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Constructive Field Theory in Zero Dimension

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arxiv 0906.3524 v1 pith:TPKFGF26 submitted 2009-06-18 math-ph math.MP

classification math-phmath.MP
keywords constructivefieldnotetheorycomputeconnectedcontaindifferent
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abstract

In this pedagogical note we propose to wander through five different methods to compute the number of connected graphs of the zero-dimensional $\phi^4$ 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.

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  1. Functional Renormalization Group meets Computational Fluid Dynamics: RG flows in a multi-dimensional field space

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    A two-dimensional Kurganov-Tadmor finite-volume scheme accurately solves FRG flow equations for effective potentials in multi-dimensional field space, benchmarked against exact zero-dimensional path integrals and appl...

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