown that a scheme for the transformation of Hamiltonians
introduced by Dyson in the early 1950's also corresponds to a particular choice
within the similarity renormalization framework, and it is argued that Dyson's
scheme is preferable to the others for ease of computation. As an example, it
is shown how a logarithmically confining potential arises simply at second
order in light-front QCD within Dyson's scheme, a result found previously for
other similarity renormalization schemes. Steps toward higher order and
nonperturbative calculations are outlined. In particular, a set of equations
analogous to Dyson-Schwinger equations is developed.Comment: REVTex, 32 pages, 7 figures (corrected references
More on the relation between the two physically inequivalent decompositions of the nucleon spin and momentum
In a series of papers, we have established the existence of two
gauge-invariant decompositions of the nucleon spin, which are physically
nonequivalent. The orbital angular momenta of quarks and gluons appearing in
these two decompositions are gauge-invariant dynamical orbital angular momenta
and "generalized" canonical orbital angular momenta with gauge-invariance,
respectively. The key quantity, which characterizes the difference between
these two types of orbital angular momenta is what-we-call the {\it potential
angular momentum}. We argue that the physical meaning of the potential angular
momentum in the nucleon can be made more transparent, by investigating a
related but much simpler example from electrodynamics. We also make clear
several remaining issues in the spin and momentum decomposition problem of the
nucleon. We clarify the relationship between the evolution equations of orbital
angular momenta corresponding to the two different decompositions above. We
also try to answer the question whether the two different decompositions of the
nucleon momentum really lead to different evolution equations, thereby
predicting conflicting asymptotic values for the quark and gluon momentum
fractions in the nucleon.Comment: The version to appear in Physical Review D, LaTeX, 47 pages, 4
figure
Two-Dimensional QCD in the Wu-Mandelstam-Leibbrandt Prescription
We find the exact non-perturbative expression for a simple Wilson loop of
arbitrary shape for U(N) and SU(N) Euclidean or Minkowskian two-dimensional
Yang-Mills theory regulated by the Wu-Mandelstam-Leibbrandt gauge prescription.
The result differs from the standard pure exponential area-law of YM_2, but
still exhibits confinement as well as invariance under area-preserving
diffeomorphisms and generalized axial gauge transformations. We show that the
large N limit is NOT a good approximation to the model at finite N and conclude
that Wu's N=infinity Bethe-Salpeter equation for QCD_2 should have no bound
state solutions. The main significance of our results derives from the
importance of the Wu-Mandelstam-Leibbrandt prescription in higher-dimensional
perturbative gauge theory.Comment: 7 pages, LaTeX, REVTE
Staggered fermions and chiral symmetry breaking in transverse lattice regulated QED
Staggered fermions are constructed for the transverse lattice regularization
scheme. The weak perturbation theory of transverse lattice non-compact QED is
developed in light-cone gauge, and we argue that for fixed lattice spacing this
theory is ultraviolet finite, order by order in perturbation theory. However,
by calculating the anomalous scaling dimension of the link fields, we find that
the interaction Hamiltonian becomes non-renormalizable for ,
where is the bare (lattice) QED coupling constant. We conjecture that
this is the critical point of the chiral symmetry breaking phase transition in
QED. Non-perturbative chiral symmetry breaking is then studied in the strong
coupling limit. The discrete remnant of chiral symmetry that remains on the
lattice is spontaneously broken, and the ground state to lowest order in the
strong coupling expansion corresponds to the classical ground state of the
two-dimensional spin one-half Heisenberg antiferromagnet.Comment: 30 pages, UFIFT-HEP-92-1
QED3 theory of pairing pseudogap in cuprates: From d-wave superconductor to antiferromagnet via "algebraic" Fermi liquid
High- cuprates differ from conventional superconductors in three crucial
aspects: the superconducting state descends from a strongly correlated
Mott-Hubbard insulator, the order parameter exhibits d-wave symmetry and
superconducting fluctuations play an all important role. We formulate a theory
of the pseudogap state in the cuprates by taking the advantage of these unusual
features. The effective low energy theory within the pseudogap phase is shown
to be equivalent to the (anisotropic) quantum electrodynamics in (2+1)
space-time dimensions (QED). The role of Dirac fermions is played by the
nodal BdG quasiparticles while the massless gauge field arises through
unbinding of quantum vortex-antivortex degrees of freedom. A detailed
derivation of this QED theory is given and some of its main physical
consequences are inferred for the pseudogap state. We focus on the properties
of symmetric QED and propose that inside the pairing protectorate it
assumes the role reminiscent of that played by the Fermi liquid theory in
conventional metals.Comment: 31 pages, 4 figures; replaced with revised versio
One-Loop Divergences in Simple Supergravity: Boundary Effects
This paper studies the semiclassical approximation of simple supergravity in
Riemannian four-manifolds with boundary, within the framework of
-function regularization. The massless nature of gravitinos, jointly
with the presence of a boundary and a local description in terms of potentials
for spin , force the background to be totally flat. First, nonlocal
boundary conditions of the spectral type are imposed on spin-
potentials, jointly with boundary conditions on metric perturbations which are
completely invariant under infinitesimal diffeomorphisms. The axial
gauge-averaging functional is used, which is then sufficient to ensure
self-adjointness. One thus finds that the contributions of ghost and gauge
modes vanish separately. Hence the contributions to the one-loop wave function
of the universe reduce to those values resulting from physical modes
only. Another set of mixed boundary conditions, motivated instead by local
supersymmetry and first proposed by Luckock, Moss and Poletti, is also
analyzed. In this case the contributions of gauge and ghost modes do not cancel
each other. Both sets of boundary conditions lead to a nonvanishing
value, and spectral boundary conditions are also studied when two concentric
three-sphere boundaries occur. These results seem to point out that simple
supergravity is not even one-loop finite in the presence of boundaries.Comment: 37 pages, Revtex. Equations (5.2), (5.3), (5.5), (5.7), (5.8) and
(5.13) have been amended, jointly with a few misprint
Semiclassical Equations for Weakly Inhomogeneous Cosmologies
The in-in effective action formalism is used to derive the semiclassical
correction to Einstein's equations due to a massless scalar quantum field
conformally coupled to small gravitational perturbations in spatially flat
cosmological models. The vacuum expectation value of the stress tensor of the
quantum field is directly derived from the renormalized in-in effective action.
The usual in-out effective action is also discussed and it is used to compute
the probability of particle creation. As one application, the stress tensor of
a scalar field around a static cosmic string is derived and the backreaction
effect on the gravitational field of the string is discussed.Comment: 35 pages, UAB-FT 316, Latex (uses a4wide.sty, a4.sty included in the
file)(replaced due to tex problems
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