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GrassmannBerezin calculus and theorems of the matrixtree type
 Adv. Appl. Math
, 2004
"... We prove two generalizations of the matrixtree theorem. The first one, a result essentially due to Moon for which we provide a new proof, extends the “all minors ” matrixtree theorem to the “massive ” case where no condition on row or column sums is imposed. The second generalization, which is new ..."
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We prove two generalizations of the matrixtree theorem. The first one, a result essentially due to Moon for which we provide a new proof, extends the “all minors ” matrixtree theorem to the “massive ” case where no condition on row or column sums is imposed. The second generalization, which is new, extends the recently discovered Pfaffiantree theorem of Masbaum and Vaintrob into a “Hyperpfaffiancactus ” theorem. Our methods are noninductive, explicit and make critical use of GrassmannBerezin calculus that was developed for the needs of modern theoretical physics. Key words: Matrixtree theorem, Pfaffiantree theorem, Fermionic integration, Hyperpfaffian, Cacti.
Feynman diagrams in algebraic combinatorics, Séminaire Lotharingien de Combinatoire 49
 2002–04), Article B49c, 45 pp. SPECIES AND FEYNMAN DIAGRAMS 37
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A RIGOROUS TREATMENT OF THE PERTURBATION THEORY FOR MANYELECTRON SYSTEMS
, 904
"... Four point correlation functions for many electrons at finite temperature in periodic lattice of dimension d ( ≥ 1) are analyzed by the perturbation theory with respect to the coupling constant. The correlation functions are characterized as a limit of finite dimensional Grassmann integrals. A lower ..."
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Four point correlation functions for many electrons at finite temperature in periodic lattice of dimension d ( ≥ 1) are analyzed by the perturbation theory with respect to the coupling constant. The correlation functions are characterized as a limit of finite dimensional Grassmann integrals. A lower bound on the radius of convergence and an upper bound on the perturbation series are obtained by evaluating the Taylor expansion of logarithm of the finite dimensional Grassmann Gaussian integrals. The perturbation series up to second order is numerically implemented along with the volumeindependent upper bounds on the sum of the higher order terms in 2 dimensional case.
Quantum Electrodynamics on the 3torus  I. first step
"... We study the ultraviolet problem for quantum electrodynamics on a three dimensional torus. We start with the lattice gauge theory on a toroidal lattice and seek to control the singularities as the lattice spacing is taken to zero. This is done by following the flow of a sequence of renormalization g ..."
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We study the ultraviolet problem for quantum electrodynamics on a three dimensional torus. We start with the lattice gauge theory on a toroidal lattice and seek to control the singularities as the lattice spacing is taken to zero. This is done by following the flow of a sequence of renormalization group transformations. The analysis is facilitated by splitting the space of gauge fields into into large fields and small fields at each step following Balaban. In this paper we explore the first step in detail.
Exponential decay of equaltime fourpoint correlation functions in the Hubbard model on the copperoxide lattice
 Ann. Henri Poincaré, Online First
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