5,750 research outputs found
Non-commutative Complex Projective Spaces and the Standard Model
The standard model fermion spectrum, including a right handed neutrino, can
be obtained as a zero-mode of the Dirac operator on a space which is the
product of complex projective spaces of complex dimension two and three. The
construction requires the introduction of topologically non-trivial background
gauge fields. By borrowing from ideas in Connes' non-commutative geometry and
making the complex spaces `fuzzy' a matrix approximation to the fuzzy space
allows for three generations to emerge. The generations are associated with
three copies of space-time. Higgs' fields and Yukawa couplings can be
accommodated in the usual way.Comment: Contribution to conference in honour of A.P. Balachandran's 65th
birthday: "Space-time and Fundamental Interactions: Quantum Aspects", Vietri
sul Mare, Italy, 25th-31st May, 2003, 10 pages, typset in LaTe
The Information Geometry of the One-Dimensional Potts Model
In various statistical-mechanical models the introduction of a metric onto
the space of parameters (e.g. the temperature variable, , and the
external field variable, , in the case of spin models) gives an alternative
perspective on the phase structure. For the one-dimensional Ising model the
scalar curvature, , of this metric can be calculated explicitly in
the thermodynamic limit and is found to be . This is positive definite and, for
physical fields and temperatures, diverges only at the zero-temperature,
zero-field ``critical point'' of the model.
In this note we calculate for the one-dimensional -state Potts
model, finding an expression of the form , where is the Potts
analogue of . This is no longer positive
definite, but once again it diverges only at the critical point in the space of
real parameters. We remark, however, that a naive analytic continuation to
complex field reveals a further divergence in the Ising and Potts curvatures at
the Lee-Yang edge.Comment: 9 pages + 4 eps figure
On the "Universal" Quantum Area Spectrum
There has been much debate over the form of the quantum area spectrum for a
black hole horizon, with the evenly spaced conception of Bekenstein having
featured prominently in the discourse. In this letter, we refine a very
recently proposed method for calibrating the Bekenstein form of the spectrum.
Our refined treatment predicts, as did its predecessor, a uniform spacing
between adjacent spectral levels of in Planck units; notably, an outcome
that already has a pedigree as a proposed ``universal'' value for this
intrinsically quantum-gravitational measure. Although the two approaches are
somewhat similar in logic and quite agreeable in outcome, we argue that our
version is conceptually more elegant and formally simpler than its precursor.
Moreover, our rendition is able to circumvent a couple of previously unnoticed
technical issues and, as an added bonus, translates to generic theories of
gravity in a very direct manner.Comment: 7 Pages; (v2) now 9 full pages, significant changes to the text and
material added but the general theme and conclusions are unchange
1D Potts, Yang-Lee Edges and Chaos
It is known that the (exact) renormalization transformations for the
one-dimensional Ising model in field can be cast in the form of a logistic map
f(x) = 4 x (1 - x) with x a function of the Ising couplings. Remarkably, the
line bounding the region of chaotic behaviour in x is precisely that defining
the Yang-Lee edge singularity in the Ising model.
In this paper we show that the one dimensional q-state Potts model for q
greater than or equal to 1 also displays such behaviour. A suitable combination
of Potts couplings can again be used to define an x satisfying f(x) = 4 x (1
-x). The Yang-Lee zeroes no longer lie on the unit circle in the complex z =
exp (h) plane, but their locus is still reproduced by the boundary of the
chaotic region in the logistic map.Comment: 6 pages, no figure
Quantum Hall Effect on the Flag Manifold F_2
The Landau problem on the flag manifold
is analyzed from an algebraic point of view. The involved magnetic background
is induced by two U(1) abelian connections. In quantizing the theory, we show
that the wavefunctions, of a non-relativistic particle living on ,
are the SU(3) Wigner -functions satisfying two constraints. Using the
algebraic and geometrical structures, we derive the Landau
Hamiltonian as well as its energy levels. The Lowest Landau level (LLL)
wavefunctions coincide with the coherent states for the mixed SU(3)
representations. We discuss the quantum Hall effect for a filling factor . where the obtained particle density is constant and finite for a strong
magnetic field. In this limit, we also show that the system behaves like an
incompressible fluid. We study the semi-classical properties of the system
confined in LLL. These will be used to discuss the edge excitations and
construct the corresponding Wess-Zumino-Witten action.Comment: 23 pages, two sections and references added, misprints corrected,
version to appear in IJMP
On the Role of Chaos in the AdS/CFT Connection
The question of how infalling matter in a pure state forms a Schwarzschild
black hole that appears to be at non-zero temperature is discussed in the
context of the AdS/CFT connection. It is argued that the phenomenon of
self-thermalization in non-linear (chaotic) systems can be invoked to explain
how the boundary theory, initially at zero temperature self thermalizes and
acquires a finite temperature. Yang-Mills theory is known to be chaotic
(classically) and the imaginary part of the gluon self-energy (damping rate of
the gluon plasma) is expected to give the Lyapunov exponent. We explain how the
imaginary part would arise in the corresponding supergravity calculation due to
absorption at the horizon of the black hole.Comment: 18 pages. Latex file. Minor changes. Final version to appear in
Modern Physics Letters
A projective Dirac operator on CP^2 within fuzzy geometry
We propose an ansatz for the commutative canonical spin_c Dirac operator on
CP^2 in a global geometric approach using the right invariant (left action-)
induced vector fields from SU(3). This ansatz is suitable for noncommutative
generalisation within the framework of fuzzy geometry. Along the way we
identify the physical spinors and construct the canonical spin_c bundle in this
formulation. The chirality operator is also given in two equivalent forms.
