12 research outputs found
The Extended Loop Group: An Infinite Dimensional Manifold Associated with the Loop Space
A set of coordinates in the non parametric loop-space is introduced. We show
that these coordinates transform under infinite dimensional linear
representations of the diffeomorphism group. An extension of the group of loops
in terms of these objects is proposed. The enlarged group behaves locally as an
infinite dimensional Lie group. Ordinary loops form a subgroup of this group.
The algebraic properties of this new mathematical structure are analized in
detail. Applications of the formalism to field theory, quantum gravity and knot
theory are considered.Comment: The resubmited paper contains the title and abstract, that were
omitted in the previous version. 42 pages, report IFFI/93.0
Instanton Contribution to the Quark Form Factor
The nonperturbative effects in the quark form factor are considered in the
Wilson loop formalism. The properties of the Wilson loops with cusp
singularities are studied taking into account the perturbative and
nonperturbative contributions, where the latter are considered within the
framework of the instanton liquid model. For the integration path corresponding
to this form factor -- the angle with infinite sides -- the explicit expression
for the vacuum expectation value of the Wilson operator is found to leading
order. The calculations are performed in the weak-field limit for the instanton
vacuum contribution and compared with the one- and two-loop order results for
the perturbative part. It is shown that the instantons produce the powerlike
corrections to the perturbative result, which are comparable in magnitude with
the perturbative part at the scale of order of the inverse average instanton
size. It is demonstrated that the instanton contributions to the quark form
factor are exponentiated to high orders in the small instanton density
parameter.Comment: Version coincident with the journal publication. LaTeX, 15 pages, 1
figur
Induced QCD and Hidden Local ZN Symmetry
We show that a lattice model for induced lattice QCD which was recently
proposed by Kazakov and Migdal has a gauge symmetry which, in the strong
coupling phase, results in a local confinement where only color singlets are
allowed to propagate along links and all Wilson loops for non-singlets average
to zero. We argue that, if this model is to give QCD in its continuum limit, it
must have a phase transition. We give arguments to support presence of such a
phase transition
Electroweak symmetry breaking in other terms
We analyse descriptions of electroweak symmetry breaking in terms of
ultralocal antisymmetric tensor fields and gauge-singlet geometric variables,
respectively; in particular, the Weinberg--Salam model and, ultimately,
dynamical electroweak symmetry breaking by technicolour theories with enhanced
symmetry groups. Our motivation is to unveil the manifestly gauge invariant
structure of the different realisations. We find, for example, parallels to
different types of torsion.Comment: 15p
Instanton Corrections to Quark Form Factor at Large Momentum Transfer
Within the Wilson integral formalism, we discuss the structure of
nonperturbative corrections to the quark form factor at large momentum transfer
analyzing the infrared renormalon and instanton effects. We show that the
nonperturbative effects determine the initial value for the perturbative
evolution of the quark form factor and attribute their general structure to the
renormalon ambiguities of the perturbative series. It is demonstrated that the
instanton contributions result in the finite renormalization of the
next-to-leading perturbative result and numerically are characterized by a
small factor reflecting the diluteness of the QCD vacuum within the instanton
liquid model.Comment: Version coincident with the journal publication, 9 pages; REVTe
Body Fixed Frame, Rigid Gauge Rotations and Large N Random Fields in QCD
The "body fixed frame" with respect to local gauge transformations is
introduced. Rigid gauge "rotations" in QCD and their \Sch equation are studied
for static and dynamic quarks. Possible choices of the rigid gauge field
configuration corresponding to a nonvanishing static colormagnetic field in the
"body fixed" frame are discussed. A gauge invariant variational equation is
derived in this frame. For large number N of colors the rigid gauge field
configuration is regarded as random with maximally random probability
distribution under constraints on macroscopic--like quantities. For the uniform
magnetic field the joint probability distribution of the field components is
determined by maximizing the appropriate entropy under the area law constraint
for the Wilson loop. In the quark sector the gauge invariance requires the
rigid gauge field configuration to appear not only as a background but also as
inducing an instantaneous quark-quark interaction. Both are random in the large
N limit.Comment: 29 pages LATEX, Weizmann Institute preprint WIS-93/40/Apr -P
Nonperturbative contributions to the quark form factor at high energy
The analysis of nonperturbative effects in high energy asymptotics of the
electomagnetic quark form factor is presented. It is shown that the
nonperturbative effects determine the initial value for the perturbative
evolution of the quark form factor and find their general structure with
respect to the high energy asymptotics. Within the Wilson integral formalism
which is natural for investigation of the soft, IR sensitive, part of the
factorized form factor, the structure of the instanton induced effects in the
evolution equation is discussed. It is demonstrated that the instanton
contributions result in the finite renormalization of the subleading
perturbative result and numerically are characterized by small factor
reflecting the diluteness of the QCD vacuum within the instanton liquid model.
The relevance of the IR renormalon induced effects in high energy asymptotic
behaviour is discussed. The consequences of the various analytization
procedures of the strong coupling constant in the IR domain are considered.Comment: REVTeX, 12 pages, 1 figure. Important references and discussions
added, misprints corrected, minor changes in tex
Exclusive Radiative B-Decays in the Light-Cone QCD Sum Rule Approach
We carry out a detailed study of exclusive radiative rare -decays in the
framework of the QCD sum rules on the light cone, which combines the
traditional QCD sum rule technique with the description of final state vector
mesons in terms of the light-cone wave functions of increasing twist. The
decays considered are: and the corresponding decays of the mesons, and . Based on our estimate of the transition
form factor F_1^{B \to K^*\pg}(0) =0.32\pm0.05, we find for the branching
ratio , which is in
agreement with the observed value measured by the CLEO collaboration. We
present detailed estimates for the ratios of the radiative decay form factors,
which are then used to predict the rates for the exclusive radiative B-decays
listed above. This in principle allows the extraction of the CKM matrix element
from the penguin-dominated CKM-suppressed radiative decays when they
are measured. We give a detailed discussion of the dependence of the form
factors on the -quark mass and on the momentum transfer, as well as their
interrelation with the CKM-suppressed semileptonic decay form factors in , which we also calculate in our approach.Comment: 32 pages, 10 uuencoded figures, LaTeX, preprint CERN-TH 7118/9
One Loop Calculations in Gauge Theories Regulated on an - Lattice
In earlier work, the planar diagrams of gauge theory have been
regulated on the light-cone by a scheme involving both discrete and
. The transverse coordinates remain continuous, but even so all
diagrams are rendered finite by this procedure. In this scheme quartic
interactions are represented as two cubics mediated by short lived fictitious
particles whose detailed behavior could be adjusted to retain properties of the
continuum theory, at least at one loop. Here we use this setup to calculate the
one loop three gauge boson triangle diagram, and so complete the calculation of
diagrams renormalizing the coupling to one loop. In particular, we find that
the cubic vertex is correctly renormalized once the couplings to the fictitious
particles are chosen to keep the gauge bosons massless.Comment: 26 pages, 36 figure
Parton interactions in the Bjorken limit of QCD
We consider the Bjorken limit in the framework of the effective action
approach and discuss its similarities to the Regge limit. The proposed
effective action allows for a rather simple calculation of the known evolution
kernels. We represent the result in terms of two-parton interaction operators
involving gluon and quark operators depending on light-ray position and
helicity and analyze their symmetry properties.Comment: 32 pages LaTex, 4 eps-figures, comments added, minor correction