4,545 research outputs found
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
New Instanton Solutions at Finite Temperature
We discuss the newly found exact instanton solutions at finite temperature
with a non-trivial Polyakov loop at infinity. They can be described in terms of
monopole constituents and we discuss in this context an old result due to
Taubes how to make out of monopoles non-trivial topological charge
configurations, with possible applications to abelian projection.Comment: 6 pages, 2 figures (in 5 parts), latex using espcrc1.sty, presented
at "QCD at Finite Baryon Density", April 27-30, 1998, Bielefeld, German
Black Hole Evaporation without Information Loss
An approach to black hole quantization is proposed wherein it is assumed that
quantum coherence is preserved. A consequence of this is that the Penrose
diagram describing gravitational collapse will show the same topological
structure as flat Minkowski space. After giving our motivations for such a
quantization procedure we formulate the background field approximation, in
which particles are divided into "hard" particles and "soft" particles. The
background space-time metric depends both on the in-states and on the
out-states. We present some model calculations and extensive discussions. In
particular, we show, in the context of a toy model, that the -matrix
describing soft particles in the hard particle background of a collapsing star
is unitary, nevertheless, the spectrum of particles is shown to be
approximately thermal. We also conclude that there is an important topological
constraint on functional integrals.Comment: 35 pages (including Figures); TEX, 3 figures in postscrip
Symmetry breaking via fermion 4-point functions
We construct the effective action and gap equations for nonperturbative
fermion 4-point functions. Our results apply to situations in which fermion
masses can be ignored, which is the case for theories of strong flavor
interactions involving standard quarks and leptons above the electroweak scale.
The structure of the gap equations is different from what a naive
generalization of the 2-point case would suggest, and we find for example that
gauge exchanges are insufficient to generate nonperturbative 4-point functions
when the number of colors is large.Comment: 36 pages, uses Revtex and eps files for figure
Analytical Results for Abelian Projection
Analytic methods for Abelian projection are developed, and a number of
results related to string tension measurements are obtained. It is proven that
even without gauge fixing, Abelian projection yields string tensions of the
underlying non-Abelian theory. Strong arguments are given for similar results
in the case where gauge fixing is employed. The subgroup used for projection
need only contain the center of the gauge group, and need not be Abelian. While
gauge fixing is shown to be in principle unnecessary for the success of Abelian
projection, it is computationally advantageous for the same reasons that
improved operators, e.g., the use of fat links, are advantageous in Wilson loop
measurements.Comment: LATTICE98(confine), 3 pages, 1 eps figur
Free energy of an SU(2) monopole-antimonopole pair
We induce an external monopole-antimonopole pair in an SU(2) lattice
gauge system and measure its free energy as a way to probe the vacuum
structure. We discuss the motivation and computational methodology of the
investigation and illustrate our preliminary results.Comment: LATTICE98(confine
Ground states of supersymmetric Yang-Mills-Chern-Simons theory
We consider minimally supersymmetric Yang-Mills theory with a Chern-Simons
term on a flat spatial two-torus. The Witten index may be computed in the weak
coupling limit, where the ground state wave-functions localize on the moduli
space of flat gauge connections. We perform such computations by considering
this moduli space as an orbifold of a certain flat complex torus. Our results
agree with those obtained previously by instead considering the moduli space as
a complex projective space. An advantage of the present method is that it
allows for a more straightforward determination of the discrete electric 't
Hooft fluxes of the ground states in theories with non-simply connected gauge
groups. A consistency check is provided by the invariance of the results under
the mapping class group of a (Euclidean) three-torus.Comment: 18 page
Potential between external monopole and antimonopole in SU(2) lattice glu odynamics
We present the results of a study of the free energy of a monopole pair in
pure
SU(2) theory at finite temperature, both below and above the deconfinement
tran sition. We find a Yukawa potential between monopoles in both phases. At
low temp erature, the screening mass is compatible with the lightest glueball
mass. At hi gh temperature, we observe an increased screening mass with no
apparent disconti nuity at the phase transition.Comment: LATTICE 99 (Topology and Confinement
More on the Subtraction Algorithm
We go on in the program of investigating the removal of divergences of a
generical quantum gauge field theory, in the context of the Batalin-Vilkovisky
formalism. We extend to open gauge-algebrae a recently formulated algorithm,
based on redefinitions of the parameters of the
classical Lagrangian and canonical transformations, by generalizing a well-
known conjecture on the form of the divergent terms. We also show that it is
possible to reach a complete control on the effects of the subtraction
algorithm on the space of the gauge-fixing parameters. A
principal fiber bundle with a connection
is defined, such that the canonical transformations are gauge
transformations for . This provides an intuitive geometrical
description of the fact the on shell physical amplitudes cannot depend on
. A geometrical description of the effect of the subtraction
algorithm on the space of the physical parameters is
also proposed. At the end, the full subtraction algorithm can be described as a
series of diffeomorphisms on , orthogonal to
(under which the action transforms as a scalar), and gauge transformations on
. In this geometrical context, a suitable concept of predictivity is
formulated. We give some examples of (unphysical) toy models that satisfy this
requirement, though being neither power counting renormalizable, nor finite.Comment: LaTeX file, 37 pages, preprint SISSA/ISAS 90/94/E
Nondifferentiable Dynamic: Two Examples
Some nondifferentiable quantities (for example, the metric signature) can be
the independent physical degrees of freedom. It is supposed that in quantum
gravity these degrees of freedom can fluctuate. Two examples of such quantum
fluctuation are considered: a quantum interchange of the sign of two components
of the 5D metric and a quantum fluctuation between Euclidean and Lorentzian
metrics. The first case leads to a spin-like structure on the throat of
composite wormhole and to a possible inner structure of the string. The second
case leads to a quantum birth of the non-singular Euclidean Universe with
frozen dimension. The probability for such quantum fluctuations is
connected with an algorithmical complexity of the Einstein equations.Comment: essential changes: the initial equations in section III are changed,
as the consequence the obtained solution describes the quantum birth of the
nonsingular Universe with the matter (electromagnetic field=nondiagonal
components of the MD metric
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