Finally, using representation theory we obtain the eigenspinors and calculate
the full spectrum. We use an argument from the fuzzy complex projective space
CP^2_F based on the fuzzy analogue of the unprojected spin_c bundle to show
that our commutative projected spin_c bundle has the correct
SU(3)-representation content.Comment: reduced to 27 pages, minor corrections, minor improvements, typos
correcte
On Effective Constraints for the Riemann-Lanczos System of Equations
There have been conflicting points of view concerning the Riemann--Lanczos
problem in 3 and 4 dimensions. Using direct differentiation on the defining
partial differential equations, Massa and Pagani (in 4 dimensions) and Edgar
(in dimensions n > 2) have argued that there are effective constraints so that
not all Riemann tensors can have Lanczos potentials; using Cartan's criteria of
integrability of ideals of differential forms Bampi and Caviglia have argued
that there are no such constraints in dimensions n < 5, and that, in these
dimensions, all Riemann tensors can have Lanczos potentials. In this paper we
give a simple direct derivation of a constraint equation, confirm explicitly
that known exact solutions of the Riemann-Lanczos problem satisfy it, and argue
that the Bampi and Caviglia conclusion must therefore be flawed. In support of
this, we refer to the recent work of Dolan and Gerber on the three dimensional
problem; by a method closely related to that of Bampi and Caviglia, they have
found an 'internal identity' which we demonstrate is precisely the three
dimensional version of the effective constraint originally found by Massa and
Pagani, and Edgar.Comment: 9pages, Te
Genetic and Modifiable Risk Factors Contributing to Cisplatin-Induced Toxicities
Effective administration of traditional cytotoxic chemotherapy is often limited by off-target toxicities. This clinical dilemma is epitomized by cisplatin, a platinating agent that has potent antineoplastic activity due to its affinity for DNA and other intracellular nucleophiles. Despite its efficacy against many adult-onset and pediatric malignancies, cisplatin elicits multiple off-target toxicities that can not only severely impact a patient’s quality of life, but also lead to dose reductions or the selection of alternative therapies that can ultimately affect outcomes. Without an effective therapeutic measure by which to successfully mitigate many of these symptoms, there have been attempts to identify a priori those individuals who are more susceptible to developing these sequelae through studies of genetic and nongenetic risk factors. Older age is associated with cisplatin induced ototoxicity, neurotoxicity and nephrotoxicity. Traditional genome-wide association studies have identified single nucleotide polymorphisms in ACYP2 and WFS1 associated with cisplatin-induced hearing loss. However, validating associations between specific genotypes and cisplatin-induced toxicities with enough stringency to warrant clinical application remains challenging. This review summarizes the current state of knowledge with regard to specific adverse sequelae following cisplatin-based therapy with a focus on ototoxicity, neurotoxicity, nephrotoxicity, myelosuppression and nausea/emesis. We discuss variables (genetic and nongenetic) contributing to these detrimental toxicities, and currently available means to prevent or treat their occurrence
Global Fits of the Large Volume String Scenario to WMAP5 and Other Indirect Constraints Using Markov Chain Monte Carlo
We present global fits to the Large Volume Scenario (LVS) of string models
using current indirect data. We use WMAP5 constraints on dark matter relic
density, b-physics and electroweak observables as well as direct search
constraints. Such data can be adequately fit by LVS, with the best-fit point
for mu>0 having chi^2=13.6 for 8 degrees of freedom. The resulting constraints
on parameter space are robust in that they do not depend much upon the prior,
or upon whether one uses Bayesian or frequentist interpretations of the data.
Sparticle masses are constrained to be well below the 1 TeV level, predicting
early SUSY discovery at the LHC. We devise a method of quantifying which are
the most important constraints. We find that the LEP2 Higgs mass constraint,
the relic density of dark matter and the anomalous magnetic moment of the muon
affect the fits to the strongest degree.Comment: 30 pages, 10 figure
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