224 research outputs found

    Constructive Field Theory in Zero Dimension

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    In this pedagogical note we propose to wander through five different methods to compute the number of connected graphs of the zero-dimensional ϕ4\phi^4 field theory,in increasing order of sophistication. The note does not contain any new result but may be helpful to summarize the heart of constructive resummations, namely a replica trick and a forest formula.Comment: 12 pages,one figur

    Constructive Matrix Theory

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    We extend the technique of constructive expansions to compute the connected functions of matrix models in a uniform way as the size of the matrix increases. This provides the main missing ingredient for a non-perturbative construction of the ϕ44\phi^{\star 4}_4 field theory on the Moyal four dimensional space.Comment: 12 pages, 3 figure

    Constructive ϕ4\phi^4 field theory without tears

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    We propose to treat the ϕ4\phi^4 Euclidean theory constructively in a simpler way. Our method, based on a new kind of "loop vertex expansion", no longer requires the painful intermediate tool of cluster and Mayer expansions.Comment: 22 pages, 10 figure

    Bosonic Monocluster Expansion

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    We compute connected Green's functions of a Bosonic field theory with cutoffs by means of a ``minimal'' expansion which in a single move, interpolating a generalized propagator, performs the usual tasks of the cluster and Mayer expansion. In this way it allows a direct construction of the infinite volume or thermodynamic limit and it brings constructive Bosonic expansions closer to constructive Fermionic expansions and to perturbation theory.Comment: 30 pages, 1 figur