562 research outputs found
Koebe 1/4-Theorem and Inequalities in N=2 Super-QCD
The critical curve on which ,
, determines hyperbolic domains whose Poincar\'e metric is
constructed in terms of and . We describe in a parametric
form related to a Schwarzian equation and prove new relations for Super
Yang-Mills. In particular, using the Koebe 1/4-theorem and Schwarz's
lemma, we obtain inequalities involving , and , which seem related
to the Renormalization Group. Furthermore, we obtain a closed form for the
prepotential as function of . Finally, we show that , where is the one-loop coefficient of the beta
function.Comment: 11 pages, LaTex file, Expanded version: new results, technical
details explained, misprints corrected and references adde
Coherence in Compton scattering at large angles
Compton scattering of laser light by an electron beam at large angles, in particular at 90°, produces coherent hard radiation if the density of the electron beam is high enough. In this case, the intensity of the scattered radiation is greatly enhanced in a small cone around the forward direction of propagation of the electron beam. As an example, the production of 1-KeV coherent X rays is discussed
The Equivalence Postulate of Quantum Mechanics
The Equivalence Principle (EP), stating that all physical systems are
connected by a coordinate transformation to the free one with vanishing energy,
univocally leads to the Quantum Stationary HJ Equation (QSHJE). Trajectories
depend on the Planck length through hidden variables which arise as initial
conditions. The formulation has manifest p-q duality, a consequence of the
involutive nature of the Legendre transform and of its recently observed
relation with second-order linear differential equations. This reflects in an
intrinsic psi^D-psi duality between linearly independent solutions of the
Schroedinger equation. Unlike Bohm's theory, there is a non-trivial action even
for bound states. No use of any axiomatic interpretation of the wave-function
is made. Tunnelling is a direct consequence of the quantum potential which
differs from the usual one and plays the role of particle's self-energy. The
QSHJE is defined only if the ratio psi^D/psi is a local self-homeomorphism of
the extended real line. This is an important feature as the L^2 condition,
which in the usual formulation is a consequence of the axiomatic interpretation
of the wave-function, directly follows as a basic theorem which only uses the
geometrical gluing conditions of psi^D/psi at q=\pm\infty as implied by the EP.
As a result, the EP itself implies a dynamical equation that does not require
any further assumption and reproduces both tunnelling and energy quantization.
Several features of the formulation show how the Copenhagen interpretation
hides the underlying nature of QM. Finally, the non-stationary higher
dimensional quantum HJ equation and the relativistic extension are derived.Comment: 1+3+140 pages, LaTeX. Invariance of the wave-function under the
action of SL(2,R) subgroups acting on the reduced action explicitly reveals
that the wave-function describes only equivalence classes of Planck length
deterministic physics. New derivation of the Schwarzian derivative from the
cocycle condition. "Legendre brackets" introduced to further make "Legendre
duality" manifest. Introduction now contains examples and provides a short
pedagogical review. Clarifications, conclusions, ackn. and references adde
Eluding SUSY at every genus on stable closed string vacua
In closed string vacua, ergodicity of unipotent flows provide a key for
relating vacuum stability to the UV behavior of spectra and interactions.
Infrared finiteness at all genera in perturbation theory can be rephrased in
terms of cancelations involving only tree-level closed strings scattering
amplitudes. This provides quantitative results on the allowed deviations from
supersymmetry on perturbative stable vacua. From a mathematical perspective,
diagrammatic relations involving closed string amplitudes suggest a relevance
of unipotent flows dynamics for the Schottky problem and for the construction
of the superstring measure.Comment: v2, 17 pages, 8 figures, typos corrected, new figure added with 3
modular images of long horocycles,(obtained with Mathematica
RG Flow Irreversibility, C-Theorem and Topological Nature of 4D N=2 SYM
We determine the exact beta function and a RG flow Lyapunov function for N=2
SYM with gauge group SU(n). It turns out that the classical discriminants of
the Seiberg-Witten curves determine the RG potential. The radial
irreversibility of the RG flow in the SU(2) case and the non-perturbative
identity relating the -modulus and the superconformal anomaly, indicate the
existence of a four dimensional analogue of the c-theorem for N=2 SYM which we
formulate for the full SU(n) theory. Our investigation provides further
evidence of the essentially topological nature of the theory.Comment: 9 pages, LaTeX file. Discussion on WDVV and integrability. References
added. Version published in PR
Exact 2-point function in Hermitian matrix model
J. Harer and D. Zagier have found a strikingly simple generating function for
exact (all-genera) 1-point correlators in the Gaussian Hermitian matrix model.
