445 research outputs found
Exercises in equivariant cohomology
Equivariant cohomology is a mathematical framework particularly well adapted to a kinematical understanding of topological gauge theories of the cohomological type. It also sheds some light on gauge fixing, a necessary field theory operation connected with the non compactness of the gauge group. The respective roles of fields and observables are emphasized throughout.Equivariant cohomology is a mathematical framework particularly well adapted to a kinematical understanding of topological gauge theories of the cohomological type. It also sheds some light on gauge fixing, a necessary field theory operation connected with the non compactness of the gauge group. The respective roles of fields and observables are emphasized throughout
BRST Cohomology of N=2 Super-Yang-Mills Theory in 4D
The BRST cohomology of the N=2 supersymmetric Yang-Mills theory in four
dimensions is discussed by making use of the twisted version of the N=2
algebra. By the introduction of a set of suitable constant ghosts associated to
the generators of N=2, the quantization of the model can be done by taking into
account both gauge invariance and supersymmetry. In particular, we show how the
twisted N=2 algebra can be used to obtain in a straightforward way the relevant
cohomology classes. Moreover, we shall be able to establish a very useful
relationship between the local gauge invariant polynomial and the
complete N=2 Yang-Mills action. This important relation can be considered as
the first step towards a fully algebraic proof of the one-loop exactness of the
N=2 beta function.Comment: 22 pages, LaTeX, final version to appear in Journ. Phys.
Generalized Born--Infeld Actions and Projective Cubic Curves
We investigate supersymmetric Born-Infeld Lagrangians with a
second non-linearly realized supersymmetry. The resulting non-linear structure
is more complex than the square root present in the standard Born-Infeld
action, and nonetheless the quadratic constraints determining these models can
be solved exactly in all cases containing three vector multiplets. The
corresponding models are classified by cubic holomorphic prepotentials. Their
symmetry structures are associated to projective cubic varieties.Comment: 17 pages, LaTeX, 1 eps figure. Comments added and misprints
corrected. Final version to appear in Fortschritte der Physik - Progress of
Physic
Perturbative Gravity in the Causal Approach
Quantum theory of the gravitation in the causal approach is studied up to the
second order of perturbation theory. We prove gauge invariance and
renormalizability in the second order of perturbation theory for the pure
gravity system (massless and massive). Then we investigate the interaction of
massless gravity with matter (described by scalars and spinors) and massless
Yang-Mills fields. We obtain a difference with respect to the classical field
theory due to the fact that in quantum field theory one cannot enforce the
divergenceless property on the vector potential and this spoils the
divergenceless property of the usual energy-momentum tensor. To correct this
one needs a supplementary ghost term in the interaction Lagrangian.Comment: 50 pages, no figures, some changes in the last sectio
Conservation of the stress tensor in perturbative interacting quantum field theory in curved spacetimes
We propose additional conditions (beyond those considered in our previous
papers) that should be imposed on Wick products and time-ordered products of a
free quantum scalar field in curved spacetime. These conditions arise from a
simple ``Principle of Perturbative Agreement'': For interaction Lagrangians
that are such that the interacting field theory can be constructed
exactly--as occurs when is a ``pure divergence'' or when is at most
quadratic in the field and contains no more than two derivatives--then
time-ordered products must be defined so that the perturbative solution for
interacting fields obtained from the Bogoliubov formula agrees with the exact
solution. The conditions derived from this principle include a version of the
Leibniz rule (or ``action Ward identity'') and a condition on time-ordered
products that contain a factor of the free field or the free
stress-energy tensor . The main results of our paper are (1) a proof
that in spacetime dimensions greater than 2, our new conditions can be
consistently imposed in addition to our previously considered conditions and
(2) a proof that, if they are imposed, then for {\em any} polynomial
interaction Lagrangian (with no restriction on the number of derivatives
appearing in ), the stress-energy tensor of the interacting
theory will be conserved. Our work thereby establishes (in the context of
perturbation theory) the conservation of stress-energy for an arbitrary
interacting scalar field in curved spacetimes of dimension greater than 2. Our
approach requires us to view time-ordered products as maps taking classical
field expressions into the quantum field algebra rather than as maps taking
Wick polynomials of the quantum field into the quantum field algebra.Comment: 88 pages, latex, no figures, v2: changes in the proof of proposition
3.
Quantum Field Theory and Differential Geometry
We introduce the historical development and physical idea behind topological
Yang-Mills theory and explain how a physical framework describing subatomic
physics can be used as a tool to study differential geometry. Further, we
emphasize that this phenomenon demonstrates that the interrelation between
physics and mathematics have come into a new stage.Comment: 29 pages, enlarged version, some typewritten mistakes have been
corrected, the geometric descrition to BRST symmetry, the chain of descent
equations and its application in TYM as well as an introduction to R-symmetry
have been added, as required by mathematicia
Exact Chiral Symmetry on the Lattice
Developments during the last eight years have refuted the folklore that
chiral symmetries cannot be preserved on the lattice. The mechanism that
permits chiral symmetry to coexist with the lattice is quite general and may
work in Nature as well. The reconciliation between chiral symmetry and the
lattice is likely to revolutionize the field of numerical QCD.Comment: 30 pages, LaTeX, reference adde
Algebraic Properties of BRST Coupled Doublets
We characterize the dependence on doublets of the cohomology of an arbitrary
nilpotent differential s (including BRST differentials and classical linearized
Slavnov-Taylor (ST) operators) in terms of the cohomology of the
doublets-independent component of s. All cohomologies are computed in the space
of local integrated formal power series. We drop the usual assumption that the
counting operator for the doublets commutes with s (decoupled doublets) and
discuss the general case where the counting operator does not commute with s
(coupled doublets). The results are purely algebraic and do not rely on
power-counting arguments.Comment: Some explanations enlarged, references adde
Algebraic Classification of Weyl Anomalies in Arbitrary Dimensions
Conformally invariant massless field systems involving only dimensionless
parameters are known to describe particle physics at very high energy. In the
presence of an external gravitational field, the conformal symmetry may
generalize to Weyl invariance. However, the latter symmetry no longer survives
after quantization: A Weyl anomaly appears. In this Letter, a purely algebraic
understanding of the universal structure of the Weyl anomalies is presented.
The results hold in arbitrary dimensions and independently of any
regularization scheme.Comment: 4 pages - accepted for publication in Physical Review Letter
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