6,988 research outputs found
Weak hamiltonian Wilson Coefficients from Lattice QCD
In this work we present a calculation of the Wilson Coefficients and
of the Effective Weak Hamiltonian to all-orders in , using
lattice simulations. Given the current availability of lattice spacings we
restrict our calculation to unphysically light bosons around 2 GeV and we
study the systematic uncertainties of the two Wilson Coefficients.Comment: 8 pages, Proceedings of the 35th International Symposium on Lattice
Field Theory, 18-24 June 2017, Granada, Spai
Weighted sub-Laplacians on M\'etivier Groups: Essential Self-Adjointness and Spectrum
Let be a M\'etivier group and let be any homogeneous norm on . For
denote by the function and consider the
weighted sub-Laplacian associated with the Dirichlet
form ,
where is the horizontal gradient on . Consider
with domain . We prove that
is essentially self-adjoint when . For
a particular , which is the norm appearing in 's fundamental
solution when is an H-type group, we prove that
has purely discrete spectrum if and only if , thus proving a
conjecture of J. Inglis.Comment: 15 pages; to appear on Proc. Amer. Math. So
Asymptotics for the Heat Kernel on H-Type Groups
We give sharp asymptotic estimates at infinity of all radial partial
derivatives of the heat kernel on H-type groups. As an application, we give a
new proof of the discreteness of the spectrum of some natural sub-Riemannian
Ornstein-Uhlenbeck operators on these groups.Comment: 29 pages; submitte
On finite simple and nonsolvable groups acting on homology 4-spheres
The only finite nonabelian simple group acting on a homology 3-sphere -
necessarily non-freely - is the dodecahedral group (in analogy, the only finite perfect group acting freely on a
homology 3-sphere is the binary dodecahedral group ). In the present paper we show that the only finite simple groups
acting on a homology 4-sphere, and in particular on the 4-sphere, are the
alternating or linear fractional groups groups
and . From this we deduce a short list of groups
which contains all finite nonsolvable groups admitting an action on a homology
4-spheres.Comment: 15 page
On finite simple and nonsolvable groups acting on closed 4-manifolds
We show that the only finite nonabelian simple groups which admit a locally
linear, homologically trivial action on a closed simply connected 4-manifold
(or on a 4-manifold with trivial first homology) are the alternating groups
, and the linear fractional group PSL(2,7) (we note that for
homologically nontrivial actions all finite groups occur). The situation
depends strongly on the second Betti number of and has been known
before if is different from two, so the main new result of the paper
concerns the case . We prove that the only simple group that occurs
in this case is , and then give a short list of finite nonsolvable groups
which contains all candidates for actions of such groups.Comment: 17 page
On finite groups acting on homology 4-spheres and finite subgroups of SO(5)
We show that a finite group which admits a faithful, smooth,
orientation-preserving action on a homology 4-sphere, and in particular on the
4-sphere, is isomorphic to a subgroup of the orthogonal group SO(5), by
explicitly determining the various groups which can occur (up to an
indetermination of index two in the case of solvable groups). As a consequence
we obtain also a characterization of the finite groups which are isomorphic to
subgroups of the orthogonal groups SO(5) and O(5).Comment: 13 page
On finite groups of isometries of handlebodies in arbitrary dimensions and finite extensions of Schottky groups
It is known that the order of a finite group of diffeomorphisms of a
3-dimensional handlebody of genus g > 1 is bounded by the linear polynomial
12(g-1), and that the order of a finite group of diffeomorphisms of a
4-dimensional handlebody (or equivalently, of its boundary 3-manifold),
faithful on the fundamental group, is bounded by a quadratic polynomial in g
(but not by a linear one). In the present paper we prove a generalization for
handlebodies of arbitrary dimension d, uniformizing handlebodies by Schottky
groups and considering finite groups of isometries of such handlebodies. We
prove that the order of a finite group of isometries of a handlebody of
dimension d acting faithfully on the fundamental group is bounded by a
polynomial of degree d/2 in g if d is even, and of degree (d+1)/2 if d is odd,
and that the degree d/2 for even d is best possible. This implies then
analogous polynomial Jordan-type bounds for arbitrary finite groups of
isometries of handlebodies (since a handlebody of dimension d > 3 admits
S^1-actions, there does not exist an upper bound for the order of the group
itself ).Comment: 13 pages; this is the final version to appear in Fund. Mat
Topological susceptibility and the sampling of field space in lattice QCD simulations
We present a measurement of the topological susceptibility in two flavor QCD.
In this observable, large autocorrelations are present and also sizable cutoff
effects have to be faced in the continuum extrapolation. Within the statistical
accuracy of the computation, the result agrees with the expectation from
leading order chiral perturbation theory.Comment: 22 pages, 7 figures; References added, minor clarifications in the
text, results unchange
On finite groups acting on acyclic low-dimensional manifolds
We consider finite groups which admit a faithful, smooth action on an acyclic
manifold of dimension three, four or five (e.g. euclidean space). Our first
main result states that a finite group acting on an acyclic 3- or 4-manifold is
isomorphic to a subgroup of the orthogonal group O(3) or O(4), respectively.
The analogue remains open in dimension five (where it is not true for arbitrary
continuous actions, however). We prove that the only finite nonabelian simple
groups admitting a smooth action on an acyclic 5-manifold are the alternating
groups A_5 and A_6, and deduce from this a short list of finite groups, closely
related to the finite subgroups of SO(5), which are the candidates for
orientation-preserving actions on acyclic 5-manifolds.Comment: 15 pages; improved versio
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