21,765 research outputs found
Neutron Stars as Dark Matter Probes
We examine whether the accretion of dark matter onto neutron stars could ever
have any visible external effects. Captured dark matter which subsequently
annihilates will heat the neutron stars, although it seems the effect will be
too small to heat close neutron stars at an observable rate whilst those at the
galactic centre are obscured by dust. Non-annihilating dark matter would
accumulate at the centre of the neutron star. In a very dense region of dark
matter such as that which may be found at the centre of the galaxy, a neutron
star might accrete enough to cause it to collapse within a period of time less
than the age of the Universe. We calculate what value of the stable dark
matter-nucleon cross section would cause this to occur for a large range of
masses.Comment: 8 pages, 7 figure
On the Consistency of a Fermion-Torsion Effective Theory
We discuss the possibility to construct an effective quantum field theory for
an axial vector coupled to a Dirac spinor field. A massive axial vector
describes antisymmetric torsion. The consistency conditions include unitarity
and renormalizability in the low-energy region. The investigation of the Ward
identities and the one- and two-loop divergences indicate serious problems
arising in the theory. The final conclusion is that torsion may exist as a
string excitation, but there are very severe restrictions for the existence of
a propagating torsion field, subject to the quantization procedure, at low
energies.Comment: LaTeX, 26 pages, 4 figure
The Teodorescu operator in Clifford analysis
Euclidean Clifford analysis is a higher dimensional function theory centred around monogenic functions, i.e., null solutions to a first order vector valued rotation invariant differential operator called the Dirac operator. More recently, Hermitian Clifford analysis has emerged as a new branch, offering yet a refinement of the Euclidean case; it focuses on the simultaneous null solutions, called Hermitian monogenic functions, to two Hermitian Dirac operators and which are invariant under the action of the unitary group. In Euclidean Clifford analysis, the Teodorescu operator is the right inverse of the Dirac operator . In this paper, Teodorescu operators for the Hermitian Dirac operators and are constructed. Moreover, the structure of the Euclidean and Hermitian Teodorescu operators is revealed by analyzing the more subtle behaviour of their components. Finally, the obtained inversion relations are still refined for the differential operators issuing from the Euclidean and Hermitian Dirac operators by splitting the Clifford algebra product into its dot and wedge parts. Their relationship with several complex variables theory is discussed
The rationality of Sol manifolds
Let be the fundamental group of a manifold modeled on three
dimensional Sol geometry. We prove that has a finite index subgroup
which has a rational growth series with respect to a natural generating
set. We do this by enumerating by a regular language. However, in contrast
to most earlier proofs of this sort our regular language is not a language of
words in the generating set, but rather reflects a different geometric
structure in .Comment: 30 pages; author's name changed to agree with published version; to
appear in Journal of Algebr
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