424 research outputs found
Integral Grothendieck-Riemann-Roch theorem
We show that, in characteristic zero, the obvious integral version of the
Grothendieck-Riemann-Roch formula obtained by clearing the denominators of the
Todd and Chern characters is true (without having to divide the Chow groups by
their torsion subgroups). The proof introduces an alternative to Grothendieck's
strategy: we use resolution of singularities and the weak factorization theorem
for birational maps.Comment: 24 page
Ultraviolet Complete Electroweak Model Without a Higgs Particle
An electroweak model with running coupling constants described by an energy
dependent entire function is utraviolet complete and avoids unitarity
violations for energies above 1 TeV. The action contains no physical scalar
fields and no Higgs particle and the physical electroweak model fields are
local and satisfy microcausality. The and masses are compatible with a
symmetry breaking , which
retains a massless photon. The vertex couplings possess an energy scale
TeV predicting scattering amplitudes that can be tested at the
LHC.Comment: 19 pages, no figures, LaTex file. Equation and text corrected.
Reference added. Results remain the same. Final version published in European
Physics Journal Plus, 126 (2011
Cohomology of skew-holomorphic Lie algebroids
We introduce the notion of skew-holomorphic Lie algebroid on a complex
manifold, and explore some cohomologies theories that one can associate to it.
Examples are given in terms of holomorphic Poisson structures of various sorts.Comment: 16 pages. v2: Final version to be published in Theor. Math. Phys.
(incorporates only very minor changes
Weak splittings of quotients of Drinfeld and Heisenberg doubles
We investigate the fine structure of the simplectic foliations of Poisson
homogeneous spaces. Two general results are proved for weak splittings of
surjective Poisson submersions from Heisenberg and Drinfeld doubles. The
implications of these results are that the torus orbits of symplectic leaves of
the quotients can be explicitly realized as Poisson-Dirac submanifolds of the
torus orbits of the doubles. The results have a wide range of applications to
many families of real and complex Poisson structures on flag varieties. Their
torus orbits of leaves recover important families of varieties such as the open
Richardson varieties.Comment: 20 pages, AMS Late
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The Next Big Match: Convergence, Competition and Sports Media Rights
Using examples from a number of different European countries, this article analyses the increasingly prominent position of traditional telecommunications companies, such as British Telecom (UK), Deutsche Telekom (Germany), France Telecom/Orange (France) and Telefonica (Spain), in the contemporary sports media rights market. The first part of the article examines the commercial strategies of telecommunications operators and highlights how their acquisition of sports rights has been driven by the need to ensure a competitive position within an increasingly converged communications market. The second part of the article then moves on to consider the regulation of the sports media rights market. Most significantly, this section emphasises the need for further regulatory intervention to ensure that increased competition for sports rights leads to improved services and lower prices for consumers, rather than merely endlessly spiralling fees for the exclusive ownership of premium rights that are then passed on to sports channel and/or broadband subscribers
Ultraviolet Complete Quantum Gravity
An ultraviolet complete quantum gravity theory is formulated in which vertex
functions in Feynman graphs are entire functions and the propagating graviton
is described by a local, causal propagator. The cosmological constant problem
is investigated in the context of the ultraviolet complete quantum gravity.Comment: 11 pages, no figures. Changes to text. Results remain the same.
References added. To be published in European Physics Journal Plu
Support varieties for selfinjective algebras
Support varieties for any finite dimensional algebra over a field were
introduced by Snashall-Solberg using graded subalgebras of the Hochschild
cohomology. We mainly study these varieties for selfinjective algebras under
appropriate finite generation hypotheses. Then many of the standard results
from the theory of support varieties for finite groups generalize to this
situation. In particular, the complexity of the module equals the dimension of
its corresponding variety, all closed homogeneous varieties occur as the
variety of some module, the variety of an indecomposable module is connected,
periodic modules are lines and for symmetric algebras a generalization of
Webb's theorem is true
Continuous non-perturbative regularization of QED
We regularize in a continuous manner the path integral of QED by construction
of a non-local version of its action by means of a regularized form of Dirac's
functions. Since the action and the measure are both invariant under
the gauge group, this regularization scheme is intrinsically non-perturbative.
