202 research outputs found
Electromagnetic current correlations in reduced quantum electrodynamics
We consider a theory of massless reduced quantum electrodynamics
(RQED), e.g., a quantum field theory where the U(1) gauge
field lives in -spacetime dimensions while the fermionic field lives
in a reduced spacetime of dimensions (). In the
case where such RQEDs are renormalizable while they are
super-renormalizable for . The 2-loop electromagnetic current
correlation function is computed exactly for a general RQED.
Focusing on RQED, the corresponding -function is shown to vanish
which implies the scale invariance of the theory. Interaction correction to the
1-loop vacuum polarization, , of RQED is found to be: \Pi =
\Pi_1 (1 + 0.056 \al) where \al is the fine structure constant. The scaling
dimension of the fermion field is computed at 1-loop and is shown to be
anomalous for RQED.Comment: (v2) Accepted for publication in PRD. Conclusion and references added
(some / referee's comments). No change in results. 8 pages, 3 figures. (v1)
LaTeX file with feynMF package. 8 pages, no figur
One-dimensional interacting electrons beyond the Dzyaloshinskii-Larkin theorem
We consider one-dimensional (1D) interacting electrons beyond the
Dzyaloshinskii-Larkin theorem, i.e., keeping forward scattering interactions
among the electrons but adding a non-linear correction to the electron
dispersion relation. The latter generates multi-loop corrections to the
polarization operator and electron self-energy thereby providing a variety of
inelastic processes affecting equilibrium as well as non-equilibrium properties
of the 1D system. We first review the computation of equilibrium properties,
e.g., the high frequency part of the dynamical structure factor and corrections
to the electron-electron scattering rate. On this basis, microscopic
equilibration processes are identified and a qualitative estimate of the
relaxation rate of thermal carriers is given.Comment: 4 pages, 5 figure
Field theoretic renormalization study of interaction corrections to the universal ac conductivity of graphene
The two-loop interaction correction coefficient to the universal ac
conductivity of disorder-free intrinsic graphene is computed with the help of a
field theoretic renormalization study using the BPHZ prescription. Non-standard
Ward identities imply that divergent subgraphs (related to Fermi velocity
renormalization) contribute to the renormalized optical conductivity.
Proceeding either via density-density or via current-current correlation
functions, a single well-defined value is obtained: in agreement with the result first obtained by Mishchenko and which is
compatible with experimental uncertainties.Comment: LaTeX file with feynMF package. (v2) Footnotes and references added
to answer referee's questions and comments. No change in results. 23 pages
(JHEP format), 4 figures (v1) 12 pages, 4 figure
Two-loop fermion self-energy in reduced quantum electrodynamics and application to the ultra-relativistic limit of graphene
We compute the two-loop fermion self-energy in massless reduced quantum
electrodynamics for an arbitrary gauge using the method of integration by
parts. Focusing on the limit where the photon field is four-dimensional, our
formula involves only recursively one-loop integrals and can therefore be
evaluated exactly. From this formula, we deduce the anomalous scaling dimension
of the fermion field as well as the renormalized fermion propagator up to two
loops. The results are then applied to the ultra-relativistic limit of graphene
and compared with similar results obtained for four-dimensional and
three-dimensional quantum electrodynamics.Comment: (v2) Accepted for publication in PRD. Footnote with reference added
per referee's comment, other minor modifications. No change in results. 23
pages, 4 figures. (v1) LaTeX file with feynMF package. 23 pages, 4 figure
Interaction corrections to the minimal conductivity of graphene via dimensional regularization
We compute the two-loop interaction correction to the minimal conductivity of
disorder-free intrinsic graphene with the help of dimensional regularization.
The calculation is done in two different ways: via density-density and via
current-current correlation functions. Upon properly renormalizing the
perturbation theory, in both cases, we find that: \sigma = \sigma_0\,( 1 +
\al\,(19-6\pi)/12) \approx \sigma_0 \,(1 + 0.01\, \al), where \al = e^2 / (4
\pi \hbar v) is the renormalized fine structure constant and . Our results are consistent with experimental uncertainties and
resolve a theoretical dispute.Comment: (v2) 5 pages, 2 figures, ref [19] added, minor typos corrected, no
change in results. (v1) 5 pages, 2 figure
Statistical properties of charged interfaces
We consider the equilibrium statistical properties of interfaces submitted to
competing interactions; a long-range repulsive Coulomb interaction inherent to
the charged interface and a short-range, anisotropic, attractive one due to
either elasticity or confinement. We focus on one-dimensional interfaces such
as strings. Model systems considered for applications are mainly aggregates of
solitons in polyacetylene and other charge density wave systems, domain lines
in uniaxial ferroelectrics and the stripe phase of oxides. At zero temperature,
we find a shape instability which lead, via phase transitions, to tilted
phases. Depending on the regime, elastic or confinement, the order of the
zero-temperature transition changes. Thermal fluctuations lead to a pure
Coulomb roughening of the string, in addition to the usual one, and to the
presence of angular kinks. We suggest that such instabilities might explain the
tilting of stripes in cuprate oxides. The 3D problem of the charged wall is
also analyzed. The latter experiences instabilities towards various tilted
phases separated by a tricritical point in the elastic regime. In the
confinement regime, the increase of dimensionality favors either the melting of
the wall into a Wigner crystal of its constituent charges or a strongly
inclined wall which might have been observed in nickelate oxides.Comment: 17 pages, 11 figure
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