10,954 research outputs found
Classification of extensions of principal bundles and transitive Lie groupoids with prescribed kernel and cokernel
The equivalence of principal bundles with transitive Lie groupoids due to
Ehresmann is a well known result. A remarkable generalisation of this
equivalence, due to Mackenzie, is the equivalence of principal bundle
extensions with those transitive Lie groupoids over the total space of a
principal bundle, which also admit an action of the structure group by
automorphisms. This paper proves the existence of suitably equivariant
transition functions for such groupoids, generalising consequently the
classification of principal bundles by means of their transition functions, to
extensions of principal bundles by an equivariant form of \v{C}ech cohomology.Comment: 23 page
Spontaneous Symmetry Breaking and the Renormalization of the Chern-Simons Term
We calculate the one-loop perturbative correction to the coefficient of the
\cs term in non-abelian gauge theory in the presence of Higgs fields, with a
variety of symmetry-breaking structures. In the case of a residual
symmetry, radiative corrections do not change the coefficient of the \cs term.
In the case of an unbroken non-abelian subgroup, the coefficient of the
relevant \cs term (suitably normalized) attains an integral correction, as
required for consistency of the quantum theory. Interestingly, this coefficient
arises purely from the unbroken non-abelian sector in question; the orthogonal
sector makes no contribution. This implies that the coefficient of the \cs term
is a discontinuous function over the phase diagram of the theory.Comment: Version to be published in Phys Lett B., minor additional change
Maxwell-Chern-Simons Q-balls
We examine the energetics of -balls in Maxwell-Chern-Simons theory in two
space dimensions. Whereas gauged -balls are unallowed in this dimension in
the absence of a Chern-Simons term due to a divergent electromagnetic energy,
the addition of a Chern-Simons term introduces a gauge field mass and renders
finite the otherwise-divergent electromagnetic energy of the -ball. Similar
to the case of gauged -balls, Maxwell-Chern-Simons -balls have a maximal
charge. The properties of these solitons are studied as a function of the
parameters of the model considered, using a numerical technique known as
relaxation. The results are compared to expectations based on qualitative
arguments.Comment: 6 pages. Talk given at Theory CANADA 2, Perimeter Institut
Anisotropy in the Antiferromagnetic Spin Fluctuations of Sr2RuO4
It has been proposed that Sr_2RuO_4 exhibits spin triplet superconductivity
mediated by ferromagnetic fluctuations. So far neutron scattering experiments
have failed to detect any clear evidence of ferromagnetic spin fluctuations
but, instead, this type of experiments has been successful in confirming the
existence of incommensurate spin fluctuations near q=(1/3 1/3 0). For this
reason there have been many efforts to associate the contributions of such
incommensurate fluctuations to the mechanism of its superconductivity. Our
unpolarized inelastic neutron scattering measurements revealed that these
incommensurate spin fluctuations possess c-axis anisotropy with an anisotropic
factor \chi''_{c}/\chi''_{a,b} of \sim 2.8. This result is consistent with some
theoretical ideas that the incommensurate spin fluctuations with a c-axis
anisotropy can be a origin of p-wave superconductivity of this material.Comment: 5 pages, 3 figures; accepted for publication in PR
Linear and multiplicative 2-forms
We study the relationship between multiplicative 2-forms on Lie groupoids and
linear 2-forms on Lie algebroids, which leads to a new approach to the
infinitesimal description of multiplicative 2-forms and to the integration of
twisted Dirac manifolds.Comment: to appear in Letters in Mathematical Physic
Layering Sel(f)ves: Finding Acceptance, Community and Praxis through Collage
There are multiple aspects that shape oneâs experience as a student teacher; however often as teacher educators, we focus on the intellectual rather than the emotional nature of the experience. Within this a/r/tographical inquiry, we render a story of what can happen when teacher educators intentionally engage the multidimensional nature of the student teaching experience through the integration of arts-informed epistemologies within the context of the student teaching seminar. Student teachers entered into a dialogic space of reflexivity and praxis where they discovered that their experiences mattered and did not occur in isolation. This project has implications for considering ways to help student teachers and teacher educators bridge the gaps between the personal, social, artistic, and academic that is teaching
A multifractal zeta function for cookie cutter sets
Starting with the work of Lapidus and van Frankenhuysen a number of papers
have introduced zeta functions as a way of capturing multifractal information.
In this paper we propose a new multifractal zeta function and show that under
certain conditions the abscissa of convergence yields the Hausdorff
multifractal spectrum for a class of measures
Magnetic ordering in Sr2RuO4 induced by nonmagnetic impurities
We report unusual effects of nonmagnetic impurities on the spin-triplet
superconductor Sr2RuO4. The substitution of nonmagnetic Ti4+ for Ru4+ induces
localized-moment magnetism characterized by unexpected Ising anisotropy with
the easy axis along the interlayer c direction. Furthermore, for x(Ti) > 0.03
magnetic ordering occurs in the metallic state with the remnant magnetization
along the c-axis. We argue that the localized moments are induced in the Ru4+
and/or oxygen ions surrounding Ti4+ and that the ordering is due to their
interaction mediated by itinerant Ru-4d electrons with strong spin
fluctuations.Comment: 5 pages, 4figure
Problems With Complex Actions
We consider Euclidean functional integrals involving actions which are not
exclusively real. This situation arises, for example, when there are -odd
terms in the the Minkowski action. Writing the action in terms of only real
fields (which is always possible), such terms appear as explicitly imaginary
terms in the Euclidean action. The usual quanization procedure which involves
finding the critical points of the action and then quantizing the spectrum of
fluctuations about these critical points fails. In the case of complex actions,
there do not exist, in general, any critical points of the action on the space
of real fields, the critical points are in general complex. The proper
definition of the function integral then requires the analytic continuation of
the functional integration into the space of complex fields so as to pass
through the complex critical points according to the method of steepest
descent. We show a simple example where this procedure can be carried out
explicitly. The procedure of finding the critical points of the real part of
the action and quantizing the corresponding fluctuations, treating the
(exponential of the) complex part of the action as a bounded integrable
function is shown to fail in our explicit example, at least perturbatively.Comment: 6+epsilon pages, no figures, presented at Theory CANADA
Coupling Poisson and Jacobi structures on foliated manifolds
Let M be a differentiable manifold endowed with a foliation F. A Poisson
structure P on M is F-coupling if the image of the annihilator of TF by the
sharp-morphism defined by P is a normal bundle of the foliation F. This notion
extends Sternberg's coupling symplectic form of a particle in a Yang-Mills
field. In the present paper we extend Vorobiev's theory of coupling Poisson
structures from fiber bundles to foliations and give simpler proofs of
Vorobiev's existence and equivalence theorems of coupling Poisson structures on
duals of kernels of transitive Lie algebroids over symplectic manifolds. Then
we discuss the extension of the coupling condition to Jacobi structures on
foliated manifolds.Comment: LateX, 38 page
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