80 research outputs found
A local (perturbative) construction of observables in gauge theories: the example of QED
Interacting fields can be constructed as formal power series in the framework
of causal perturbation theory. The local field algebra is obtained without performing the adiabatic limit; the (usually bad)
infrared behavior plays no role. To construct the observables in gauge theories
we use the Kugo-Ojima formalism; we define the BRST-transformation
as a graded derivation on the algebra of interacting fields and use the
implementation of by the Kugo-Ojima operator . Since
our treatment is local, the operator differs from the
corresponding operator of the free theory. We prove that the Hilbert space
structure present in the free case is stable under perturbations. All
assumptions are shown to be satisfied in QED.Comment: corrected typos, a few supplements, 34 pages, written by TEX, some
macros are at the beginning of the file. To appear in Commun. Math. Phy
The Master Ward Identity
In the framework of perturbative quantum field theory (QFT) we propose a new,
universal (re)normalization condition (called 'master Ward identity') which
expresses the symmetries of the underlying classical theory. It implies for
example the field equations, energy-momentum, charge- and ghost-number
conservation, renormalized equal-time commutation relations and BRST-symmetry.
It seems that the master Ward identity can nearly always be satisfied, the
only exceptions we know are the usual anomalies. We prove the compatibility of
the master Ward identity with the other (re)normalization conditions of causal
perturbation theory, and for pure massive theories we show that the 'central
solution' of Epstein and Glaser fulfills the master Ward identity, if the
UV-scaling behavior of its individual terms is not relatively lowered.
Application of the master Ward identity to the BRST-current of non-Abelian
gauge theories generates an identity (called 'master BRST-identity') which
contains the information which is needed for a local construction of the
algebra of observables, i.e. the elimination of the unphysical fields and the
construction of physical states in the presence of an adiabatically switched
off interaction.Comment: 73 pages, version to appear in Rev. Math. Phy
Deformation stability of BRST-quantization
To avoid the problems which are connected with the long distance behavior of
perturbative gauge theories we present a local construction of the observables
which does not involve the adiabatic limit. First we construct the interacting
fields as formal power series by means of causal perturbation theory. The
observables are defined by BRST invariance where the BRST-transformation
acts as a graded derivation on the algebra of interacting fields.
Positivity, i.e. the existence of Hilbert space representations of the local
algebras of observables is shown with the help of a local Kugo-Ojima operator
which implements on a local algebra and differs from
the corresponding operator of the free theory. We prove that the Hilbert
space structure present in the free case is stable under perturbations. All
assumptions are shown to be satisfied in QED in a finite spatial volume with
suitable boundary conditions. As a by-product we find that the
BRST-quantization is not compatible with periodic boundary conditions for
massless free gauge fields.Comment: 10 pages, the paper is written by means of LATEX, some macros are at
the beginning of the fil
Algebraic Quantum Field Theory, Perturbation Theory, and the Loop Expansion
The perturbative treatment of quantum field theory is formulated within the
framework of algebraic quantum field theory. We show that the algebra of
interacting fields is additive, i.e. fully determined by its subalgebras
associated to arbitrary small subregions of Minkowski space. We also give an
algebraic formulation of the loop expansion by introducing a projective system
of observables ``up to loops'' where is
the Poisson algebra of the classical field theory. Finally we give a local
algebraic formulation for two cases of the quantum action principle and compare
it with the usual formulation in terms of Green's functions.Comment: 29 page
Diphoton decay of the higgs from the Epstein--Glaser viewpoint
We revisit a nearly ten-year old controversy on the diphoton decay of the
Higgs particle. To a large extent, the controversy turned around the respective
merits of the regularization techniques employed. The novel aspect of our
approach is that no regularization techniques are brought to bear: we work
within the Bogoliubov--Epstein--Glaser scheme of renormalization by extension
of distributions. Solving the problem actually required an expansion of this
method's toolkit, furnished in the paper.Comment: 45 pages, to appear in Eur. Phys. J.
Counter-term charges generate bulk symmetries
We further explore the counter-term subtraction definition of charges (e.g.,
energy) for classical gravitating theories in spacetimes of relevance to
gauge/gravity dualities; i.e., in asymptotically anti-de Sitter spaces and
their kin. In particular, we show in general that charges defined via the
counter-term subtraction method generate the desired asymptotic symmetries. As
a result, they can differ from any other such charges, such as those defined by
bulk spacetime-covariant techniques, only by a function of auxiliary
non-dynamical structures such as a choice of conformal frame at infinity (i.e.,
a function of the boundary fields alone). Our argument is based on the Peierls
bracket, and in the AdS context allows us to demonstrate the above result even
for asymptotic symmetries which generate only conformal symmetries of the
boundary (in the chosen conformal frame). We also generalize the counter-term
subtraction construction of charges to the case in which additional
non-vanishing boundary fields are present.Comment: 13 pages, Latex, no figures, v3: errors fixed, boundary terms
carefully controlled, awkward assumption removed, references update
Perturbative Construction of Models of Algebraic Quantum Field Theory
We review the construction of models of algebraic quantum field theory by
renormalized perturbation theory.Comment: 38 page
Quantum Gravitational Bremsstrahlung, Massless versus Massive Gravity
The massive spin-2 quantum gauge theory previously developed is applied to
calculate gravitational bremsstrahlung. It is shown that this theory is unique
and free from defects. In particular, there is no strong coupling if the
graviton mass becomes small. The cross sections go over smoothly into the ones
of the massless theory in the limit of vanishing graviton mass. The massless
cross sections are calculated for the full tensor theory.Comment: 13 pages, 1 figur
Massive gravity from descent equations
Both massless and massive gravity are derived from descent equations
(Wess-Zumino consistency conditions). The massive theory is a continuous
deformation of the massless one.Comment: 8 pages, no figur
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