1,246 research outputs found
Weak equivalence and non-classifiability of measure preserving actions
Abért and Weiss have shown that the Bernoulli shift s_Γ of a countably infinite group Γ is weakly contained in any free measure preserving action ɑ of Γ. Proving a conjecture of Ioana, we establish a strong version of this result by showing that s_Γ×ɑ is weakly equivalent to ɑ. Using random Bernoulli shifts introduced by Abért, Glasner, and Virag, we generalize this to non-free actions, replacing s_Γ with a random Bernoulli shift associated to an invariant random subgroup, and replacing the product action with a relatively independent joining. The result for free actions is used along with the theory of Borel reducibility and Hjorth’s theory of turbulence to show that, on the weak equivalence class of a free measure preserving action, the equivalence relations of isomorphism, weak isomorphism, and unitary equivalence are not classifiable by countable structures. This in particular shows that there are no free weakly rigid actions, that is, actions whose weak equivalence class and isomorphism class coincide, answering negatively a question of Abért and Elek. We also answer a question of Kechris regarding two ergodic theoretic properties of residually finite groups. A countably infinite residually finite group Γ is said to have property EMD∗ if the action p_Γ of Γ on its profinite completion weakly contains all ergodic measure preserving actions of Γ, and Γ is said to have property MD if ι×p_Γ weakly contains all measure preserving actions of Γ, where ι denotes the identity action on a standard non-atomic probability space. Kechris has shown that EMD∗ implies MD and asked if the two properties are actually equivalent. We provide a positive answer to this question by studying the relationship between convexity and weak containment in the space of measure preserving actions
Ultraproducts of measure preserving actions and graph combinatorics
Ultraproducts of measure preserving actions of countable groups are used to study the graph combinatorics associated with such actions, including chromatic, independence and matching numbers. Applications are also given to the theory of random colorings of Cayley graphs and sofic actions and equivalence relations
String Fields and the Standard Model
The Cremmer-Scherk mechanism is generalised in a non-Abelian context. In the
presence of the Higgs scalars of the standard model it is argued that fields
arising from the low energy effective string action may contribute to the mass
generation of the observed vector bosons that mediate the electroweak
interactions and that future analyses of experimental data should consider the
possibility of string induced radiative corrections to the Weinberg angle
coming from physics beyond the standard model.Comment: 4 pages, LATEX, no figure
Non-Riemannian Gravity and the Einstein-Proca System
We argue that all Einstein-Maxwell or Einstein-Proca solutions to general
relativity may be used to construct a large class of solutions (involving
torsion and non-metricity) to theories of non-Riemannian gravitation that have
been recently discussed in the literature.Comment: 9 pages Plain Tex (No Figures), Letter to Editor Classical and
Quantum Gravit
Dark Matter Gravitational Interactions
We argue that the conjectured dark mater in the Universe may be endowed with
a new kind of gravitational charge that couples to a short range gravitational
interaction mediated by a massive vector field. A model is constructed that
assimilates this concept into ideas of current inflationary cosmology. The
model is also consistent with the observed behaviour of galactic rotation
curves according to Newtonian dynamics. The essential idea is that stars
composed of ordinary (as opposed to dark matter) experience Newtonian forces
due to the presence of an all pervading background of massive gravitationally
charged cold dark matter. The novel gravitational interactions are predicted to
have a significant influence on pre-inflationary cosmology. The precise details
depend on the nature of a gravitational Proca interaction and the description
of matter. A gravitational Proca field configuration that gives rise to
attractive forces between dark matter charges of like polarity exhibits
homogeneous isotropic eternal cosmologies that are free of cosmological
curvature singularities thus eliminating the horizon problem associated with
the standard big-bang scenario. Such solutions do however admit dense hot
pre-inflationary epochs each with a characteristic scale factor that may be
correlated with the dark matter density in the current era of expansion. The
model is based on a theory in which a modification of Einsteinian gravity at
very short distances can be expressed in terms of the gradient of the Einstein
metric and the torsion of a non-Riemannian connection on the bundle of linear
frames over spacetime. Indeed we demonstrate that the genesis of the model
resides in a remarkable simplification that occurs when one analyses the
variational equations associated with a broad class of non-Riemannian actions.Comment: 40 pages, 4 Postscript figure
Association of Social Risk Factors With Mortality among Us adults With a New Cancer Diagnosis
This cohort study examines the associations of multiple social risk factors with mortality risk among patients newly diagnosed with cancer in the US
On the motion of spinning test particles in plane gravitational waves
The Mathisson-Papapetrou-Dixon equations for a massive spinning test particle
in plane gravitational waves are analysed and explicit solutions constructed in
terms of solutions of certain linear ordinary differential equations. For
harmonic waves this system reduces to a single equation of Mathieu-Hill type.
In this case spinning particles may exhibit parametric excitation by
gravitational fields. For a spinning test particle scattered by a gravitational
wave pulse, the final energy-momentum of the particle may be related to the
width, height, polarisation of the wave and spin orientation of the particle.Comment: 11 page
An Einstein-Hilbert Action for Axi-Dilaton Gravity in 4-Dimensions
We examine the axi-dilatonic sector of low energy string theory and
demonstrate how the gravitational interactions involving the axion and dilaton
fields may be derived from a geometrical action principle involving the
curvature scalar associated with a non-Riemannian connection. In this geometry
the antisymmetric tensor 3-form field determines the torsion of the connection
on the frame bundle while the gradient of the metric is determined by the
dilaton field. By expressing the theory in terms of the Levi-Civita connection
associated with the metric in the ``Einstein frame'' we confirm that the field
equations derived from the non-Riemannian Einstein-Hilbert action coincide with
the axi-dilaton sector of the low energy effective action derived from string
theory.Comment: 6 pages Plain Tex (No Figures), Letter to Editor Classical and
Quantum Gravit
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