4 citations · 9 across the 8 of their papers we have counts for
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Enumerative Methods in Quantum Electrodynamics
Ali Assem Mahmoud
We show that observables in QED-type theories can be realized in terms of a combinatorial structure called chord diagrams. One advantage of this combinatorial representation is tha…
An Asymptotic Expansion for the Number of 2-Connected Chord Diagrams
Ali Assem Mahmoud
We derive a functional relation between the generating functions of connected chord diagrams and 2-connected chord diagrams. This relation enables us to calculate an asymptotic exp…
Connected Chord Diagrams and the Combinatorics of Asymptotic Expansions
Ali Assem Mahmoud, Karen Yeats
In this article we study an asymptotic expansion for , the number of connected chord diagrams on chords. The expansion is obtained in earlier work by means of alien deriva…
Modules with Non-Cyclic Socle and the Extension Property
Ali Assem Mahmoud
In 2009, J. Wood proved that Frobenius bimodules have the extension property for symmetrized weight compositions. More generally, it was later shown that having a cyclic socle is s…
On the Enumerative Structures in Quantum Field Theory
Ali Assem Mahmoud
This thesis addresses a number of enumerative problems that arise in the context of quantum field theory and in the process of renormalization. In particular, the enumeration of ro…
Diffeomorphisms of Scalar Quantum Fields via Generating Functions
Ali Assem Mahmoud, Karen Yeats
We study the application of formal diffeomorphisms to scalar fields. We give a new proof that interacting tree amplitudes vanish in the resulting theories. Our proof is directly at…