74 research outputs found
A New Approach to Numerical Quantum Field Theory
In this note we present a new numerical method for solving Lattice Quantum
Field Theory. This Source Galerkin Method is fundamentally different in concept
and application from Monte Carlo based methods which have been the primary mode
of numerical solution in Quantum Field Theory. Source Galerkin is not
probabilistic and treats fermions and bosons in an equivalent manner.Comment: 10 pages, LaTeX, BROWN-HET-908([email protected]),
([email protected]), ([email protected]
Source Galerkin Calculations in Scalar Field Theory
In this paper, we extend previous work on scalar theory using the
Source Galerkin method. This approach is based on finding solutions to
the lattice functional equations for field theories in the presence of an
external source . Using polynomial expansions for the generating functional
, we calculate propagators and mass-gaps for a number of systems. These
calculations are straightforward to perform and are executed rapidly compared
to Monte Carlo. The bulk of the computation involves a single matrix inversion.
The use of polynomial expansions illustrates in a clear and simple way the
ideas of the Source Galerkin method. But at the same time, this choice has
serious limitations. Even after exploiting symmetries, the size of calculations
become prohibitive except for small systems. The calculations in this paper
were made on a workstation of modest power using a fourth order polynomial
expansion for lattices of size ,, in , , and . In
addition, we present an alternative to the Galerkin procedure that results in
sparse matrices to invert.Comment: 31 pages, latex, figures separat
New Numerical Method for Fermion Field Theory
A new deterministic, numerical method to solve fermion field theories is
presented. This approach is based on finding solutions to the lattice
functional equations for field theories in the presence of an external source
. Using Grassmann polynomial expansions for the generating functional ,
we calculate propagators for systems of interacting fermions. These
calculations are straightforward to perform and are executed rapidly compared
to Monte Carlo. The bulk of the computation involves a single matrix inversion.
Because it is not based on a statistical technique, it does not have many of
the difficulties often encountered when simulating fermions. Since no
determinant is ever calculated, solutions to problems with dynamical fermions
are handled more easily. This approach is very flexible, and can be taylored to
specific problems based on convenience and computational constraints. We
present simple examples to illustrate the method; more general schemes are
desirable for more complicated systems.Comment: 24 pages, latex, figures separat
Numerical Quantum Field Theory on the Continuum and a New Look at Perturbation Theory
The Source Galerkin method finds approximate solutions to the functional
differential equations of field theories in the presence of external sources.
While developing this process, it was recognized that approximations of the
spectral representations of the Green's functions by Sinc function expansions
are an extremely powerful calculative tool. Specifically, this understanding
makes it not only possible to apply the Source Galerkin method to higher
dimensional field theories, but also leads to a new approach to perturbation
theory calculations in scalar and fermionic field theories. This report
summarizes the methodologies for solving quantum field theories with the Source
Galerkin method and for performing perturbation theory calculations using Sinc
approximations.Comment: Lattice2001(theorydevelop
Dilaton as the Higgs boson
We propose a model where the role of the electroweak Higgs field is played by
the dilaton. The model contains terms which explicitly violate gauge
invariance, however it is shown that this violation is fictitious, so that the
model is a consistent low energy effective theory. In the simplest version of
the idea the resulting low energy effective theory is the same as the top mode
standard model.Comment: 6 pages, v2 with expanded discussio
Alternative Numerical Techniques
Two new approaches to numerical QFT are presented.Comment: Lattice2002(theoretical), 3 page
Charmed Strange Pentaquarks in the Large Limit
The properties of pentaquarks containing a heavy anti-quark and strange
quarks are studied in the bound state picture. In the flavor SU(3) limit, there
are many pentaquark states with the same binding energy. When the SU(3)
symmetry breaking effects are included, however, three states become
particularly stable due to a ``Gell-Mann--Okubo mechanism''. They are the and states discussed by Lipkin, and a a previously
unstudied state. These states will have and
their masses are estimated. These states, if exist, may be seen in experiments
in the near future.Comment: 12 pages in REVTeX, no figure
A Supersymmetric Stueckelberg U(1) Extension of the MSSM
A Stueckelberg extension of the MSSM with only one abelian vector and one
chiral superfield as an alternative to an abelian extension with Higgs scalars
is presented. The bosonic sector contains a new gauge boson Z' which is a sharp
resonance, and a new CP-even scalar, which combines with the MSSM Higgs bosons
to produce three neutral CP-even massive states. The neutral fermionic sector
has two additional fermions which mix with the four MSSM neutralinos to produce
an extended 6x6 neutralino mass matrix. For the case when the LSP is composed
mostly of the Stueckelberg fermions, the LSP of the MSSM will be unstable,
which leads to exotic decays of sparticles with many leptons in final states.
Prospects for supersymmetry searches and for dark matter are discussed.Comment: 10 page
Physical Unitarity for Massive Non-abelian Gauge Theories in the Landau Gauge: Stueckelberg and Higgs
We discuss the problem of unitarity for Yang-Mills theory in the Landau gauge
with a mass term a la Stueckelberg. We assume that the theory
(non-renormalizable) makes sense in some subtraction scheme (in particular the
Slavnov-Taylor identities should be respected!) and we devote the paper to the
study of the space of the unphysical modes. We find that the theory is unitary
only under the hypothesis that the 1-PI two-point function of the vector mesons
has no poles (at p^2=0). This normalization condition might be rather crucial
in the very definition of the theory. With all these provisos the theory is
unitary. The proof of unitarity is given both in a form that allows a direct
transcription in terms of Feynman amplitudes (cutting rules) and in the
operatorial form. The same arguments and conclusions apply verbatim to the case
of non-abelian gauge theories where the mass of the vector meson is generated
via Higgs mechanism. To the best of our knowledge, there is no mention in the
literature on the necessary condition implied by physical unitarity.Comment: References added. 22 pages. Final version to appear in the journa
Experimental Constraints on Heavy Fermions in Higgsless Models
Using an effective Lagrangian approach we analyze a generic Higgsless model
with composite heavy fermions, transforming as SU(2)_{L+R} Doublets. Assuming
that the Standard Model fermions acquire mass through mixing with the new heavy
fermions, we constrain the free parameters of the effective Lagrangian studying
Flavour Changing Neutral Current processes. In so doing we obtain bounds that
can be applied to a wide range of models characterized by the same fermion
mixing hypothesis.Comment: 23 pages, 10 figure
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