Dihedral symmetries of multiple logarithms

This paper finds relationships between multiple logarithms with a dihedral group action on the arguments. I generalize the combinatorics developed in Gangl, Goncharov and Levin's R-deco polygon representation of multiple logarithms to find these relations. By writing multiple logarithms as iterated integrals, my arguments are valid for iterated integrals as over an arbitrary field

Generalizing the Connes Moscovici Hopf algebra to contain all rooted trees

This paper defines a generalization of the Connes-Moscovici Hopf algebra, $\mathcal{H}(1)$ that contains the entire Hopf algebra of rooted trees. A relationship between the former, a much studied object in non-commutative geometry, and the later, a much studied object in perturbative Quantum Field Theory, has been established by Connes and Kreimer. The results of this paper open the door to study the cohomology of the Hopf algebra of rooted trees

Alternative values for sin(2beta) measured from electron/positron collisions at Babar

Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Physics, 2001.Includes bibliographical references (leaves 38-39).Babar is measuring the value for sin(2[beta]) in the unitary triangle of neutral Bd mesons produced in e⁺e⁻ collision. This thesis explores a model of the [gamma]T(4S) resonance created in this collision that is composed of two one-state systems instead of one two-state system. Considering only neutral mesons, I write a Monte Carlo simulation to determine an adjusted value for [Delta]m and use this value to fit the data that Babar published. Based on this analysis, I find sin(2[beta]) = .75 ± .27, about double the value that Babar measures.by Susama Agarwala.S.B

Geometrically relating momentum cut-off and dimensional regularization

The $\beta$ function for a scalar field theory describes the dependence of the coupling constant on the renormalization mass scale. This dependence is affected by the choice of regularization scheme. I explicitly relate the $\beta$-functions of momentum cut-off regularization and dimensional regularization on scalar field theories by a gauge transformation using the Hopf algebras of the Feynman diagrams of the theories.Comment: As submitted to IJGMMP; International Journal of Geometric Methods in Mathematical Physics, 2013, Volume 10, Number