Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. We study continuous quantum phase transitions that can occur in bilayer fractional quantum Hall (FQH) systems as th...

We generalize the computation of Feynman integrals of log divergent graphs in terms of the Kirchhoff polynomial to the case of graphs with both fermionic and bosonic edges, to which we assign a set of ordinary and Grassmann variables. This procedure gives a computation of the Feynman integrals in terms of a period on a supermanifold, for graphs admitting a basis of the first homology satisfying...

Consider degenerations of Abelian differentials with prescribed number and multiplicity of zeros and poles. Motivated by the theory of limit linear series, we define twisted canonical divisors on pointed nodal curves to study degenerate differentials, give dimension bounds for their moduli spaces, and establish smoothability criteria. As applications, we show that the spin parity of holomorphic...

We compute the two-loop $\beta$-function of scalar and spinorial quantum electrodynamics as well pure Yang-Mills chromodynamics using background field method in a fully quadridimensional setup Implicit Regularization (IREG). Moreover, thorough comparison with dimensional approaches such conventional regularization (CDR) reduction (DRED) is presented. Subtleties related to Lorentz algebra contra...

for a polynomial p(z) of degree n, having all zeros in |z|< k, k< 1, dewan et al [k. k. dewan, n. singh and a. mir, extension of some polynomial inequalities to the polar derivative, j. math. anal. appl. 352 (2009) 807-815] obtained inequality between the polar derivative of p(z) and maximum modulus of p(z). in this paper we improve and extend the above inequality. our result generalizes certai...

Paul Garrett [email protected] http://www.math.umn.edu/ g̃arrett/ [This document is http://www.math.umn.edu/ ̃garrett/m/fun/notes 2012-13/06c cpt ab gps.pdf] 1. Approximate identities on topological groups 2. Uniqueness of invariant measure 3. Simultaneous eigenfunctions for integral operators 4. Simultaneous eigenfunctions are characters The spectral theory for normal compact operators on Hil...

We use a gauge-invariant regularization procedure, called split dimensional regularization, to evaluate the quark self-energy Σ(p) and quark-quark-gluon vertex function Λμ(p , p) in the Coulomb gauge, ~ ▽ · ~ A = 0. The technique of split dimensional regularization was designed to regulate Coulomb-gauge Feynman integrals in non-Abelian theories. The technique which is based on two complex regul...