Implementing Unitarity in Perturbation Theory

Unitarity cannot be perserved order by order in ordinary perturbation theory because the constraint UU^\dagger=\1 is nonlinear. However, the corresponding constraint for $K=\ln U$, being $K=-K^\dagger$, is linear so it can be maintained in every order in a perturbative expansion of $K$. The perturbative expansion of $K$ may be considered as a non-abelian generalization of the linked-cluster expansion in probability theory and in statistical mechanics, and possesses similar advantages resulting from separating the short-range correlations from long-range effects. This point is illustrated in two QCD examples, in which delicate cancellations encountered in summing Feynman diagrams of are avoided when they are calculated via the perturbative expansion of $K$. Applications to other problems are briefly discussed.Comment: to appear in Phys. Rev.

On Exceptional Vertex Operator (Super) Algebras

We consider exceptional vertex operator algebras and vertex operator superalgebras with the property that particular Casimir vectors constructed from the primary vectors of lowest conformal weight are Virasoro descendents of the vacuum. We show that the genus one partition function and characters for simple ordinary modules must satisfy modular linear differential equations. We show the rationality of the central charge and module lowest weights, modularity of solutions, the dimension of each graded space is a rational function of the central charge and that the lowest weight primaries generate the algebra. We also discuss conditions on the reducibility of the lowest weight primary vectors as a module for the automorphism group. Finally we analyse solutions for exceptional vertex operator algebras with primary vectors of lowest weight up to 9 and for vertex operator superalgebras with primary vectors of lowest weight up to 17/2. Most solutions can be identified with simple ordinary modules for known algebras but there are also four conjectured algebras generated by weight two primaries and three conjectured extremal vertex operator algebras generated by primaries of weight 3, 4 and 6 respectively.Comment: 37 page

Higher-order non-symmetric counterterms in pure Yang-Mills theory

We analyze the restoration of the Slavnov-Taylor (ST) identities for pure massless Yang-Mills theory in the Landau gauge within the BPHZL renormalization scheme with IR regulator. We obtain the most general form of the action-like part of the symmetric regularized action, obeying the relevant ST identities and all other relevant symmetries of the model, to all orders in the loop expansion. We also give a cohomological characterization of the fulfillment of BPHZL IR power-counting criterion, guaranteeing the existence of the limit where the IR regulator goes to zero. The technique analyzed in this paper is needed in the study of the restoration of the ST identities for those models, like the MSSM, where massless particles are present and no invariant regularization scheme is known to preserve the full set of ST identities of the theory.Comment: Final version published in the journa

The b Distribution and the Velocity Structure of Absorption Peaks in the Lyman-Alpha Forest

A theory is developed which relates the observed b-parameter of a Lyman-alpha absorption line to the velocity-curvature of the corresponding peak in the optical depth fluctuation. Its relation to the traditional interpretation of b as the thermal broadening width is discussed. It is demonstrated that, independent of the details of the cosmological model, the differential b distribution has a high b asymptote of $dN/db \propto b^{-m}$, where $m \geq 5$, when we make the reasonable assumption that low-curvature fluctuations are statistically favored over high-curvature ones. There in general always exist absorption lines much broader than the thermal width. We then develop a linear perturbative analysis of the optical depth fluctuation, which yields a single-parameter prediction for the full b distribution: in addition to exhibiting the general high velocity tail, it explains the observed sharp low b cut-off. The dependence of the b distribution on cosmological parameters, such as $\Omega$ and the power spectrum, and reionization history as well as observation/simulation resolution is derived and discussed.Comment: 18 pages, Latex with aaspp4.sty, submitted to Ap

Mutual information--based approach to adaptive homodyne detection of quantum optical states

I propose an approach to adaptive homodyne detection of digitally modulated quantum optical pulses in which the phase of the local oscillator is chosen to maximize the average information gain, i.e., the mutual information, at each step of the measurement. I study the properties of this adaptive detection scheme by considering the problem of classical information content of ensembles of coherent states. Using simulations of quantum trajectories and visualizations of corresponding measurement operators, I show that the proposed measurement scheme adapts itself to the features of each ensemble. For all considered ensembles of coherent states, it consistently outperforms heterodyne detection and Wiseman's adaptive scheme for phase measurements [H.M. Wiseman, Phys. Rev. Lett. 75, 4587 (1995)].Comment: Submutted to Phys. Rev.

