218 research outputs found
Exact flow equation for bound states
We develop a formalism to describe the formation of bound states in quantum
field theory using an exact renormalization group flow equation. As a concrete
example we investigate a nonrelativistic field theory with instantaneous
interaction where the flow equations can be solved exactly. However, the
formalism is more general and can be applied to relativistic field theories, as
well. We also discuss expansion schemes that can be used to find approximate
solutions of the flow equations including the essential momentum dependence.Comment: 22 pages, references added, published versio
Wilsonian effective action for SU(2) Yang-Mills theory with Cho-Faddeev-Niemi-Shabanov decomposition
The Cho-Faddeev-Niemi-Shabanov decomposition of the SU(2) Yang-Mills field is
employed for the calculation of the corresponding Wilsonian effective action to
one-loop order with covariant gauge fixing. The generation of a mass scale is
observed, and the flow of the marginal couplings is studied. Our results
indicate that higher-derivative terms of the color-unit-vector
field are necessary for the description of topologically stable knotlike
solitons which have been conjectured to be the large-distance degrees of
freedom.Comment: 15 pages, no figures, v2: minor improvements, one reference added,
version to appear in PR
Inflation with blowing-up solution of cosmological constant problem
The cosmological constant problem is how one chooses, without fine-tuning,
one singular point for the 4D cosmological constant. We argue
that some recently discovered {\it weak self-tuning} solutions can be viewed as
blowing-up this one point into a band of some parameter. These weak self-tuning
solutions may have a virtue that only de Sitter space solutions are allowed
outside this band, allowing an inflationary period. We adopt the hybrid
inflation at the brane to exit from this inflationary phase and to enter into
the standard Big Bang cosmology.Comment: LaTeX file of 20 pages including 2 eps figure
Towards a renormalizable standard model without fundamental Higgs scalar
We investigate the possibility of constructing a renormalizable standard
model with purely fermionic matter content. The Higgs scalar is replaced by
point-like fermionic self-interactions with couplings growing large at the
Fermi scale. An analysis of the UV behavior in the point-like approximation
reveals a variety of non-Gaussian fixed points for the fermion couplings. If
real, such fixed points would imply nonperturbative renormalizability and evade
triviality of the Higgs sector. For point-like fermionic self-interactions and
weak gauge couplings, one encounters a hierarchy problem similar to the one for
a fundamental Higgs scalar.Comment: 18 pages, 4 figure
Renormalization flow of Yang-Mills propagators
We study Landau-gauge Yang-Mills theory by means of a nonperturbative vertex
expansion of the quantum effective action. Using an exact renormalization group
equation, we compute the fully dressed gluon and ghost propagators to lowest
nontrivial order in the vertex expansion. In the mid-momentum regime,
, we probe the propagator flow with various
{\em ans\"atze} for the three- and four-point correlations. We analyze the
potential of these truncation schemes to generate a nonperturbative scale. We
find universal infrared behavior of the propagators, if the gluon dressing
function has developed a mass-like structure at mid-momentum. The resulting
power laws in the infrared support the Kugo-Ojima confinement scenario.Comment: 28 pages, 5 figures. V2: Typos corrected and reference adde
Introduction to the functional RG and applications to gauge theories
These lectures contain an introduction to modern renormalization group (RG)
methods as well as functional RG approaches to gauge theories. In the first
lecture, the functional renormalization group is introduced with a focus on the
flow equation for the effective average action. The second lecture is devoted
to a discussion of flow equations and symmetries in general, and flow equations
and gauge symmetries in particular. The third lecture deals with the flow
equation in the background formalism which is particularly convenient for
analytical computations of truncated flows. The fourth lecture concentrates on
the transition from microscopic to macroscopic degrees of freedom; even though
this is discussed here in the language and the context of QCD, the developed
formalism is much more general and will be useful also for other systems.Comment: 60 pages, 14 figures, Lectures held at the 2006 ECT* School
"Renormalization Group and Effective Field Theory Approaches to Many-Body
Systems", Trento, Ital
Do Instantons Like a Colorful Background?
We investigate chiral symmetry breaking and color symmetry breaking in QCD.
The effective potential of the corresponding scalar condensates is discussed in
the presence of non-perturbative contributions from the semiclassical
one-instanton sector. We concentrate on a color singlet scalar background which
can describe chiral condensation, as well as a color octet scalar background
which can generate mass for the gluons. Whereas a non-vanishing singlet chiral
field is favored by the instantons, we have found no indication for a
preference of color octet backgrounds.Comment: 25 pages, 7 figure
Fluctuations and the QCD phase diagram
In this contribution the role of quantum fluctuations for the QCD phase
diagram is discussed. This concerns in particular the importance of the matter
back-reaction to the gluonic sector. The impact of these fluctuations on the
location of the confinement/deconfinement and the chiral transition lines as
well as their interrelation are investigated. Consequences of our findings for
the size of a possible quarkyonic phase and location of a critical endpoint in
the phase diagram are drawn.Comment: 7 pages, 3 figures, to appear in Physics of Atomic Nucle
Rigorous approach to the comparison between experiment and theory in Casimir force measurements
In most experiments on the Casimir force the comparison between measurement
data and theory was done using the concept of the root-mean-square deviation, a
procedure that has been criticized in literature. Here we propose a special
statistical analysis which should be performed separately for the experimental
data and for the results of the theoretical computations. In so doing, the
random, systematic, and total experimental errors are found as functions of
separation, taking into account the distribution laws for each error at 95%
confidence. Independently, all theoretical errors are combined to obtain the
total theoretical error at the same confidence. Finally, the confidence
interval for the differences between theoretical and experimental values is
obtained as a function of separation. This rigorous approach is applied to two
recent experiments on the Casimir effect.Comment: 10 pages, iopart.cls is used, to appear in J. Phys. A (special issue:
Proceedings of QFEXT05, Barcelona, Sept. 5-9, 2005
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