8,618 research outputs found
The generalized Lichnerowicz formula and analysis of Dirac operators
We study Dirac operators acting on sections of a Clifford module \
over a Riemannian manifold . We prove the intrinsic decomposition formula
for their square, which is the generalisation of the well-known formula due to
Lichnerowicz [L]. This formula enables us to distinguish Dirac operators of
simple type. For each Dirac operator of this natural class the local
Atiyah-Singer index theorem holds. Furthermore, if \ is compact and
{{\petit \rm dim}\;M=2n\ge 4}, we derive an expression for the Wodzicki
function , which is defined via the non-commutative residue on the
space of all Dirac operators . We calculate this function
for certain Dirac operators explicitly. From a physical point of view this
provides a method to derive gravity, resp. combined gravity/Yang-Mills actions
from the Dirac operators in question.Comment: 25 pages, plain te
Unification of Gravity and Yang-Mills-Higgs Gauge Theories
In this letter we show how the action functional of the standard model and of
gravity can be derived from a specific Dirac operator. Far from being exotic
this particular Dirac operator turns out to be structurally determined by the
Yukawa coupling term. The main feature of our approach is that it naturally
unifies the action of the standard model with gravity.Comment: 8 pages, late
Multi-wavelength Observations of Blazar AO 0235+164 in the 2008-2009 Flaring State
The blazar AO 0235+164 (z = 0.94) has been one of the most active objects observed by Fermi Large Area Telescope (LAT) since its launch in Summer 2008. In addition to the continuous coverage by Fermi, contemporaneous observations were carried out from the radio to Îł-ray bands between 2008 September and 2009 February. In this paper, we summarize the rich multi-wavelength data collected during the campaign (including F-GAMMA, GASP-WEBT, Kanata, OVRO, RXTE, SMARTS, Swift, and other instruments), examine the cross-correlation between the light curves measured in the different energy bands, and interpret the resulting spectral energy distributions in the context of well-known blazar emission models. We find that the Îł-ray activity is well correlated with a series of near-IR/optical flares, accompanied by an increase in the optical polarization degree. On the other hand, the X-ray light curve shows a distinct 20 day high state of unusually soft spectrum, which does not match the extrapolation of the optical/UV synchrotron spectrum. We tentatively interpret this feature as the bulk Compton emission by cold electrons contained in the jet, which requires an accretion disk corona with an effective covering factor of 19% at a distance of 100 R_g. We model the broadband spectra with a leptonic model with external radiation dominated by the infrared emission from the dusty torus
Second constant of motion for two-dimensional positronium in a magnetic field
Recent numerical work indicates that the classical motion of positronium in a
constant magnetic field does not exhibit chaotic behavior if the system is
confined to two dimensions. One would therefore expect this system to possess a
second constant of the motion in addition to the total energy. In this paper we
construct a generalization of the Laplace-Runge-Lenz vector and show that a
component of this vector is a constant of the motion.Comment: 4 pages, no figure
Dispersion processes
We study a synchronous dispersion process in which particles are
initially placed at a distinguished origin vertex of a graph . At each time
step, at each vertex occupied by more than one particle at the beginning of
this step, each of these particles moves to a neighbour of chosen
independently and uniformly at random. The dispersion process ends once the
particles have all stopped moving, i.e. at the first step at which each vertex
is occupied by at most one particle.
For the complete graph and star graph , we show that for any
constant , with high probability, if , then the
process finishes in steps, whereas if , then
the process needs steps to complete (if ever). We also show
that an analogous lazy variant of the process exhibits the same behaviour but
for higher thresholds, allowing faster dispersion of more particles.
For paths, trees, grids, hypercubes and Cayley graphs of large enough sizes
(in terms of ) we give bounds on the time to finish and the maximum distance
traveled from the origin as a function of the number of particles
H2 molecule in strong magnetic fields
The Pauli-Hamiltonian of a molecule with fixed nuclei in a strong constant
magnetic field is asymptotic, in norm-resolvent sense, to an effective
Hamiltonian which has the form of a multi-particle Schr\"odinger operator with
interactions given by one-dimensional \delta-potentials. We study this
effective Hamiltonian in the case of the H2 -molecule and establish existence
of the ground state. We also show that the inter-nuclear equilibrium distance
tends to 0 as the field-strength tends to infinity
Rationales and functions of disliked music: An in-depth interview study
BACKGROUND AND OBJECTIVES: With a few exceptions, musical taste has been researched via likes or preferences of certain types of music. The present study focuses on disliked music and takes a broad approach to cover explanatory strategies related to personal dislikes. METHODS: In-depth interviews were conducted with 21 participants in five age groups. Interviewees were asked to prepare a list of their disliked music, and for each item they were asked about the reasons for the dislike. To ensure that the complexity and range of the participantsâ dislikes and rationales were captured in the analysis, a structuring content analysis as a mostly theory-driven approach was combined with inductive category creation out of the interview data. RESULTS: The most often mentioned type of dislike was musical style, followed by artist and genre. Five main reference points were identified for describing musical dislikes: the music itself, lyrics, performance, artist, and the people who listen to it. The identified rationales for disliked music were assigned to three larger categories: object-related reasons, such as music-compositional aspects, aesthetic dichotomies or lyrics; subject-related reasons, such as emotional or bodily effects, or discrepancies with the self-image; social reasons, which refer to oneâs social environment and the taste judgments common to it (in-group) or to other groups of which the participants do not feel part of (out-group). Apart from the rationales for disliked music, the participants described specific reactions when they are confronted with their disliked music, such as emotional, physical, and social reactions. CONCLUSIONS: While musical dislikes have already been shown to fulfill important social functions, the current study extends the rationales to music-related and self-related reasons. Musical dislikes fulfill similar functions to liked music, such as preservation of a good mood, identity expression and construction, strengthening of group cohesion as well as social distinction
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