Delta Expansion on the Lattice and Dilated Scaling Region

A new kind of delta expansion is applied on the lattice to the d=2 non-linear sigma model at N=infinity and N=1 which corresponds to the Ising model. We introduce the parameter delta for the dilation of the scaling region of the model with the replacement of the lattice spacing a to (1-delta)^{1/2}a. Then, we demonstrate that the expansion in delta admits an approximation of the scaling behavior of the model at both limits of N from the information at a large lattice spacing a.Comment: 11 pages, 18 figure

A Generating Function for Fatgraphs

We study a generating function for the sum over fatgraphs with specified valences of vertices and faces, inversely weighted by the order of their symmetry group. A compact expression is found for general (i.e. non necessarily connected) fatgraphs. This expression admits a matrix integral representation which enables to perform semi--classical computations, leading in particular to a closed formula corresponding to (genus zero, connected) trees.Comment: 24 pages, uses harvmac macro, 1 figure not included, Saclay preprint SPhT/92-16

Non-perturbative decay of udd and QLd flat directions

The Minimal Supersymmetric Standard Model has several flat directions, which can naturally be excited during inflation. If they have a slow (perturbative) decay, they may affect the thermalization of the inflaton decay products. In the present paper, we consider the system of udd and QLd flat directions, which breaks the U(1)xSU(2)xSU(3) symmetry completely. In the unitary gauge and assuming a general soft breaking mass configuration, we show that for a range of parameters, the background condensate of flat directions can undergo a fast non-perturbative decay, due to non-adiabatic evolution of the eigenstates. We find that both the background evolution and part of the decay can be described accurately by previously studied gauged toy models of flat direction decay.Comment: 32 pages, 1 figur

Quantum intersection rings

We examine a few problems of enumerative geometry and present their solutions in the framework of deformed (quantum) cohomology rings.Comment: 73 p, uuencoded, uses harvmac in b mode, 6 figures include

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

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.Comment: 26 pages, LaTeX + AMS + eepic; minor corrections and modification

Efficient simulation of relativistic fermions via vertex models

We have developed an efficient simulation algorithm for strongly interacting relativistic fermions in two-dimensional field theories based on a formulation as a loop gas. The loop models describing the dynamics of the fermions can be mapped to statistical vertex models and our proposal is in fact an efficient simulation algorithm for generic vertex models in arbitrary dimensions. The algorithm essentially eliminates critical slowing down by sampling two-point correlation functions and it allows simulations directly in the massless limit. Moreover, it generates loop configurations with fluctuating topological boundary conditions enabling to simulate fermions with arbitrary periodic or anti-periodic boundary conditions. As illustrative examples, the algorithm is applied to the Gross-Neveu model and to the Schwinger model in the strong coupling limit.Comment: 5 pages, 4 figure

Non-Gaussian wave functionals in Coulomb gauge Yang--Mills theory

A general method to treat non-Gaussian vacuum wave functionals in the Hamiltonian formulation of a quantum field theory is presented. By means of Dyson--Schwinger techniques, the static Green functions are expressed in terms of the kernels arising in the Taylor expansion of the exponent of the vacuum wave functional. These kernels are then determined by minimizing the vacuum expectation value of the Hamiltonian. The method is applied to Yang--Mills theory in Coulomb gauge, using a vacuum wave functional whose exponent contains up to quartic terms in the gauge field. An estimate of the cubic and quartic interaction kernels is given using as input the gluon and ghost propagators found with a Gaussian wave functional.Comment: 27 pages, 21 figure

Renormalization without infinities

Most renormalizable quantum field theories can be rephrased in terms of Feynman diagrams that only contain dressed irreducible 2-, 3-, and 4-point vertices. These irreducible vertices in turn can be solved from equations that also only contain dressed irreducible vertices. The diagrams and equations that one ends up with do not contain any ultraviolet divergences. The original bare Lagrangian of the theory only enters in terms of freely adjustable integration constants. It is explained how the procedure proposed here is related to the renormalization group equations. The procedure requires the identification of unambiguous "paths" in a Feynman diagrams, and it is shown how to define such paths in most of the quantum field theories that are in use today. We do not claim to have a more convenient calculational scheme here, but rather a scheme that allows for a better conceptual understanding of ultraviolet infinities. Dedicated to Paul Frampton's 60th birthdayComment: 8 pages, 11 figures. Proc. Coral Gables Conference, dec. 16-21, 200

An equivalence of two mass generation mechanisms for gauge fields

Two mass generation mechanisms for gauge theories are studied. It is proved that in the abelian case the topological mass generation mechanism introduced in hep-th/9301060, hep-th/9512216 is equivalent to the mass generation mechanism defined in hep-th/0510240, hep-th/0605050 with the help of ``localization'' of a nonlocal gauge invariant action. In the nonabelian case the former mechanism is known to generate a unitary renormalizable quantum field theory describing a massive vector field.Comment: 18 page

Lattice theory for nonrelativistic fermions in one spatial dimension

I derive a loop representation for the canonical and grand-canonical partition functions for an interacting four-component Fermi gas in one spatial dimension and an arbitrary external potential. The representation is free of the "sign problem" irrespective of population imbalance, mass imbalance, and to a degree, sign of the interaction strength. This property is in sharp contrast with the analogous three-dimensional two-component interacting Fermi gas, which exhibits a sign problem in the case of unequal masses, chemical potentials, and repulsive interactions. The one-dimensional system is believed to exhibit many phenomena in common with its three-dimensional counterpart, including an analog of the BCS-BEC crossover, and nonperturbative universal few- and many-body physics at scattering lengths much larger than the range of interaction, making the theory an interesting candidate for numerical study. Positivity of the probability measure for the partition function allows for a mean-field treatment of the model; here, I present such an analysis for the interacting Fermi gas in the SU(4) (unpolarized, mass-symmetric) limit, and demonstrate that there exists a phase in which a continuum limit may be defined.Comment: 12 pages, 6 figures, references adde