95 research outputs found
The Gribov parameter and the dimension two gluon condensate in Euclidean Yang-Mills theories in the Landau gauge
The local composite operator A^2 is added to the Zwanziger action, which
implements the restriction to the Gribov region in Euclidean Yang-Mills
theories in the Landau gauge. We prove the renormalizability of this action to
all orders of perturbation theory. This allows to study the dimension two gluon
condensate by the local composite operator formalism when the restriction
is taken into account. The effective action is evaluated at one-loop order in
the MSbar scheme. We obtain explicit values for the Gribov parameter and for
the mass parameter due to , but the expansion parameter turns out to be
rather large. Furthermore, an optimization of the perturbative expansion in
order to reduce the dependence on the renormalization scheme is performed. The
properties of the vacuum energy, with or without , are investigated. It is
shown that in the original Gribov-Zwanziger formulation (without ), the
vacuum energy is always positive at 1-loop order, independently from the
renormalization scheme and scale. With , we are unable to come to a
definite conclusion at the order considered. In the MSbar scheme, we still find
a positive vacuum energy, again with a relatively large expansion parameter,
but there are renormalization schemes in which the vacuum energy is negative,
albeit the dependence on the scheme itself appears to be strong. We recover the
well known consequences of the restriction, and this in the presence of :
an infrared suppression of the gluon propagator and an enhancement of the ghost
propagator. This behaviour is in qualitative agreement with the results
obtained from the studies of the Schwinger-Dyson equations and from lattice
simulations.Comment: 42 pages, 10 .eps figures. v2: Version accepted for publication in
Phys.Rev.D. Added references. Technical details have been collected in two
appendice
Extremality of Gaussian quantum states
We investigate Gaussian quantum states in view of their exceptional role
within the space of all continuous variables states. A general method for
deriving extremality results is provided and applied to entanglement measures,
secret key distillation and the classical capacity of Bosonic quantum channels.
We prove that for every given covariance matrix the distillable secret key rate
and the entanglement, if measured appropriately, are minimized by Gaussian
states. This result leads to a clearer picture of the validity of frequently
made Gaussian approximations. Moreover, it implies that Gaussian encodings are
optimal for the transmission of classical information through Bosonic channels,
if the capacity is additive.Comment: 4 page
Generic Bell correlation between arbitrary local algebras in quantum field theory
We prove that for any two commuting von Neumann algebras of infinite type,
the open set of Bell correlated states for the two algebras is norm dense. We
then apply this result to algebraic quantum field theory -- where all local
algebras are of infinite type -- in order to show that for any two spacelike
separated regions, there is an open dense set of field states that dictate Bell
correlations between the regions. We also show that any vector state cyclic for
one of a pair of commuting nonabelian von Neumann algebras is entangled (i.e.,
nonseparable) across the algebras -- from which it follows that every field
state with bounded energy is entangled across any two spacelike separated
regions.Comment: Third version; correction in the proof of Proposition
Caltech Faint Galaxy Redshift Survey X: A Redshift Survey in the Region of the Hubble Deep Field North
A redshift survey has been carried out in the region of the Hubble Deep Field
North using the Low Resolution Imaging Spectrograph at the Keck Observatory.
The resulting redshift catalog, which contains 671 entries, is a compendium of
our own data together with published LRIS/Keck data. It is more than 92%
complete for objects, irrespective of morphology, to mag in the HDF
itself and to mag in the Flanking Fields within a diameter of 8 arcmin
centered on the HDF, an unusually high completion for a magnitude limited
survey performed with a large telescope. A median redshift is reached
at .
Strong peaks in the redshift distribution, which arise when a group or poor
cluster of galaxies intersect the area surveyed, can be identified to in this dataset. More than 68% of the galaxies are members of these
redshift peaks. In a few cases, closely spaced peaks in can be resolved
into separate groups of galaxies that can be distinguished in both velocity and
location on the sky.
The radial separation of these peaks in the pencil-beam survey is consistent
with a characteristic length scale for the their separation of 70 Mpc
in our adopted cosmology (, ). Strong
galaxy clustering is in evidence at all epochs back to . (abstract
abridged)Comment: Accepted to the ApJ. This version contains all the figures and
tables. 2 minor typos in table 2b correcte
On fermionic tilde conjugation rules and thermal bosonization. Hot and cold thermofields
A generalization of Ojima tilde conjugation rules is suggested, which reveals
the coherent state properties of thermal vacuum state and is useful for the
thermofield bosonization. The notion of hot and cold thermofields is introduced
to distinguish different thermofield representations giving the correct normal
form of thermofield solution for finite temperature Thirring model with correct
renormalization and anticommutation properties.Comment: 13 page
Scattering into Cones and Flux across Surfaces in Quantum Mechanics: a Pathwise Probabilistic Approach
We show how the scattering-into-cones and flux-across-surfaces theorems in
Quantum Mechanics have very intuitive pathwise probabilistic versions based on
some results by Carlen about large time behaviour of paths of Nelson
diffusions. The quantum mechanical results can be then recovered by taking
expectations in our pathwise statements.Comment: To appear in Journal of Mathematical Physic
Parity and the Spin-Statistics Connection
The spin-statistics connection is obtained in a simple and elementary way for
general causal fields by using the parity operation to exchange spatial
coordinates in the scalar product of a locally commuting field operator,
evaluated at position x, with the same field operator evaluated at -x, at equal
times.Comment: 6 page
Twisted duality of the CAR-Algebra
We give a complete proof of the twisted duality property M(q)'= Z M(q^\perp)
Z* of the (self-dual) CAR-Algebra in any Fock representation. The proof is
based on the natural Halmos decomposition of the (reference) Hilbert space when
two suitable closed subspaces have been distinguished. We use modular theory
and techniques developed by Kato concerning pairs of projections in some
essential steps of the proof.
As a byproduct of the proof we obtain an explicit and simple formula for the
graph of the modular operator. This formula can be also applied to fermionic
free nets, hence giving a formula of the modular operator for any double cone.Comment: 32 pages, Latex2e, to appear in Journal of Mathematical Physic
A Many-body Problem with Point Interactions on Two Dimensional Manifolds
A non-perturbative renormalization of a many-body problem, where
non-relativistic bosons living on a two dimensional Riemannian manifold
interact with each other via the two-body Dirac delta potential, is given by
the help of the heat kernel defined on the manifold. After this renormalization
procedure, the resolvent becomes a well-defined operator expressed in terms of
an operator (called principal operator) which includes all the information
about the spectrum. Then, the ground state energy is found in the mean field
approximation and we prove that it grows exponentially with the number of
bosons. The renormalization group equation (or Callan-Symanzik equation) for
the principal operator of the model is derived and the function is
exactly calculated for the general case, which includes all particle numbers.Comment: 28 pages; typos are corrected, three figures are adde
A study of the zero modes of the Faddeev-Popov operator in Euclidean Yang-Mills theories in the Landau gauge in d=2,3,4 dimensions
Examples of normalizable zero modes of the Faddeev-Popov operator in SU(2)
Euclidean Yang-Mills theories in the Landau gauge are constructed in d=2,3,4
dimensions.Comment: 18 pages. Text modifications. References added. Version accepted for
publication in the EPJ
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