69 research outputs found
Space-time paraproducts for paracontrolled calculus, 3d-PAM and multiplicative Burgers equations
We sharpen in this work the tools of paracontrolled calculus in order to
provide a complete analysis of the parabolic Anderson model equation and
Burgers system with multiplicative noise, in a -dimensional Riemannian
setting, in either bounded or unbounded domains. With that aim in mind, we
introduce a pair of intertwined space-time paraproducts on parabolic H\"older
spaces, with good continuity, that happens to be pivotal and provides one of
the building blocks of higher order paracontrolled calculus.Comment: v3, 56 pages. Different points about renormalisation matters have
been clarified. Typos correcte
Stochastic perturbation of sweeping process and a convergence result for an associated numerical scheme
Here we present well-posedness results for first order stochastic
differential inclusions, more precisely for sweeping process with a stochastic
perturbation. These results are provided in combining both deterministic
sweeping process theory and methods concerning the reflection of a Brownian
motion. In addition, we prove convergence results for a Euler scheme,
discretizing theses stochastic differential inclusions.Comment: 30 page
Loop amplitudes in gauge theories: modern analytic approaches
This article reviews on-shell methods for analytic computation of loop
amplitudes, emphasizing techniques based on unitarity cuts. Unitarity
techniques are formulated generally but have been especially useful for
calculating one-loop amplitudes in massless theories such as Yang-Mills theory,
QCD, and QED.Comment: 34 pages. Invited review for a special issue of Journal of Physics A
devoted to "Scattering Amplitudes in Gauge Theories." v2: typesetting macro
error fixe
Scattering AMplitudes from Unitarity-based Reduction Algorithm at the Integrand-level
SAMURAI is a tool for the automated numerical evaluation of one-loop
corrections to any scattering amplitudes within the dimensional-regularization
scheme. It is based on the decomposition of the integrand according to the
OPP-approach, extended to accommodate an implementation of the generalized
d-dimensional unitarity-cuts technique, and uses a polynomial interpolation
exploiting the Discrete Fourier Transform. SAMURAI can process integrands
written either as numerator of Feynman diagrams or as product of tree-level
amplitudes. We discuss some applications, among which the 6- and 8-photon
scattering in QED, and the 6-quark scattering in QCD. SAMURAI has been
implemented as a Fortran90 library, publicly available, and it could be a
useful module for the systematic evaluation of the virtual corrections oriented
towards automating next-to-leading order calculations relevant for the LHC
phenomenology.Comment: 35 pages, 7 figure
- …