2,682 research outputs found
Symmetry-deforming interactions of chiral p-forms
No-go theorems on gauge-symmetry-deforming interactions of chiral p-forms are
reviewed. We consider the explicit case of p=4, D=10 and show that the only
symmetry-deforming consistent vertex for a system of one chiral 4-form and two
2-forms is the one that occurs in the type II B supergravity Lagrangian.Comment: 7 pages, tiny typo corrections, based on a talk given by M. H. at the
conference "Constrained Dynamics and Quantum Gravity " held in Villasimius
(Sardinia), September 13-17 1999, to appear in the proceedings of the meeting
(Nucl. Phys. B Proc. Suppl.
On The Gauge-Fixed BRST Cohomology
A crucial property of the standard antifield-BRST cohomology at non negative
ghost number is that any cohomological class is completely determined by its
antifield independent part. In particular, a BRST cocycle that vanishes when
the antifields are set equal to zero is necessarily exact.\ \ This property,
which follows from the standard theorems of homological perturbation theory,
holds not only in the algebra of local functions, but also in the space of
local functionals. The present paper stresses how important it is that the
antifields in question be the usual antifields associated with the gauge
invariant description. By means of explicit counterexamples drawn from the free
Maxwell-Klein-Gordon system, we show that the property does not hold, in the
case of local functionals, if one replaces the antifields of the gauge
invariant description by new antifields adapted to the gauge fixation. In terms
of these new antifields, it is not true that a local functional weakly
annihilated by the gauge-fixed BRST generator determines a BRST cocycle; nor
that a BRST cocycle which vanishes when the antifields are set equal to zero is
necessarily exact.Comment: 14 pages Latex fil
Uniqueness of the Freedman-Townsend Interaction Vertex For Two-Form Gauge Fields
Let () be a system of free two-form gauge
fields, with field strengths and free action equal to (). It is shown that in dimensions,
the only consistent local interactions that can be added to the free action are
given by functions of the field strength components and their derivatives (and
the Chern-Simons forms in mod dimensions). These interactions do not
modify the gauge invariance of the free theory. By contrast, there exist in
dimensions consistent interactions that deform the gauge symmetry of the free
theory in a non trivial way. These consistent interactions are uniquely given
by the well-known Freedman-Townsend vertex. The method of proof uses the
cohomological techniques developed recently in the Yang-Mills context to
establish theorems on the structure of renormalized gauge-invariant operators.Comment: 12 pages Latex fil
Ghosts of ghosts for second class constraints
When one uses the Dirac bracket, second class constraints become first class.
Hence, they are amenable to the BRST treatment characteristic of ordinary first
class constraints. This observation is the starting point of a recent
investigation by Batalin and Tyutin, in which all the constraints are put on
the same footing. However, because second class constraints identically vanish
as operators in the quantum theory, they are quantum-mechanically reducible and
require therefore ghosts of ghosts. Otherwise, the BRST cohomology would not
yield the correct physical spectrum. We discuss how to incorporate this feature
in the formalism and show that it leads to an infinite tower of ghosts of
ghosts. An alternative treatment, in which the brackets of the ghosts are
modified, is also mentioned.Comment: 7 pages in LaTex, ULB-PMIF/93-0
Consistent Interactions Between Gauge Fields: The Cohomological Approach
The cohomological approach to the problem of consistent interactions between
fields with a gauge freedom is reviewed. The role played by the BRST symmetry
is explained. Applications to massless vector fields and 2-form gauge fields
are surveyed.Comment: late
Geometric Interpretation of the Quantum Master Equation in the BRST--anti-BRST Formalism
The geometric interpretation of the antibracket formalism given by Witten is
extended to cover the anti-BRST symmetry. This enables one to formulate the
quantum master equation for the BRST--anti-BRST formalism in terms of
integration theory over a supermanifold. A proof of the equivalence of the
standard antibracket formalism with the antibracket formalism for the
BRST--anti-BRST symmetry is also given.Comment: 12 page
Spacetime locality of the antifield formalism : a "mise au point"
Some general techniques and theorems on the spacetime locality of the
antifield formalism are illustrated in the familiar cases of the free scalar
field, electromagnetism and Yang-Mills theory. The analysis explicitly shows
that recent criticisms of the usual approach to dealing with locality are
ill-founded.Comment: 15 pages in LaTeX, ULB-PMIF-93/0
Homological Algebra and Yang-Mills Theory
The antifield-BRST formalism and the various cohomologies associated with it
are surveyed and illustrated in the context of Yang-Mills gauge theory. In
particular, the central role played by the Koszul-Tate resolution and its
relation to the characteristic cohomology are stressed.Comment: 20 pages in LaTe
Gauge Invariance for Generally Covariant Systems
Previous analyses on the gauge invariance of the action for a generally
covariant system are generalized. It is shown that if the action principle is
properly improved, there is as much gauge freedom at the endpoints for an
arbitrary gauge system as there is for a system with ``internal'' gauge
symmetries. The key point is to correctly identify the boundary conditions for
the allowed histories and to include the appropriate end-point contribution in
the action. The path integral is then discussed. It is proved that by employing
the improved action, one can use time-independent canonical gauges even in the
case of generally covariant theories. From the point of view of the action and
the path integral, there is thus no conceptual difference between general
covariance and ``ordinary gauge invariance''. The discussion is illustrated in
the case of the point particle, for which various canonical gauges are
considered.Comment: 41 pages, ULB-PMIF-92-0
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