3,087 research outputs found
Combining gravity with the forces of the standard model on a cosmological scale
We prove the existence of a spectral resolution of the Wheeler-DeWitt
equation when the underlying spacetime is a Friedman universe with flat spatial
slices and where the matter fields are comprised of the strong interaction,
with \SU(3) replaced by a general \SU(n), , and the electro-weak
interaction. The wave functions are maps from to a subspace of the
antisymmetric Fock space, and one noteworthy result is that, whenever the
electro-weak interaction is involved, the image of an eigenfunction is in
general not one dimensional, i.e., in general it makes no sense specifying a
fermion and looking for an eigenfunction the range of which is contained in the
one dimensional vector space spanned by the fermion.Comment: 53 pages, v6: some typos correcte
Expansion of pinched hypersurfaces of the Euclidean and hyperbolic space by high powers of curvature
We prove convergence results for expanding curvature flows in the Euclidean
and hyperbolic space. The flow speeds have the form , where and
is a positive, strictly monotone and 1-homogeneous curvature function. In
particular this class includes the mean curvature . We prove that a
certain initial pinching condition is preserved and the properly rescaled
hypersurfaces converge smoothly to the unit sphere. We show that an example due
to Andrews-McCoy-Zheng can be used to construct strictly convex initial
hypersurfaces, for which the inverse mean curvature flow to the power
loses convexity, justifying the necessity to impose a certain pinching
condition on the initial hypersurface.Comment: 18 pages. We included an example for the loss of convexity and
pinching. In the third version we dropped the concavity assumption on F.
Comments are welcom
Mean Curvature Flow of Spacelike Graphs
We prove the mean curvature flow of a spacelike graph in of a map from a closed Riemannian
manifold with to a complete Riemannian manifold
with bounded curvature tensor and derivatives, and with
sectional curvatures satisfying , remains a spacelike graph,
exists for all time, and converges to a slice at infinity. We also show, with
no need of the assumption , that if , or if and
, constant, any map is trivially
homotopic provided where
, in case , and
in case . This largely extends some known results for
constant and compact, obtained using the Riemannian structure
of , and also shows how regularity theory on the mean
curvature flow is simpler and more natural in pseudo-Riemannian setting then in
the Riemannian one.Comment: version 5: Math.Z (online first 30 July 2010). version 4: 30 pages:
we replace the condition by the the weaker one .
The proofs are essentially the same. We change the title to a shorter one. We
add an applicatio
The prescribed mean curvature equation in weakly regular domains
We show that the characterization of existence and uniqueness up to vertical
translations of solutions to the prescribed mean curvature equation, originally
proved by Giusti in the smooth case, holds true for domains satisfying very
mild regularity assumptions. Our results apply in particular to the
non-parametric solutions of the capillary problem for perfectly wetting fluids
in zero gravity. Among the essential tools used in the proofs, we mention a
\textit{generalized Gauss-Green theorem} based on the construction of the weak
normal trace of a vector field with bounded divergence, in the spirit of
classical results due to Anzellotti, and a \textit{weak Young's law} for
-minimizers of the perimeter.Comment: 23 pages, 1 figure --- The results on the weak normal trace of vector
fields have been now extended and moved in a self-contained paper available
at: arXiv:1708.0139
Brane Formation and Cosmological Constraint on the Number of Extra Dimensions
Special relativity is generalized to extra dimensions and quantized energy
levels of particles are obtained. By calculating the probability of particles'
motion in extra dimensions at high temperature of the early universe, it is
proposed that the branes may have not existed since the very beginning of the
universe, but formed later. Meanwhile, before the formation, particles of the
universe may have filled in the whole bulk, not just on the branes. This
scenario differs from that in the standard big bang cosmology in which all
particles are assumed to be in the 4D spacetime. So, in brane models, whether
our universe began from a 4D big bang singularity is questionable. A
cosmological constraint on the number of extra dimensions is also given which
favors .Comment: 11 pages, no figures. To appear in IJT
Convex Functions and Spacetime Geometry
Convexity and convex functions play an important role in theoretical physics.
To initiate a study of the possible uses of convex functions in General
Relativity, we discuss the consequences of a spacetime or an
initial data set admitting a suitably defined convex
function. We show how the existence of a convex function on a spacetime places
restrictions on the properties of the spacetime geometry.Comment: 26 pages, latex, 7 figures, improved version. some claims removed,
references adde
Imaging Transient Blood Vessel Fusion Events by Correlative Volume Electron Microscopy
Extended abstract of a paper presented at Microscopy and Microanalysis 2010 in Portland, Oregon, USA, August 1 - August 5, 201
Music-evoked incidental happiness modulates probability weighting during risky lottery choices
We often make decisions with uncertain consequences. The outcomes of the choices we make are usually not perfectly predictable but probabilistic, and the probabilities can be known or unknown. Probability judgments, i.e., the assessment of unknown probabilities, can be influenced by evoked emotional states. This suggests that also the weighting of known probabilities in decision making under risk might be influenced by incidental emotions, i.e., emotions unrelated to the judgments and decisions at issue. Probability weighting describes the transformation of probabilities into subjective decision weights for outcomes and is one of the central components of cumulative prospect theory (CPT) that determine risk attitudes. We hypothesized that music-evoked emotions would modulate risk attitudes in the gain domain and in particular probability weighting. Our experiment featured a within-subject design consisting of four conditions in separate sessions. In each condition, the 41 participants listened to a different kind of music-happy, sad, or no music, or sequences of random tones-and performed a repeated pairwise lottery choice task. We found that participants chose the riskier lotteries significantly more often in the "happy" than in the "sad" and "random tones" conditions. Via structural regressions based on CPT, we found that the observed changes in participants' choices can be attributed to changes in the elevation parameter of the probability weighting function: in the "happy" condition, participants showed significantly higher decision weights associated with the larger payoffs than in the "sad" and "random tones" conditions. Moreover, elevation correlated positively with self-reported music-evoked happiness. Thus, our experimental results provide evidence in favor of a causal effect of incidental happiness on risk attitudes that can be explained by changes in probability weighting
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