Renormalization in Nonrelativistic Quantum Mechanics

The importance and usefulness of renormalization are emphasized in nonrelativistic quantum mechanics. The momentum space treatment of both two-body bound state and scattering problems involving some potentials singular at the origin exhibits ultraviolet divergence. The use of renormalization techniques in these problems leads to finite converged results for both the exact and perturbative solutions. The renormalization procedure is carried out for the quantum two-body problem in different partial waves for a minimal potential possessing only the threshold behavior and no form factors. The renormalized perturbative and exact solutions for this problem are found to be consistent with each other. The useful role of the renormalization group equations for this problem is also pointed out.Comment: 16 page

Boson-fermion unification, superstrings, and Bohmian mechanics

Bosonic and fermionic particle currents can be introduced in a more unified way, with the cost of introducing a preferred spacetime foliation. Such a unified treatment of bosons and fermions naturally emerges from an analogous superstring current, showing that the preferred spacetime foliation appears only at the level of effective field theory, not at the fundamental superstring level. The existence of the preferred spacetime foliation allows an objective definition of particles associated with quantum field theory in curved spacetime. Such an objective definition of particles makes the Bohmian interpretation of particle quantum mechanics more appealing. The superstring current allows a consistent Bohmian interpretation of superstrings themselves, including a Bohmian description of string creation and destruction in terms of string splitting. The Bohmian equations of motion and the corresponding probabilistic predictions are fully relativistic covariant and do not depend on the preferred foliation.Comment: 30 pages, 1 figure, revised, to appear in Found. Phy

An assessment of Evans' unified field theory I

Evans developed a classical unified field theory of gravitation and electromagnetism on the background of a spacetime obeying a Riemann-Cartan geometry. This geometry can be characterized by an orthonormal coframe theta and a (metric compatible) Lorentz connection Gamma. These two potentials yield the field strengths torsion T and curvature R. Evans tried to infuse electromagnetic properties into this geometrical framework by putting the coframe theta to be proportional to four extended electromagnetic potentials A; these are assumed to encompass the conventional Maxwellian potential in a suitable limit. The viable Einstein-Cartan(-Sciama-Kibble) theory of gravity was adopted by Evans to describe the gravitational sector of his theory. Including also the results of an accompanying paper by Obukhov and the author, we show that Evans' ansatz for electromagnetism is untenable beyond repair both from a geometrical as well as from a physical point of view. As a consequence, his unified theory is obsolete.Comment: 39 pages of latex, modified because of referee report, mistakes and typos removed, partly reformulated, taken care of M.W.Evans' rebutta

Dimensional versus cut-off renormalization and the nucleon-nucleon interaction

The role of dimensional regularization is discussed and compared with that of cut-off regularization in some quantum mechanical problems with ultraviolet divergence in two and three dimensions with special emphasis on the nucleon-nucleon interaction. Both types of renormalizations are performed for attractive divergent one- and two-term separable potentials, a divergent tensor potential, and the sum of a delta function and its derivatives. We allow energy-dependent couplings, and determine the form that these couplings should take if equivalence between the two regularization schemes is to be enforced. We also perform renormalization of an attractive separable potential superposed on an analytic divergent potential.Comment: 19 pages + one postscript figur

Hysteresis, Avalanches, and Disorder Induced Critical Scaling: A Renormalization Group Approach

We study the zero temperature random field Ising model as a model for noise and avalanches in hysteretic systems. Tuning the amount of disorder in the system, we find an ordinary critical point with avalanches on all length scales. Using a mapping to the pure Ising model, we Borel sum the $6-\epsilon$ expansion to $O(\epsilon^5)$ for the correlation length exponent. We sketch a new method for directly calculating avalanche exponents, which we perform to $O(\epsilon)$. Numerical exponents in 3, 4, and 5 dimensions are in good agreement with the analytical predictions.Comment: 134 pages in REVTEX, plus 21 figures. The first two figures can be obtained from the references quoted in their respective figure captions, the remaining 19 figures are supplied separately in uuencoded forma

Semen cryopreservation, utilisation and reproductive outcome in men treated for Hodgkin's disease

Between 1978 and 1990, 122 men underwent semen analysis before starting sterilising chemotherapy for Hodgkin's disease. Eighty-one (66%) had semen quality within the normal range, 25 were oligospermic (<20×106 sperm per ml) and five were azoospermic (no sperm in the ejaculate). Semen from 115 men was cryopreserved and after a median follow-up time of 10.1 years, 33 men have utilised stored semen (actuarial rate 27%) and nine partners have become pregnant resulting in 11 live births and one termination for foetal malformation. Actuarial 10 year rates of destruction of semen before death or utilisation and death before utilisation are 19% and 13% respectively. This retrospective cohort study demonstrates that approximately one-quarter of men utilising cryopreserved semen after treatment for Hodgkin's disease obtain a live birth. The high non-utilisation rate is intriguing and warrants further investigation

A Chromosomal Inversion Unique to the Northern White-Cheeked Gibbon

The gibbon family belongs to the superfamily Hominoidea and includes 15 species divided into four genera. Each genus possesses a distinct karyotype with chromosome numbers varying from 38 to 52. This diversity is the result of numerous chromosomal changes that have accumulated during the evolution of the gibbon lineage, a quite unique feature in comparison with other hominoids and most of the other primates. Some gibbon species and subspecies rank among the most endangered primates in the world. Breeding programs can be extremely challenging and hybridization plays an important role within the factors responsible for the decline of captive gibbons. With less than 500 individuals left in the wild, the northern white-cheeked gibbon (Nomascus leucogenys leucogenys, NLE) is the most endangered primate in a successful captive breeding program. We present here the analysis of an inversion that we show being specific for the northern white-cheeked gibbon and can be used as one of the criteria to distinguish this subspecies from other gibbon taxa. The availability of the sequence spanning for one of the breakpoints of the inversion allows detecting it by a simple PCR test also on low quality DNA. Our results demonstrate the important role of genomics in providing tools for conservation efforts

Measurements of fiducial and differential cross sections for Higgs boson production in the diphoton decay channel at s√=8 TeV with ATLAS

Measurements of fiducial and differential cross sections are presented for Higgs boson production in proton-proton collisions at a centre-of-mass energy of s√=8 TeV. The analysis is performed in the H → γγ decay channel using 20.3 fb−1 of data recorded by the ATLAS experiment at the CERN Large Hadron Collider. The signal is extracted using a fit to the diphoton invariant mass spectrum assuming that the width of the resonance is much smaller than the experimental resolution. The signal yields are corrected for the effects of detector inefficiency and resolution. The pp → H → γγ fiducial cross section is measured to be 43.2 ±9.4(stat.) − 2.9 + 3.2 (syst.) ±1.2(lumi)fb for a Higgs boson of mass 125.4GeV decaying to two isolated photons that have transverse momentum greater than 35% and 25% of the diphoton invariant mass and each with absolute pseudorapidity less than 2.37. Four additional fiducial cross sections and two cross-section limits are presented in phase space regions that test the theoretical modelling of different Higgs boson production mechanisms, or are sensitive to physics beyond the Standard Model. Differential cross sections are also presented, as a function of variables related to the diphoton kinematics and the jet activity produced in the Higgs boson events. The observed spectra are statistically limited but broadly in line with the theoretical expectations

Songs with Obbligato

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