25,353 research outputs found
Gluon Condensation in Nonperturbative Flow Equations
We employ nonperturbative flow equations for an investigation of the
effective action in Yang-Mills theories. We compute the effective action
for constant color magnetic fields and examine Savvidy's
conjecture of an unstable perturbative vacuum. Our results indicate that the
absolute minimum of occurs for B=0. Gluon condensation is described
by a nonvanishing expectation value of the regularized composite operator
which agrees with phenomenological estimates.Comment: 64 pages, late
Truncated Schwinger-Dyson Equations and Gauge Covariance in QED3
We study the Landau-Khalatnikov-Fradkin transformations (LKFT) in momentum
space for the dynamically generated mass function in QED3. Starting from the
Landau gauge results in the rainbow approximation, we construct solutions in
other covariant gauges. We confirm that the chiral condensate is gauge
invariant as the structure of the LKFT predicts. We also check that the gauge
dependence of the constituent fermion mass is considerably reduced as compared
to the one obtained directly by solving SDE.Comment: 17 pages, 11 figures. v3. Improved and Expanded. To appear in Few
Body System
Galilean invariant resummation schemes of cosmological perturbations
Many of the methods proposed so far to go beyond Standard Perturbation Theory
break invariance under time-dependent boosts (denoted here as extended Galilean
Invariance, or GI). This gives rise to spurious large scale effects which spoil
the small scale predictions of these approximation schemes. By using
consistency relations we derive fully non-perturbative constraints that GI
imposes on correlation functions. We then introduce a method to quantify the
amount of GI breaking of a given scheme, and to correct it by properly tailored
counterterms. Finally, we formulate resummation schemes which are manifestly
GI, discuss their general features, and implement them in the so called
Time-Flow, or TRG, equations.Comment: 21 pages, 5 figure
Quantum Einstein Gravity
We give a pedagogical introduction to the basic ideas and concepts of the
Asymptotic Safety program in Quantum Einstein Gravity. Using the continuum
approach based upon the effective average action, we summarize the state of the
art of the field with a particular focus on the evidence supporting the
existence of the non-trivial renormalization group fixed point at the heart of
the construction. As an application, the multifractal structure of the emerging
space-times is discussed in detail. In particular, we compare the continuum
prediction for their spectral dimension with Monte Carlo data from the Causal
Dynamical Triangulation approach.Comment: 87 pages, 13 figures, review article prepared for the New Journal of
Physics focus issue on Quantum Einstein Gravit
Extreme Value laws for dynamical systems under observational noise
In this paper we prove the existence of Extreme Value Laws for dynamical
systems perturbed by instrument-like-error, also called observational noise. An
orbit perturbed with observational noise mimics the behavior of an
instrumentally recorded time series. Instrument characteristics - defined as
precision and accuracy - act both by truncating and randomly displacing the
real value of a measured observable. Here we analyze both these effects from a
theoretical and numerical point of view. First we show that classical extreme
value laws can be found for orbits of dynamical systems perturbed with
observational noise. Then we present numerical experiments to support the
theoretical findings and give an indication of the order of magnitude of the
instrumental perturbations which cause relevant deviations from the extreme
value laws observed in deterministic dynamical systems. Finally, we show that
the observational noise preserves the structure of the deterministic attractor.
This goes against the common assumption that random transformations cause the
orbits asymptotically fill the ambient space with a loss of information about
any fractal structures present on the attractor
Nonperturbative Evolution Equation for Quantum Gravity
A scale--dependent effective action for gravity is introduced and an exact
nonperturbative evolution equation is derived which governs its renormalization
group flow. It is invariant under general coordinate transformations and
satisfies modified BRS Ward--Identities. The evolution equation is solved for a
simple truncation of the space of actions. In 2+epsilon dimensions,
nonperturbative corrections to the beta--function of Newton's constant are
derived and its dependence on the cosmological constant is investigated. In 4
dimensions, Einstein gravity is found to be ``antiscreening'', i.e., Newton's
constant increases at large distances.Comment: 35 pages, late
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