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169
The multivariate Tutte polynomial (alias Potts model) for graphs and matroids
 Surveys in Combinatorics, 2005, 173–226
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An Infinite Volume Expansion for Many Fermion Green's Functions
, 1992
"... We prove the convergence of a simplified cluster/Mayer expansion at one energy scale for three spacetime dimensional many Fermion systems. The bounds are uniform in the scale. We iterate them to show that the sum of all diagrams that contain no two or fourlegged subdiagrams converges. Our results ..."
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Cited by 43 (26 self)
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We prove the convergence of a simplified cluster/Mayer expansion at one energy scale for three spacetime dimensional many Fermion systems. The bounds are uniform in the scale. We iterate them to show that the sum of all diagrams that contain no two or fourlegged subdiagrams converges. Our results are suited to a multiscale construction of the full system. Research supported in part by the Natural Sciences and Engineering Research Council of Canada and the Schweizerischer Nationalfonds zur Forderung der wissenschaftlichen Forschung y Research supported in part by the Forschungsinstitut fur Mathematik, Zurich xI Introduction In this paper we consider many Fermion systems formally characterized by the effective potential G(/ e ; ¯ / e ) = log 1 Z Z e \GammaV (/+/ e ; ¯ /+ ¯ / e ) d¯C (/; ¯ /) for the external fields / e ; ¯ / e . Here, d¯C (/; ¯ /) is the fermionic Gaussian measure in the Grassmann variables f/(¸); ¯ /(¸) j ¸ 2 IR \Theta IR d \Theta ...
A Renormalizable 4dimensional Tensor Field Theory
, 2012
"... We prove that an integrated version of the Gurau colored tensor model supplemented with the usual Bosonic propagator on U(1)4 is renormalizable to all orders in perturbation theory. The model is of the type expected for quantization of spacetime in 4D Euclidean gravity and is the first example of ..."
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Cited by 42 (8 self)
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We prove that an integrated version of the Gurau colored tensor model supplemented with the usual Bosonic propagator on U(1)4 is renormalizable to all orders in perturbation theory. The model is of the type expected for quantization of spacetime in 4D Euclidean gravity and is the first example of a renormalizable model of this kind. Its vertex and propagator are fourstranded like in 4D group field theories, but without gauge averaging on the strands. Surprisingly perhaps, the model is of the φ6 rather than of the φ4 type, since two different φ6type interactions are logdivergent, i.e. marginal in the renormalization group sense. The renormalization proof relies on a multiscale analysis. It identifies all divergent graphs through a power counting theorem. These divergent graphs have internal and external structure of a particular kind called melonic. Melonic graphs dominate the 1/N expansion of colored tensor models and generalize the planar ribbon graphs of matrix models. A new locality principle is established for this category of graphs which allows to renormalize their divergences through counterterms of the form of the bare Lagrangian interactions. The model also has an unexpected anomalous logdivergent ( φ2)2 term, which can be interpreted as the generation of a scalar matter field out of pure gravity.
Quantum YangMills Theory
"... importan tin describin elemen tary particle physics are gauge theories. The classical example of a gauge theory is the theory of electromagnDHnD The gauge group is the abelian group U(1). If Aden(FC the U(1) gauge conHFFCFH0 which locallycan be regarded as aonCF;)H on spacetime,then the curvature ..."
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Cited by 31 (3 self)
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importan tin describin elemen tary particle physics are gauge theories. The classical example of a gauge theory is the theory of electromagnDHnD The gauge group is the abelian group U(1). If Aden(FC the U(1) gauge conHFFCFH0 which locallycan be regarded as aonCF;)H on spacetime,then the curvature or electromagnFC fieldtenHC is the twoform F = dA, an Maxwell'sequation read 0 = dF = d # F . Here # is the Hodge duality operator; HodgeinzF( in troduced his celebrated theory of harmonQ forms as a gen;;FH0Cz;QF to pforms of Maxwell'sequationC Maxwell'sequation describe large scale electric an magnQH fields an also  as Maxwell discovered  thepropagation of light waves, at a characteristic velocity, the speed of light. YanF)P(H0 theory ornHCFC elian gauge theorycan at the classical level, be described similarly, with<F11.96
Noncommutative deformations of Wightman quantum field theories, JHEP 0809
, 2008
"... Abstract: Quantum field theories on noncommutative Minkowski space are studied in a modelindependent setting by treating the noncommutativity as a deformation of quantum field theories on commut ative space. Starting from an arbitrary Wightman theory, we consider special vacuum representations of i ..."
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Cited by 30 (3 self)
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Abstract: Quantum field theories on noncommutative Minkowski space are studied in a modelindependent setting by treating the noncommutativity as a deformation of quantum field theories on commut ative space. Starting from an arbitrary Wightman theory, we consider special vacuum representations of its WeylWigner deformed counterpart. In such representations, the effect of the noncommutativity on the basic structures of Wightman theory, in particular the covariance, locality and regularity properties of the fields, the structure of the Wightman functions, and the commutative limit, is analyzed. Despite the nonlocal structure introduced by the noncommutativity, the deformed quantum fields can still be localized in certain wedgeshaped regions, and may therefore be used to compute noncommutative corrections to twoparticle Smatrix elements.
Quantum Gravity and Renormalization: The Tensor Track
 AIP Conf. Proc. 1444, 18 (2011) [arXiv:1112.5104 [hepth
"... We propose a new program to quantize and renormalize gravity based on recent progress on the analysis of large random tensors. We compare it briefly with other existing approaches. LPT20XXxx ..."
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Cited by 28 (5 self)
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We propose a new program to quantize and renormalize gravity based on recent progress on the analysis of large random tensors. We compare it briefly with other existing approaches. LPT20XXxx
Constructive φ 4 field theory without tears
 Annales Henri Poincare
"... We propose to treat the φ 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. 1 ..."
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Cited by 21 (5 self)
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We propose to treat the φ 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. 1
An Explicit Large Versus Small Field Multiscale
 Cluster Expansion, Rev. Math. Phys. 9
, 1997
"... We introduce a new type of cluster expansion which generalizes a previous formula of Brydges and Kennedy. The method is especially suited for performing a phasespace multiscale expansion in a just renormalizable theory, and allows the writing of explicit nonperturbative formulas for the Schwinger ..."
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Cited by 20 (13 self)
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We introduce a new type of cluster expansion which generalizes a previous formula of Brydges and Kennedy. The method is especially suited for performing a phasespace multiscale expansion in a just renormalizable theory, and allows the writing of explicit nonperturbative formulas for the Schwinger functions. The procedure is quite model independent, but for simplicity we chose the infrared φ 4 4 model as a testing ground. We used also a large field versus small field expansion. The polymer amplitudes, corresponding to graphs without almost local two and for point functions, are shown to satisfy the polymer bound. 1