4,758 research outputs found
Lambda Polarization in an Exact Rotating and Expanding fluid dynamical model for peripheral heavy ion reactions
We calculate the Lambda polarization in an exact analytical, rotating model
based on parameters extracted from a high resolution (3+1)D Particle-in-Cell
Relativistic hydrodynamics calculation. The polarization is attributed to
effects from thermal vorticity and for the first time the effects of the radial
and axial acceleration are also studied separatel
Point-Particle Effective Field Theory III: Relativistic Fermions and the Dirac Equation
We formulate point-particle effective field theory (PPEFT) for relativistic
spin-half fermions interacting with a massive, charged finite-sized source
using a first-quantized effective field theory for the heavy compact object and
a second-quantized language for the lighter fermion with which it interacts.
This description shows how to determine the near-source boundary condition for
the Dirac field in terms of the relevant physical properties of the source, and
reduces to the standard choices in the limit of a point source. Using a
first-quantized effective description is appropriate when the compact object is
sufficiently heavy, and is simpler than (though equivalent to) the effective
theory that treats the compact source in a second-quantized way. As an
application we use the PPEFT to parameterize the leading energy shift for the
bound energy levels due to finite-sized source effects in a model-independent
way, allowing these effects to be fit in precision measurements. Besides
capturing finite-source-size effects, the PPEFT treatment also efficiently
captures how other short-distance source interactions can shift bound-state
energy levels, such as due to vacuum polarization (through the Uehling
potential) or strong interactions for Coulomb bound states of hadrons, or any
hypothetical new short-range forces sourced by nuclei.Comment: 29 pages plus appendices, 3 figure
Point-Particle Effective Field Theory I: Classical Renormalization and the Inverse-Square Potential
Singular potentials (the inverse-square potential, for example) arise in many
situations and their quantum treatment leads to well-known ambiguities in
choosing boundary conditions for the wave-function at the position of the
potential's singularity. These ambiguities are usually resolved by developing a
self-adjoint extension of the original problem; a non-unique procedure that
leaves undetermined which extension should apply in specific physical systems.
We take the guesswork out of this picture by using techniques of effective
field theory to derive the required boundary conditions at the origin in terms
of the effective point-particle action describing the physics of the source. In
this picture ambiguities in boundary conditions boil down to the allowed
choices for the source action, but casting them in terms of an action provides
a physical criterion for their determination. The resulting extension is
self-adjoint if the source action is real (and involves no new degrees of
freedom), and not otherwise (as can also happen for reasonable systems). We
show how this effective-field picture provides a simple framework for
understanding well-known renormalization effects that arise in these systems,
including how renormalization-group techniques can resum non-perturbative
interactions that often arise, particularly for non-relativistic applications.
In particular we argue why the low-energy effective theory tends to produce a
universal RG flow of this type and describe how this can lead to the phenomenon
of reaction {\em catalysis}, in which physical quantities (like scattering
cross sections) can sometimes be surprisingly large compared to the underlying
scales of the source in question. We comment in passing on the possible
relevance of these observations to the phenomenon of the catalysis of
baryon-number violation by scattering from magnetic monopoles.Comment: LaTeX, 20 pages plus appendi
Stable Allocations of Risk
Measuring risk can be axiomatized by the concept of coherent measures of risk. A risk environment specifies some individual portfolios' realization vectors and a coherent measure of risk. We consider sharing the risk of the aggregate portfolio by studying transferable utility cooperative games: risk allocation games. We show that the class of risk allocation games coincides with the class of totally balanced games. As a limit case the aggregate portfolio can have the same payoff in all states of nature. We prove that the class of risk allocation games with no aggregate uncertainty coincides with the class of exact games.Coherent Measures of Risk, Risk Allocation Games, Totally Balanced Games, Exact Games
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