3,257 research outputs found

### 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

### Regularization Dependence of the Zero Mode Dynamics in the Schwinger Model

I compare heatkernel regularization with sharp gauge invariant cutoffs in the
Hamiltonian formulation of the Coulomb gauged Schwinger model on a circle. The
effective potential for the zero mode of the gauge field in a given fermionic
configuration is different in these two regularizations, the difference being
independent of the chosen fermionic configuration. In the continuum limit the
gauge field can be localized or delocalized depending on the regulator.Comment: 7 pages, latex , (revised because of TEX problem

### 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

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