No-Switching Quantum Key Distribution using Broadband Modulated Coherent Light

We realize an end-to-end no-switching quantum key distribution protocol using continuous-wave coherent light. We encode weak broadband Gaussian modulations onto the amplitude and phase quadratures of light beams at the Shannon's information limit. Our no-switching protocol achieves high secret key rate via a post-selection protocol that utilizes both quadrature information simultaneously. We establish a secret key rate of 25 Mbits/s for a lossless channel and 1 kbit/s, per 17 MHz of detected bandwidth, for 90% channel loss. Since our scheme is truly broadband, it can potentially deliver orders of magnitude higher key rates by extending the encoding bandwidth with higher-end telecommunication technology.Comment: 5 pages, 3 figures, publishe

Self-aligned nanoscale SQUID on a tip

A nanometer-sized superconducting quantum interference device (nanoSQUID) is fabricated on the apex of a sharp quartz tip and integrated into a scanning SQUID microscope. A simple self-aligned fabrication method results in nanoSQUIDs with diameters down to 100 nm with no lithographic processing. An aluminum nanoSQUID with an effective area of 0.034 $\mu$m$^2$ displays flux sensitivity of 1.8$\cdot 10^{-6}$ $\Phi_0/\mathrm{Hz}^{1/2} and operates in fields as high as 0.6 T. With projected spin sensitivity of 65$\mu_B/\mathrm{Hz}^{1/2}$ and high bandwidth, the SQUID on a tip is a highly promising probe for nanoscale magnetic imaging and spectroscopy.Comment: 14 manuscript pages, 5 figure

Combined use of zoledronic acid and 153Sm-EDTMP in hormone-refractory prostate cancer patients with bone metastases

Purpose: 153Sm-ethylenediaminetetramethylenephosphonic acid (EDTMP; Quadramet®) is indicated for the treatment of painful bone metastases, whereas zoledronic acid (Zometa®) is indicated for the prevention of skeletal complications. Because of the different therapeutic effects, combining the treatments may be beneficial. Both, however, accumulate in areas with increased osteoblastic activity. Possible drug interactions were investigated. Methods: Patients with hormone-refractory prostate cancer were treated with 18.5 MBq/kg 153Sm-EDTMP in weeks 1 and 3 and with 37 MBq/kg in week 15. Treatment with 4 mg zoledronic acid began in week 3 and continued every 4 weeks through week 23. In weeks 3 and 15, zoledronic acid was administered 2 days before 153Sm-EDTMP treatment. Urine was collected 48 h after injection of 153Sm-EDTMP, and whole-body images were obtained 6, 24 and 48 h post-injection. The effect of zoledronic acid on total bone uptake of 153Sm-EDTMP was measured indirectly by the cumulative activity excreted in the urine in weeks 1, 3 and 15. Biodistribution, safety, tolerability and effect on prostate-specific antigen level were also studied. Results: The urinary excretion in week 3 divided by the urinary excretion in week 1 (baseline) times 100% was mean 98.4±11.6% (median 96.2%). From week 1 to 15, after four zoledronic acid treatments, the mean ratio was 101.9±10.7% (median 101.8%). Bioequivalence could be concluded by using a two-sample t test for both perprotocol (n=13) and full-analysis sets (n=18). Toxicity was comparable to of monotherapy with 153Sm-EDTMP. Conclusion: Zoledronic acid treatment does not influence 153Sm-EDTMP skeletal uptake. Combined treatment is feasible and safe

Landau gauge within the Gribov horizon

We consider a model which effectively restricts the functional integral of Yang--Mills theories to the fundamental modular region. Using algebraic arguments, we prove that this theory has the same divergences as ordinary Yang Mills theory in the Landau gauge and that it is unitary. The restriction of the functional integral is interpreted as a kind of spontaneous breakdown of the $BRS$ symmetry.Comment: 17 pages, NYU-TH-93/10/0

Two-soliton solution for the derivative nonlinear Schr\"odinger equation with nonvanishing boundary conditions

An explicit two-soliton solution for the derivative nonlinear Schr\"odinger equation with nonvanishing boundary conditions is derived, demonstrating details of interactions between two bright solitons, two dark solitons, as well as one bright soliton and one dark soliton. Shifts of soliton positions due to collisions are analytically obtained, which are irrespective of the bright or dark characters of the participating solitons.Comment: 11 pages, 4 figures. Phys. Lett. A 2006 (in press