631 research outputs found
The arithmetic of hyperelliptic curves
We summarise recent advances in techniques for solving Diophantine problems on hyperelliptic curves; in particular, those for finding the rank of the Jacobian, and the set of rational points on the curve
Probing Quantum Geometry at LHC
We present an evidence, that the volumes of compactified spaces as well as
the areas of black hole horizons must be quantized in Planck units. This
quantization has phenomenological consequences, most dramatic being for micro
black holes in the theories with TeV scale gravity that can be produced at LHC.
We predict that black holes come in form of a discrete tower with well defined
spacing. Instead of thermal evaporation, they decay through the sequence of
spontaneous particle emissions, with each transition reducing the horizon area
by strictly integer number of Planck units. Quantization of the horizons can be
a crucial missing link by which the notion of the minimal length in gravity
eliminates physical singularities. In case when the remnants of the black holes
with the minimal possible area and mass of order few TeV are stable, they might
be good candidates for the cold dark matter in the Universe.Comment: 14 pages, Late
Center of mass, spin supplementary conditions, and the momentum of spinning particles
We discuss the problem of defining the center of mass in general relativity
and the so-called spin supplementary condition. The different spin conditions
in the literature, their physical significance, and the momentum-velocity
relation for each of them are analyzed in depth. The reason for the
non-parallelism between the velocity and the momentum, and the concept of
"hidden momentum", are dissected. It is argued that the different solutions
allowed by the different spin conditions are equally valid descriptions for the
motion of a given test body, and their equivalence is shown to dipole order in
curved spacetime. These different descriptions are compared in simple examples.Comment: 45 pages, 7 figures. Some minor improvements, typos fixed, signs in
some expressions corrected. Matches the published version. Published as part
of the book "Equations of Motion in Relativistic Gravity", D. Puetzfeld et
al. (eds.), Fundamental Theories of Physics 179, Springer, 201
Motion in classical field theories and the foundations of the self-force problem
This article serves as a pedagogical introduction to the problem of motion in
classical field theories. The primary focus is on self-interaction: How does an
object's own field affect its motion? General laws governing the self-force and
self-torque are derived using simple, non-perturbative arguments. The relevant
concepts are developed gradually by considering motion in a series of
increasingly complicated theories. Newtonian gravity is discussed first, then
Klein-Gordon theory, electromagnetism, and finally general relativity. Linear
and angular momenta as well as centers of mass are defined in each of these
cases. Multipole expansions for the force and torque are then derived to all
orders for arbitrarily self-interacting extended objects. These expansions are
found to be structurally identical to the laws of motion satisfied by extended
test bodies, except that all relevant fields are replaced by effective versions
which exclude the self-fields in a particular sense. Regularization methods
traditionally associated with self-interacting point particles arise as
straightforward perturbative limits of these (more fundamental) results.
Additionally, generic mechanisms are discussed which dynamically shift ---
i.e., renormalize --- the apparent multipole moments associated with
self-interacting extended bodies. Although this is primarily a synthesis of
earlier work, several new results and interpretations are included as well.Comment: 68 pages, 1 figur
Testing A (Stringy) Model of Quantum Gravity
I discuss a specific model of space-time foam, inspired by the modern
non-perturbative approach to string theory (D-branes). The model views our
world as a three brane, intersecting with D-particles that represent stringy
quantum gravity effects, which can be real or virtual. In this picture, matter
is represented generically by (closed or open) strings on the D3 brane
propagating in such a background. Scattering of the (matter) strings off the
D-particles causes recoil of the latter, which in turn results in a distortion
of the surrounding space-time fluid and the formation of (microscopic, i.e.
Planckian size) horizons around the defects. As a mean-field result, the
dispersion relation of the various particle excitations is modified, leading to
non-trivial optical properties of the space time, for instance a non-trivial
refractive index for the case of photons or other massless probes. Such models
make falsifiable predictions, that may be tested experimentally in the
foreseeable future. I describe a few such tests, ranging from observations of
light from distant gamma-ray-bursters and ultra high energy cosmic rays, to
tests using gravity-wave interferometric devices and terrestrial particle
physics experients involving, for instance, neutral kaons.Comment: 25 pages LATEX, four figures incorporated, uses special proceedings
style. Invited talk at the third international conference on Dark Matter in
Astro and Particle Physics, DARK2000, Heidelberg, Germany, July 10-15 200
Anti-tumour activity and toxicity of the new prodrug9-aminocamptothecin glucuronide (9ACG) in mice
Cancer chemotherapy is limited by the modest therapeutic index of most antineoplastic drugs. Some glucuronide prodrugs may display selective anti-tumour activity against tumours that accumulate ÎČ-glucuronidase. We examined the toxicity and anti-tumour activity of 9-aminocamptothecin glucuronide, a new glucuronide prodrug of 9-aminocamptothecin, to evaluate its potential clinical utility. 9-aminocamptothecin glucuronide was 25â60 times less toxic than 9-aminocamptothecin to five human cancer cell lines. ÎČ-glucuronidase activated 9-aminocamptothecin glucuronide to produce similar cell killing as 9-aminocamptothecin or topotecan. The in vivo toxicity of 9-aminocamptothecin glucuronide in BALB/c mice was dose-, route-, sex- and age-dependent. 9-aminocamptothecin glucuronide was significantly less toxic to female than to male mice but the difference decreased with age. 9-aminocamptothecin glucuronide and 9-aminocamptothecin produced similar inhibition (âŒ80%) of LS174T human colorectal carcinoma tumours. 9-aminocamptothecin glucuronide cured a high percentage of CL1-5 human lung cancer xenografts with efficacy that was similar to or greater than 9-aminocamptothecin, irinotecan and topotecan. The potent anti-tumour activity of 9-aminocamptothecin glucuronide suggests that this prodrug should be further evaluated for cancer treatment
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