In this paper we generalize their result to 2-point correlators, using Toda
integrability of the model. Remarkably, this exact 2-point correlation function
turns out to be an elementary function - arctangent. Relation to the standard
2-point resolvents is pointed out. Some attempts of generalization to 3-point
and higher functions are described.Comment: 31 pages, 1 figur
Non-holomorphic terms in N=2 SUSY Wilsonian actions and RG equation
In this paper we first investigate the Ansatz of one of the present authors
for K(\Psi,\bar\Psi), the adimensional modular invariant non-holomorphic
correction to the Wilsonian effective Lagrangian of an N=2 globally
supersymmetric gauge theory. The renormalisation group beta-function of the
theory crucially allows us to express K(\Psi,\bar\Psi) in a form that easily
generalises to the case in which the theory is coupled to N_F hypermultiplets
in the fundamental representation of the gauge group. This function satisfies
an equation which should be viewed as a fully non-perturbative ``non-chiral
superconformal Ward identity". We also determine its renormalisation group
equation. Furthermore, as a first step towards checking the validity of this
Ansatz, we compute the contribution to K(\Psi,\bar\Psi) from instantons of
winding number k=1 and k=2. As a by-product of our analysis we check a
non-renormalisation theorem for N_F=4.Comment: 39 pages, LaTex file, no figure
The Ventricular System Enlarges Abnormally in the Seventies, Earlier in Men, and First in the Frontal Horn: A Study Based on More Than 3,000 Scans
Objectives: To detect on computed tomography (CT) brain scans the trajectories of normal and abnormal ventricular enlargement during aging. Methods: For each 1-year age cohort, we assessed in 3,193 axial CT scans the Evans’ index (EI) in the anterior frontal horns and the parieto-occipital (POR) and temporal ratio (TR) in the posterior and inferior horns. Cut-off values for abnormal enlargement were based on previous clinical studies. Results: The mean age associated with normal linear measures was 71 years. Values for all three measures increased with age, showing a linear relationship below—but not above—each cut-off value. The mean age of participants with abnormal enlargement on CT progressed from 79 years for EI to 83 years for POR to 87 years for TR. These results suggested that ventricular dilatation progresses in an age–location relationship. First comes enlargement of the frontal horns (13.8% of scans), followed by the parieto-occipital horns (15.1% of scans) and then temporal horn enlargement (6.8% of scans). Scans from men displayed abnormal values earlier than scans from women (on average 6 years). Risk increased 5.1% annually for abnormal EI, 9.0% for abnormal POR, and 11% for abnormal TR (all p < 0.001). The most frequent agreement between categories (normal–abnormal) for values of neuroimaging measures was identified for POR–TR. Conclusion: The results of this large radiological study suggest that the ventricular system enlarges progressively during aging, and in a subset of patients follows an abnormal consecutive geometric dilatation, influenced by age and sex
On the property of Cachazo-Intriligator-Vafa prepotential at the extremum of the superpotential
We consider CIV-DV prepotential F for N=1 SU(n) SYM theory at the extremum of
the effective superpotential and prove the relation Comment: LaTeX, 10 pages; v2: some misprints corrected; v3: submitted to
Phys.Rev.
Abelian gerbes as a gauge theory of quantum mechanics on phase space
We construct a U(1) gerbe with a connection over a finite-dimensional,
classical phase space P. The connection is given by a triple of forms A,B,H: a
potential 1-form A, a Neveu-Schwarz potential 2-form B, and a field-strength
3-form H=dB. All three of them are defined exclusively in terms of elements
already present in P, the only external input being Planck's constant h. U(1)
gauge transformations acting on the triple A,B,H are also defined, parametrised
either by a 0-form or by a 1-form. While H remains gauge invariant in all
cases, quantumness vs. classicality appears as a choice of 0-form gauge for the
1-form A. The fact that [H]/2i\pi is an integral class in de Rham cohomology is
related with the discretisation of symplectic area on P. This is an equivalent,
coordinate-free reexpression of Heisenberg's uncertainty principle. A choice of
1-form gauge for the 2-form B relates our construction with generalised complex
structures on classical phase space. Altogether this allows one to interpret
the quantum mechanics corresponding to P as an Abelian gauge theory.Comment: 18 pages, 1 figure available from the authors upon reques
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