16,637 research outputs found
Global Maximizers for the Sphere Adjoint Fourier Restriction Inequality
We show that constant functions are global maximizers for the adjoint Fourier
restriction inequality for the sphere.Comment: corrected few typos and the value of the best constant of the
estimate which was not computed correctly in the first draw of the pape
Background field method, Batalin-Vilkovisky formalism and parametric completeness of renormalization
We investigate the background field method with the Batalin-Vilkovisky
formalism, to generalize known results, study parametric completeness and
achieve a better understanding of several properties. In particular, we study
renormalization and gauge dependence to all orders. Switching between the
background field approach and the usual approach by means of canonical
transformations, we prove parametric completeness without making use of
cohomological theorems, namely show that if the starting classical action is
sufficiently general all divergences can be subtracted by means of parameter
redefinitions and canonical transformations. Our approach applies to
renormalizable and non-renormalizable theories that are manifestly free of
gauge anomalies and satisfy the following assumptions: the gauge algebra is
irreducible and closes off shell, the gauge transformations are linear
functions of the fields, and closure is field-independent. Yang-Mills theories
and quantum gravity in arbitrary dimensions are included, as well as effective
and higher-derivative versions of them, but several other theories, such as
supergravity, are left out.Comment: 40 pages; v2: minor changes, PRD versio
Fakeons, Microcausality And The Classical Limit Of Quantum Gravity
We elaborate on the idea of fake particle and study its physical
consequences. When a theory contains fakeons, the true classical limit is
determined by the quantization and a subsequent process of "classicization".
One of the major predictions due to the fake particles is the violation of
microcausality, which survives the classical limit. This fact gives hope to
detect the violation experimentally. A fakeon of spin 2, together with a scalar
field, is able to make quantum gravity renormalizable while preserving
unitarity. We claim that the theory of quantum gravity emerging from this
construction is the right one. By means of the classicization, we work out the
corrections to the field equations of general relativity. We show that the
finalized equations have, in simple terms, the form ,
where is an average that includes a little bit of "future".Comment: 27 pages, 4 figures; v2: expanded intro and bibliography, Class. Q.
Gra
Fermi acceleration at supernova remnant shocks
We investigate the physics of particle acceleration at non-relativistic
shocks exploiting two different and complementary approaches, namely a
semi-analytic modeling of cosmic-ray modified shocks and large hybrid (kinetic
protons/fluid electrons) simulations. The former technique allows us to extract
some information from the multi-wavelength observations of supernova remnants,
especially in the gamma-ray band, while the latter returns fundamental insights
into the details of particle injection and magnetic field amplification via
plasma instabilities. In particular, we present the results of large hybrid
simulations of non-relativistic shocks, discussing the properties of the
transition from the thermal to the non-thermal component, the spectrum of which
turns out to be the power-law predicted by first-order Fermi acceleration.
Along with a rather effective magnetic field amplification, we find that more
than 20% of the bulk energy is converted in non-thermal particles, altering
significantly the dynamics of the shock and leading to the formation of a
precursor.Comment: 4 pages, 1 figure - Proceedings of the 5th International Symposium on
High-Energy Gamma-Ray Astronomy - Heidelberg, Germany, July 9-13th, 201
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