Despite the fact that the non-local action converges formally to the local one
as the cutoff goes to infinity, the regularized theory keeps trace of the
non-locality through the appearance of a quadratic divergence in the transverse
part of the polarization operator. This term which is uniquely defined by the
choice of the cutoff functions can be removed by a redefinition of the
regularized action. We notice that as for chiral fermions on the lattice, there
is an obstruction to construct a continuous and non ambiguous regularization in
four dimensions. With the help of the regularized equations of motion, we
calculate the one particle irreducible functions which are known to be
divergent by naive power counting at the one loop order.Comment: 23 pages, LaTeX, 5 Encapsulated Postscript figures. Improved and
revised version, to appear in Phys. Rev.
‘Warrant’ revisited: Integrating mathematics teachers’ pedagogical and epistemological considerations into Toulmin’s model for argumentation
In this paper, we propose an approach to analysing teacher arguments that takes into account field dependence—namely, in Toulmin’s sense, the dependence of warrants deployed in an argument on the field of activity to which the argument relates. Freeman, to circumvent issues that emerge when we attempt to determine the field(s) that an argument relates to, proposed a classification of warrants (a priori, empirical, institutional and evaluative). Our approach to analysing teacher arguments proposes an adaptation of Freeman’s classification that distinguishes between: epistemological and pedagogical a priori warrants, professional and personal empirical warrants, epistemological and curricular institutional warrants, and evaluative warrants. Our proposition emerged from analyses conducted in the course of a written response and interview study that engages secondary mathematics teachers with classroom scenarios from the mathematical areas of analysis and algebra. The scenarios are hypothetical, grounded on seminal learning and teaching issues, and likely to occur in actual practice. To illustrate our proposed approach to analysing teacher arguments here, we draw on the data we collected through the use of one such scenario, the Tangent Task. We demonstrate how teacher arguments, not analysed for their mathematical accuracy only, can be reconsidered, arguably more productively, in the light of other teacher considerations and priorities: pedagogical, curricular, professional and personal
Automatic regularization by quantization in reducible representations of CCR: Point-form quantum optics with classical sources
Electromagnetic fields are quantized in manifestly covariant way by means of
a class of reducible representations of CCR. transforms as a Hermitian
four-vector field in Minkowski four-position space (no change of gauge), but in
momentum space it splits into spin-1 massless photons (optics) and two massless
scalars (similar to dark matter). Unitary dynamics is given by point-form
interaction picture, with minimal-coupling Hamiltonian constructed from fields
that are free on the null-cone boundary of the Milne universe. SL(2,C)
transformations and dynamics are represented unitarily in positive-norm Hilbert
space describing four-dimensional oscillators. Vacuum is a Bose-Einstein
condensate of the -oscillator gas. Both the form of and its
transformation properties are determined by an analogue of the twistor
equation. The same equation guarantees that the subspace of vacuum states is,
as a whole, Poincar\'e invariant. The formalism is tested on quantum fields
produced by pointlike classical sources. Photon statistics is well defined even
for pointlike charges, with UV/IR regularizations occurring automatically as a
consequence of the formalism. The probabilities are not Poissonian but of a
R\'enyi type with . The average number of photons occurring in
Bremsstrahlung splits into two parts: The one due to acceleration, and the one
that remains nonzero even if motion is inertial. Classical Maxwell
electrodynamics is reconstructed from coherent-state averaged solutions of
Heisenberg equations. Static pointlike charges polarize vacuum and produce
effective charge densities and fields whose form is sensitive to both the
choice of representation of CCR and the corresponding vacuum state.Comment: 2 eps figures; in v2 notation in Eq. (39) and above Eq. (38) is
correcte
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