35,088 research outputs found
Automatic Computation of Feynman Diagrams
Quantum corrections significantly influence the quantities observed in modern
particle physics. The corresponding theoretical computations are usually quite
lengthy which makes their automation mandatory. This review reports on the
current status of automatic calculation of Feynman diagrams in particle
physics. The most important theoretical techniques are introduced and their
usefulness is demonstrated with the help of simple examples. A survey over
frequently used programs and packages is provided, discussing their abilities
and fields of applications. Subsequently, some powerful packages which have
already been applied to important physical problems are described in more
detail. The review closes with the discussion of a few typical applications for
the automated computation of Feynman diagrams, addressing current physical
questions like properties of the and Higgs boson, four-loop corrections to
renormalization group functions and two-loop electroweak corrections.Comment: Latex, 62 pages. Typos corrected, references updated and some
comments added. Vertical offset changed. The complete paper is also available
via anonymous ftp at ftp://ttpux2.physik.uni-karlsruhe.de/ttp98/ttp98-41/ or
via www at http://www-ttp.physik.uni-karlsruhe.de/Preprints
The fermionic limit of the delta-function Bose gas: a pseudopotential approach
We use first-order perturbation theory near the fermionic limit of the
delta-function Bose gas in one dimension (i.e., a system of weakly interacting
fermions) to study three situations of physical interest. The calculation is
done using a pseudopotential which takes the form of a two-body
delta''-function interaction. The three cases considered are the behavior of
the system with a hard wall, with a point where the strength of the
pseudopotential changes discontinuously, and with a region of finite length
where the pseudopotential strength is non-zero (this is sometimes used as a
model for a quantum wire). In all cases, we obtain exact expressions for the
density to first order in the pseudopotential strength. The asymptotic
behaviors of the densities are in agreement with the results obtained from
bosonization for a Tomonaga-Luttinger liquid, namely, an interaction dependent
power-law decay of the density far from the hard wall, a reflection from the
point of discontinuity, and transmission resonances for the interacting region
of finite length. Our results provide a non-trivial verification of the
Tomonaga-Luttinger liquid description of the delta-function Bose gas near the
fermionic limit.Comment: LaTeX, 17 pages, no figure
Probing Quantized Einstein-Rosen Waves with Massless Scalar Matter
The purpose of this paper is to discuss in detail the use of scalar matter
coupled to linearly polarized Einstein-Rosen waves as a probe to study quantum
gravity in the restricted setting provided by this symmetry reduction of
general relativity. We will obtain the relevant Hamiltonian and quantize it
with the techniques already used for the purely gravitational case. Finally we
will discuss the use of particle-like modes of the quantized fields to
operationally explore some of the features of quantum gravity within this
framework. Specifically we will study two-point functions, the Newton-Wigner
propagator, and radial wave functions for one-particle states.Comment: Accepted for publication in Physical Review
Phase transitions in multi-cut matrix models and matched solutions of Whitham hierarchies
We present a method to study phase transitions in the large N limit of matrix
models using matched solutions of Whitham hierarchies. The endpoints of the
eigenvalue spectrum as functions of the temperature are characterized both as
solutions of hodograph equations and as solutions of a system of ordinary
differential equations. In particular we show that the free energy of the
matrix model is the quasiclassical tau-function of the associated hierarchy,
and that critical processes in which the number of cuts changes in one unit are
third-order phase transitions described by C1 matched solutions of Whitham
hierarchies. The method is illustrated with the Bleher-Eynard model for the
merging of two cuts. We show that this model involves also a birth of a cut
Eigenvalue distributions from a star product approach
We use the well-known isomorphism between operator algebras and function
spaces equipped with a star product to study the asymptotic properties of
certain matrix sequences in which the matrix dimension tends to infinity.
Our approach is based on the coherent states which allow for a
systematic 1/D expansion of the star product. This produces a trace formula for
functions of the matrix sequence elements in the large- limit which includes
higher order (finite-) corrections. From this a variety of analytic results
pertaining to the asymptotic properties of the density of states, eigenstates
and expectation values associated with the matrix sequence follows. It is shown
how new and existing results in the settings of collective spin systems and
orthogonal polynomial sequences can be readily obtained as special cases. In
particular, this approach allows for the calculation of higher order
corrections to the zero distributions of a large class of orthogonal
polynomials.Comment: 25 pages, 8 figure
On quasi-local charges and Newman--Penrose type quantities in Yang--Mills theories
We generalize the notion of quasi-local charges, introduced by P. Tod for
Yang--Mills fields with unitary groups, to non-Abelian gauge theories with
arbitrary gauge group, and calculate its small sphere and large sphere limits
both at spatial and null infinity. We show that for semisimple gauge groups no
reasonable definition yield conserved total charges and Newman--Penrose (NP)
type quantities at null infinity in generic, radiative configurations. The
conditions of their conservation, both in terms of the field configurations and
the structure of the gauge group, are clarified. We also calculate the NP
quantities for stationary, asymptotic solutions of the field equations with
vanishing magnetic charges, and illustrate these by explicit solutions with
various gauge groups.Comment: 22 pages, typos corrected, appearing in Classical and Quantum Gravit
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