78 research outputs found
A characterization of Dirac morphisms
Relating the Dirac operators on the total space and on the base manifold of a
horizontally conformal submersion, we characterize Dirac morphisms, i.e. maps
which pull back (local) harmonic spinor fields onto (local) harmonic spinor
fields.Comment: 18 pages; restricted to the even-dimensional cas
On the integral cohomology of smooth toric varieties
Let be a smooth, not necessarily compact toric variety. We show
that a certain complex, defined in terms of the fan , computes the
integral cohomology of , including the module structure over the
homology of the torus. In some cases we can also give the product. As a
corollary we obtain that the cycle map from Chow groups to integral Borel-Moore
homology is split injective for smooth toric varieties. Another result is that
the differential algebra of singular cochains on the Borel construction of
is formal.Comment: 10 page
Some Remarks on Group Bundles and C*-dynamical systems
We introduce the notion of fibred action of a group bundle on a C(X)-algebra.
By using such a notion, a characterization in terms of induced C*-bundles is
given for C*-dynamical systems such that the relative commutant of the
fixed-point algebra is minimal (i.e., it is generated by the centre of the
given C*-algebra and the centre of the fixed-point algebra). A class of
examples in the setting of the Cuntz algebra is given, and connections with
superselection structures with nontrivial centre are discussed.Comment: 22 pages; to appear on Comm. Math. Phy
GALEX J201337.6+092801: The lowest gravity subdwarf B pulsator
We present the recent discovery of a new subdwarf B variable (sdBV), with an
exceptionally low surface gravity. Our spectroscopy of J20136+0928 places it at
Teff = 32100 +/- 500, log(g) = 5.15 +/- 0.10, and log(He/H) = -2.8 +/- 0.1.
With a magnitude of B = 12.0, it is the second brightest V361 Hya star ever
found. Photometry from three different observatories reveals a temporal
spectrum with eleven clearly detected periods in the range 376 to 566 s, and at
least five more close to our detection limit. These periods are unusually long
for the V361 Hya class of short-period sdBV pulsators, but not unreasonable for
p- and g-modes close to the radial fundamental, given its low surface gravity.
Of the ~50 short period sdB pulsators known to date, only a single one has been
found to have comparable spectroscopic parameters to J20136+0928. This is the
enigmatic high-amplitude pulsator V338 Ser, and we conclude that J20136+0928 is
the second example of this rare subclass of sdB pulsators located well above
the canonical extreme horizontal branch in the HR diagram.Comment: 5 pages, accepted for publication in ApJ Letter
Topological Invariants, Instantons and Chiral Anomaly on Spaces with Torsion
In a spacetime with nonvanishing torsion there can occur topologically stable
configurations associated with the frame bundle which are independent of the
curvature. The relevant topological invariants are integrals of local scalar
densities first discussed by Nieh and Yan (N-Y). In four dimensions, the N-Y
form is the only closed
4-form invariant under local Lorentz rotations associated with the torsion of
the manifold. The integral of over a compact D-dimensional (Euclidean)
manifold is shown to be a topological invariant related to the Pontryagin
classes of SO(D+1) and SO(D). An explicit example of a topologically nontrivial
configuration carrying nonvanishing instanton number proportional to
is costructed. The chiral anomaly in a four-dimensional spacetime with torsion
is also shown to contain a contribution proportional to , besides the usual
Pontryagin density related to the spacetime curvature. The violation of chiral
symmetry can thus depend on the instanton number of the tangent frame bundle of
the manifold. Similar invariants can be constructed in D>4 dimensions and the
existence of the corresponding nontrivial excitations is also discussed.Comment: 6 pages, RevTeX, no figures, two column
The extended algebra of observables for Dirac fields and the trace anomaly of their stress-energy tensor
We discuss from scratch the classical structure of Dirac spinors on an
arbitrary globally hyperbolic, Lorentzian spacetime, their formulation as a
locally covariant quantum field theory, and the associated notion of a Hadamard
state. Eventually, we develop the notion of Wick polynomials for spinor fields,
and we employ the latter to construct a covariantly conserved stress-energy
tensor suited for back-reaction computations. We shall explicitly calculate its
trace anomaly in particular.Comment: 65 page
Coisotropic deformations of algebraic varieties and integrable systems
Coisotropic deformations of algebraic varieties are defined as those for
which an ideal of the deformed variety is a Poisson ideal. It is shown that
coisotropic deformations of sets of intersection points of plane quadrics,
cubics and space algebraic curves are governed, in particular, by the dKP,
WDVV, dVN, d2DTL equations and other integrable hydrodynamical type systems.
Particular attention is paid to the study of two- and three-dimensional
deformations of elliptic curves. Problem of an appropriate choice of Poisson
structure is discussed.Comment: 17 pages, no figure
(Contravariant) Koszul duality for DG algebras
A DG algebras over a field with connected and
has a unique up to isomorphism DG module with . It is proved
that if is degreewise finite, then RHom_A(?,K): D^{df}_{+}(A)^{op}
\equiv D_{df}^{+}}(RHom_A(K,K)) is an exact equivalence of derived categories
of DG modules with degreewise finite-dimensional homology. It induces an
equivalences of and the category of perfect DG
-modules, and vice-versa. Corresponding statements are proved also
when is simply connected and .Comment: 33 page
On Schubert's Problem of Characteristics
The Schubert varieties on a flag manifold G/P give rise to a cell
decomposition on G/P whose Kronecker duals, known as the Schubert classes on
G/P, form an additive base of the integral cohomology of G/P. The Schubert's
problem of characteristics asks to express a monomial in the Schubert classes
as a linear combination in the Schubert basis.
We present a unified formula expressing the characteristics of a flag
manifold G/P as polynomials in the Cartan numbers of the group G. As
application we develop a direct approach to our recent works on the Schubert
presentation of the cohomology rings of flag manifolds G/P.Comment: 27page
The Seven-sphere and its Kac-Moody Algebra
We investigate the seven-sphere as a group-like manifold and its extension to
a Kac-Moody-like algebra. Covariance properties and tensorial composition of
spinors under are defined. The relation to Malcev algebras is
established. The consequences for octonionic projective spaces are examined.
Current algebras are formulated and their anomalies are derived, and shown to
be unique (even regarding numerical coefficients) up to redefinitions of the
currents. Nilpotency of the BRST operator is consistent with one particular
expression in the class of (field-dependent) anomalies. A Sugawara construction
is given.Comment: 22 pages. Macropackages used: phyzzx, epsf. Three epsf figure files
appende
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