Renormalization of the Non-Linear Sigma Model in Four Dimensions. A two-loop example

The renormalization procedure of the non-linear SU(2) sigma model in D=4 proposed in hep-th/0504023 and hep-th/0506220 is here tested in a truly non-trivial case where the non-linearity of the functional equation is crucial. The simplest example, where the non-linear term contributes, is given by the two-loop amplitude involving the insertion of two \phi_0 (the constraint of the non-linear sigma model) and two flat connections. In this case we verify the validity of the renormalization procedure: the recursive subtraction of the pole parts at D=4 yields amplitudes that satisfy the defining functional equation. As a by-product we give a formal proof that in D dimensions (without counterterms) the Feynman rules provide a perturbative symmetric solution.Comment: Latex, 3 figures, 19 page

Wannier functions and Fractional Quantum Hall Effect

We introduce and study the Wannier functions for an electron moving in a plane under the influence of a perpendicular uniform and constant magnetic field. The relevance for the Fractional Quantum Hall Effect is discussed; in particular it shown that an interesting Hartree-Fock state can be constructed in terms of Wannier functions.Comment: 7 pages, RevTeX 3.0, 5 tar-compressed and uu-encoded figure

Path-integral over non-linearly realized groups and Hierarchy solutions

The technical problem of deriving the full Green functions of the elementary pion fields of the nonlinear sigma model in terms of ancestor amplitudes involving only the flat connection and the nonlinear sigma model constraint is a very complex task. In this paper we solve this problem by integrating, order by order in the perturbative loop expansion, the local functional equation derived from the invariance of the SU(2) Haar measure under local left multiplication. This yields the perturbative definition of the path-integral over the non-linearly realized SU(2) group.Comment: 26 page

Numerical analysis of the master equation

Applied to the master equation, the usual numerical integration methods, such as Runge-Kutta, become inefficient when the rates associated with various transitions differ by several orders of magnitude. We introduce an integration scheme that remains stable with much larger time increments than can be used in standard methods. When only the stationary distribution is required, a direct iteration method is even more rapid; this method may be extended to construct the quasi-stationary distribution of a process with an absorbing state. Applications to birth-and-death processes reveal gains in efficiency of two or more orders of magnitude.Comment: 7 pages 3 figure

Theoretical implications of the second time derivative of the period of the pulsar NP0532

Theoretical implications of second time derivative with existing magnetic dipole model

Living with stable angina: patients' pathway and needs in angina.

AIMS: There is evidence that stable angina patients may suffer from emotional disorders that further impair their quality of life. However, the emotional experience of living with stable angina from the patient's perspective still has to be explored. Thus, the main aim of this study was to explore patients' emotional experience of having stable angina and their reported needs during the pathway from the first symptoms, through the process of diagnosis, to management and related lifestyle changes. METHODS: A survey was conducted in 75 chronic ischemic heart disease patients with angina (Brazil, China, Romania, Russia, and Turkey) using a 75-min, face-to-face in-depth interview. RESULTS AND CONCLUSION: Patients' responses highlighted the need to increase individuals' awareness on the first signs and symptoms of the disease. The survey also showed that chronic stable angina patients need constant emotional support to overcome stress, anxiety, and depression. Finally, this study suggests the need to offer greater space for dialogue with healthcare professionals to get more comprehensive and 'patient-friendly' information

The Hierarchy Principle and the Large Mass Limit of the Linear Sigma Model

In perturbation theory we study the matching in four dimensions between the linear sigma model in the large mass limit and the renormalized nonlinear sigma model in the recently proposed flat connection formalism. We consider both the chiral limit and the strong coupling limit of the linear sigma model. Our formalism extends to Green functions with an arbitrary number of pion legs,at one loop level,on the basis of the hierarchy as an efficient unifying principle that governs both limits. While the chiral limit is straightforward, the matching in the strong coupling limit requires careful use of the normalization conditions of the linear theory, in order to exploit the functional equation and the complete set of local solutions of its linearized form.Comment: Latex, 41 pages, corrected typos, final version accepted by IJT