735 research outputs found

### A nilpotent symmetry of quantum gauge theories

For the Becchi-Rouet-Stora-Tyutin (BRST) invariant extended action for any
gauge theory, there exists another off-shell nilpotent symmetry. For linear
gauges, it can be elevated to a symmetry of the quantum theory and used in the
construction of the quantum effective action. Generalizations for nonlinear
gauges and actions with higher order ghost terms are also possible.Comment: RevTeX, 9 pages, several changes to include generalizations to
quartic and higher ghost terms and non-linear gauges. Abstract changed. Final
version to be publishe

### A Functional and Lagrangian Formulation of Two-Dimensional Topological Gravity

We reconsider two-dimensional topological gravity in a functional and
lagrangian framework. We derive its Slavnov-Taylor identities and discuss its
(in)dependence on the background gauge. Correlators of reparamerization
invariant observables are shown to be globally defined forms on moduli space.
The potential obstruction to their gauge-independence is the non-triviality of
the line bundle on moduli space ${\cal L}_x$, whose first Chern-class is
associated to the topological invariants of Mumford, Morita and Miller. Based
on talks given at the Fubini Fest, Torino, 24-26 February 1994, and at the
Workshop on String Theory, Trieste, 20-22 April 1994.Comment: 11 pages, harvmac, CERN-TH-7302/94, GEF-Th-6/199

### The Renormalization of Non-Commutative Field Theories in the Limit of Large Non-Commutativity

We show that renormalized non-commutative scalar field theories do not reduce
to their planar sector in the limit of large non-commutativity. This follows
from the fact that the RG equation of the Wilson-Polchinski type which
describes the genus zero sector of non-commutative field theories couples
generic planar amplitudes with non-planar amplitudes at exceptional values of
the external momenta. We prove that the renormalization problem can be
consistently restricted to this set of amplitudes. In the resulting
renormalized theory non-planar divergences are treated as UV divergences
requiring appropriate non-local counterterms. In 4 dimensions the model turns
out to have one more relevant (non-planar) coupling than its commutative
counterpart. This non-planar coupling is ``evanescent'': although in the
massive (but not in the massless) case its contribution to planar amplitudes
vanishes when the floating cut-off equals the renormalization scale, this
coupling is needed to make the Wilsonian effective action UV finite at all
values of the floating cut-off.Comment: 35 pages, 8 figures; typos correcte

### BRS "Symmetry", prehistory and history

Prehistory - Starting from 't Hooft's (1971) we have a short look at Taylor's
and Slavnov's works (1971-72) and at the lectures given by Rouet and Stora in
Lausanne-1973 which determine the transition from pre-history to history.
History - We give a brief account of the main analyses and results of the BRS
collaboration concerning the renormalized gauge theories, in particular the
method of the regularization independent, algebraic renormalization, the
algebraic proof of S-matrix unitarity and that of gauge choice independence of
the renormalized physics. We conclude this report with a suggestion to the
crucial question: what could remain of BRS invariance beyond perturbation
theory.Comment: Talk given at: A Special day in honour of Raymond Stora, Annecy, July
8, 201

### Constructive algebraic renormalization of the abelian Higgs-Kibble model

We propose an algorithm, based on Algebraic Renormalization, that allows the
restoration of Slavnov-Taylor invariance at every order of perturbation
expansion for an anomaly-free BRS invariant gauge theory. The counterterms are
explicitly constructed in terms of a set of one-particle-irreducible Feynman
amplitudes evaluated at zero momentum (and derivatives of them). The approach
is here discussed in the case of the abelian Higgs-Kibble model, where the zero
momentum limit can be safely performed. The normalization conditions are
imposed by means of the Slavnov-Taylor invariants and are chosen in order to
simplify the calculation of the counterterms. In particular within this model
all counterterms involving BRS external sources (anti-fields) can be put to
zero with the exception of the fermion sector.Comment: Jul, 1998, 31 page

### On the correspondence between the classical and quantum gravity

The relationship between the classical and quantum theories of gravity is
reexamined. The value of the gravitational potential defined with the help of
the two-particle scattering amplitudes is shown to be in disagreement with the
classical result of General Relativity given by the Schwarzschild solution. It
is shown also that the potential so defined fails to describe whatever
non-Newtonian interactions of macroscopic bodies. An alternative interpretation
of the $\hbar^0$-order part of the loop corrections is given directly in terms
of the effective action. Gauge independence of that part of the one-loop
radiative corrections to the gravitational form factors of the scalar particle
is proved, justifying the interpretation proposed.Comment: Latex 2.09, 3 ps. figures, 17 page

### On a class of embeddings of massive Yang-Mills theory

A power-counting renormalizable model into which massive Yang-Mills theory is
embedded is analyzed. The model is invariant under a nilpotent BRST
differential s. The physical observables of the embedding theory, defined by
the cohomology classes of s in the Faddeev-Popov neutral sector, are given by
local gauge-invariant quantities constructed only from the field strength and
its covariant derivatives.Comment: LATEX, 34 pages. One reference added. Version published in the
journa

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