1,655 research outputs found

### 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

### 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

### 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

### Equations différentielles covariantes et représentations de l'algèbre de Virasoro

URL: http://www-spht.cea.fr/Docspht/articles/t93/020/ Org.: Norguet F., Ofman S., Szczeciniarz J.-J.Equations différentielles covariantes et représentations de l'algèbre de Virasor

### Local electric current correlation function in an exponentially decaying magnetic field

The effect of an exponentially decaying magnetic field on the dynamics of
Dirac fermions in 3+1 dimensions is explored. The spatially decaying magnetic
field is assumed to be aligned in the third direction, and is defined by
{\mathbf{B}}(x)=B(x){\mathbf{e}}_{z}, with B(x)=B_{0}e^{-\xi\ x/\ell_{B}}.
Here, \xi\ is a dimensionless damping factor and \ell_{B}=(eB_{0})^{-1/2} is
the magnetic length. As it turns out, the energy spectrum of fermions in this
inhomogeneous magnetic field can be analytically determined using the Ritus
method. Assuming the magnetic field to be strong, the chiral condensate and the
\textit{local} electric current correlation function are computed in the lowest
Landau level (LLL) approximation and the results are compared with those
arising from a strong homogeneous magnetic field. Although the constant
magnetic field B_{0} can be reproduced by taking the limit of \xi-> 0 and/or
x-> 0 from B(x), these limits turn out to be singular once the quantum
corrections are taken into account.Comment: V1: 16 pages, 7 figures, 2 tables; V2: Section II improved,
references added. Version accepted for publication in PR

### 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

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