Angela Mestre

Publications (6)0 Total impact

• Source

  Available from: ArXiv

  Article: Combinatorics of 1-particle irreducible n-point functions via coalgebra in quantum field theory

  Angela Mestre
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  ABSTRACT: We give a coalgebra structure on 1-vertex irreducible graphs which is that of a cocommutative coassociative graded connected coalgebra. We generalize the coproduct to the algebraic representation of graphs so as to express a bare 1-particle irreducible n-point function in terms of its loop order contributions. The algebraic representation is so that graphs can be evaluated as Feynman graphs.
  01/2010;
• Source

  Available from: ArXiv

  Article: On the decomposition of connected graphs into their biconnected components

  Angela Mestre
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  ABSTRACT: We give a recursion formula to generate all equivalence classes of biconnected graphs with coefficients given by the inverses of the orders of their groups of automorphisms. We give a linear map to produce a connected graph with say, u, biconnected components from one with u-1 biconnected components. We use such map to extend the aforesaid result to connected or 2-edge connected graphs. The underlying algorithms are amenable to computer implementation.
  01/2010;
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  Available from: ArXiv

  Article: Hopf algebras and the combinatorics of connected graphs in quantum field theory

  Angela Mestre, Robert Oeckl
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  ABSTRACT: In this talk, we are concerned with the formulation and understanding of the combinatorics of time-ordered n-point functions in terms of the Hopf algebra of field operators. Mathematically, this problem can be formulated as one in combinatorics or graph theory. It consists in finding a recursive algorithm that generates all connected graphs in their Hopf algebraic representation. This representation can be used directly and efficiently in evaluating Feynman graphs as contributions to the n-point functions.
  08/2008;
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  Available from: ArXiv

  Article: Generating connected and biconnected graphs

  Angela Mestre
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  ABSTRACT: We focus on the algorithm underlying the main result of [A. Mestre, R. Oeckl, Generating loop graphs via Hopf algebra in quantum field theory. J. Math. Phys., 47, 122302, 2006]. This is an algebraic formula to generate all connected graphs in a recursive and efficient manner. The key feature is that each graph carries a scalar factor given by the inverse of the order of its group of automorphisms. In the present paper, we revise that algorithm on the level of graphs. Moreover, we extend the result subsequently to further classes of connected graphs, namely, (edge) biconnected, simple and loopless graphs. Our method consists of basic graph transformations only. Comment: v4, v5: minor corrections; v3: 30 pages, substantially revised version; two new sections with alternative recursion formula for loopless graphs and with algorithmic considerations added; v2: 25 pages, substantially revised notation and terminology; new section with recursion formula for simple graphs added; appendixes added
  10/2007;
• Source

  Available from: arxiv.org

  Article: Generating loop graphs via Hopf algebra in quantum field theory

  Angela Mestre, Robert Oeckl
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  ABSTRACT: We use the Hopf algebra structure of the time-ordered algebra of field operators to generate all connected weighted Feynman graphs in a recursive and efficient manner. The algebraic representation of the graphs is such that they can be evaluated directly as contributions to the connected n-point functions. The recursion proceeds by loop order and vertex number.
  08/2006;
• Source

  Available from: arxiv.org

  Article: Combinatorics of n-point functions via Hopf algebra in quantum field theory

  Angela Mestre, Robert Oeckl
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  ABSTRACT: We use a coproduct on the time-ordered algebra of field operators to derive simple relations between complete, connected and 1-particle irreducible n-point functions. Compared to traditional functional methods our approach is much more intrinsic and leads to efficient algorithms suitable for concrete computations. It may also be used to efficiently perform tree level computations.
  06/2005;