711 research outputs found
Background field technique and renormalization in lattice gauge theory
Lattice gauge theory with a background gauge field is shown to be
renormalizable to all orders of perturbation theory. No additional counterterms
are required besides those already needed in the absence of the background
field. The argument closely follows the treatment given earlier for the case of
dimensional regularization by Kluberg-Stern and Zuber. It is based on the BRS,
background gauge and shift symmetries of the lattice functional integral.Comment: 26 pages, uuencoded compressed postscript fil
Effective Field Theory for Highly Ionized Plasmas
We examine the equilibrium properties of hot, dilute, non-relativistic
plasmas. The partition function and density correlation functions of a
classical plasma with several species are expressed in terms of a functional
integral over electrostatic potential distributions. The leading order,
field-theoretic tree approximation automatically includes the effects of Debye
screening. Subleading, one-loop corrections are easily evaluated. The two-loop
corrections, however, have ultraviolet divergences. These correspond to the
short-distance, logarithmic divergence which is encountered in the spatial
integral of the Boltzmann exponential when it is expanded to third order in the
Coulomb potential. Such divergences do not appear in the underlying quantum
theory --- they are rendered finite by quantum fluctuations. We show how such
divergences may be removed and the correct finite theory obtained by
introducing additional local interactions in the manner of modern effective
quantum field theories. We obtain explicit results for density-density
correlation functions through two-loop order and thermodynamic quantities
through three-loop order. The induced couplings are shown to obey
renormalization group equations, and these equations are used to characterize
all leading logarithmic contributions in the theory. A linear combination of
pressure and energy and number densities is shown to be described by a
field-theoretic anomaly. The effective theory allows us to evaluate very easily
the algebraic long-distance decay of density correlation functions.Comment: 194 pages, uses elsevier & epsf.sty; final corrections include
Initial Conditions for a Universe
In physical theories, boundary or initial conditions play the role of
selecting special situations which can be described by a theory with its
general laws. Cosmology has long been suspected to be different in that its
fundamental theory should explain the fact that we can observe only one
particular realization. This is not realized, however, in the classical
formulation and in its conventional quantization; the situation is even worse
due to the singularity problem. In recent years, a new formulation of quantum
cosmology has been developed which is based on quantum geometry, a candidate
for a theory of quantum gravity. Here, the dynamical law and initial conditions
turn out to be linked intimately, in combination with a solution of the
singularity problem.Comment: 7 pages, this essay was awarded First Prize in the Gravity Research
Foundation Essay Contest 200
J/\Psi production in two-photon collisions at next-to-leading order
In this paper, we report on the calculation of the cross section of J/\Psi
plus jet inclusive production in direct two-photon collisions at
next-to-leading order within the factorization formalism of nonrelativistic
quantum chromodynamics (NRQCD). Theoretical predictions for the future e^+e^-
linear collider TESLA are also presented.Comment: 5 pages, 2 figures, talk given at the 7th DESY Workshop on Elementary
Particle Theory: Loops and Legs in Quantum Field Theory, Zinnowitz, Germany,
25-30 April, 2004: added references for section
The Dark Matter Problem in Light of Quantum Gravity
We show how, by considering the cumulative effect of tiny quantum
gravitational fluctuations over very large distances, it may be possible to:
() reconcile nucleosynthesis bounds on the density parameter of the Universe
with the predictions of inflationary cosmology, and () reproduce the
inferred variation of the density parameter with distance. Our calculation can
be interpreted as a computation of the contribution of quantum gravitational
degrees of freedom to the (local) energy density of the Universe.Comment: 13 pages, LaTeX, (3 figues, not included
Diffraction in the Semiclassical Approximation to Feynman's Path Integral Representation of the Green Function
We derive the semiclassical approximation to Feynman's path integral
representation of the energy Green function of a massless particle in the
shadow region of an ideal obstacle in a medium. The wavelength of the particle
is assumed to be comparable to or smaller than any relevant length of the
problem. Classical paths with extremal length partially creep along the
obstacle and their fluctuations are subject to non-holonomic constraints. If
the medium is a vacuum, the asymptotic contribution from a single classical
path of overall length L to the energy Green function at energy E is that of a
non-relativistic particle of mass E/c^2 moving in the two-dimensional space
orthogonal to the classical path for a time \tau=L/c. Dirichlet boundary
conditions at the surface of the obstacle constrain the motion of the particle
to the exterior half-space and result in an effective time-dependent but
spatially constant force that is inversely proportional to the radius of
curvature of the classical path. We relate the diffractive, classically
forbidden motion in the "creeping" case to the classically allowed motion in
the "whispering gallery" case by analytic continuation in the curvature of the
classical path. The non-holonomic constraint implies that the surface of the
obstacle becomes a zero-dimensional caustic of the particle's motion. We solve
this problem for extremal rays with piecewise constant curvature and provide
uniform asymptotic expressions that are approximately valid in the penumbra as
well as in the deep shadow of a sphere.Comment: 37 pages, 5 figure
The Inverse Scale Factor in Isotropic Quantum Geometry
The inverse scale factor, which in classical cosmological models diverges at
the singularity, is quantized in isotropic models of loop quantum cosmology by
using techniques which have been developed in quantum geometry for a
quantization of general relativity. This procedure results in a bounded
operator which is diagonalizable simultaneously with the volume operator and
whose eigenvalues are determined explicitly. For large scale factors (in fact,
up to a scale factor slightly above the Planck length) the eigenvalues are
close to the classical expectation, whereas below the Planck length there are
large deviations leading to a non-diverging behavior of the inverse scale
factor even though the scale factor has vanishing eigenvalues. This is a first
indication that the classical singularity is better behaved in loop quantum
cosmology.Comment: 17 pages, 4 figure
A Massive Renormalizable Abelian Gauge Theory in 2+1 Dimensions
The standard formulation of a massive Abelian vector field in
dimensions involves a Maxwell kinetic term plus a Chern-Simons mass term; in
its place we consider a Chern-Simons kinetic term plus a Stuekelberg mass term.
In this latter model, we still have a massive vector field, but now the
interaction with a charged spinor field is renormalizable (as opposed to super
renormalizable). By choosing an appropriate gauge fixing term, the Stuekelberg
auxiliary scalar field decouples from the vector field. The one-loop spinor
self energy is computed using operator regularization, a technique which
respects the three dimensional character of the antisymmetric tensor
. This method is used to evaluate the vector self
energy to two-loop order; it is found to vanish showing that the beta function
is zero to two-loop order. The canonical structure of the model is examined
using the Dirac constraint formalism.Comment: LaTeX, 17 pages, expanded reference list and discussion of
relationship to previous wor
Canonical Quantum Supergravity in Three Dimensions, (some lines lost during submission)
We discuss the canonical treatment and quantization of matter coupled
supergravity in three dimensions, with special emphasis on supergravity.
We then analyze the quantum constraint algebra; certain operator ordering
ambiguities are found to be absent due to local supersymmetry. We show that the
supersymmetry constraints can be partially solved by a functional analog of the
method of characteristics. We also consider extensions of Wilson loop integrals
of the type previously found in ordinary gravity, but now with connections
involving the bosonic and fermionic matter fields in addition to the
gravitational connection. In a separate section of this paper, the canonical
treatment and quantization of non-linear coset space sigma models are discussed
in a self contained way.Comment: 40 pages, LaTeX, DESY 93-07
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