398 research outputs found
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
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
Isomorphisms between the Batalin-Vilkovisky antibracket and the Poisson bracket
One may introduce at least three different Lie algebras in any Lagrangian
field theory : (i) the Lie algebra of local BRST cohomology classes equipped
with the odd Batalin-Vilkovisky antibracket, which has attracted considerable
interest recently~; (ii) the Lie algebra of local conserved currents equipped
with the Dickey bracket~; and (iii) the Lie algebra of conserved, integrated
charges equipped with the Poisson bracket. We show in this paper that the
subalgebra of (i) in ghost number and the other two algebras are
isomorphic for a field theory without gauge invariance. We also prove that, in
the presence of a gauge freedom, (ii) is still isomorphic to the subalgebra of
(i) in ghost number , while (iii) is isomorphic to the quotient of (ii) by
the ideal of currents without charge. In ghost number different from , a
more detailed analysis of the local BRST cohomology classes in the Hamiltonian
formalism allows one to prove an isomorphism theorem between the antibracket
and the extended Poisson bracket of Batalin, Fradkin and Vilkovisky.Comment: 36 pages Latex fil
The Action for Twisted Self-Duality
One may write the Maxwell equations in terms of two gauge potentials, one
electric and one magnetic, by demanding that their field strengths should be
dual to each other. This requirement is the condition of twisted self-duality.
It can be extended to p-forms in spacetime of D dimensions, and it survives the
introduction of a variety of couplings among forms of different rank, and also
to spinor and scalar fields, which emerge naturally from supergravity. In this
paper we provide a systematic derivation of the action principle, whose
equations of motion are the condition of twisted self-duality. The derivation
starts from the standard Maxwell action, extended to include the aforementioned
couplings, and proceeds via the Hamiltonian formalism through the resolution of
Gauss' law. In the pure Maxwell case we recover in this way an action that had
been postulated by other authors, through an ansatz based on an action given
earlier by us for untwisted self-duality. Those authors also extended their
ansatz to include Chern-Simons couplings. In that case, we find a different
result. The derivation from the standard extended Maxwell action implies of
course that the theory is Lorentz-invariant and can be locally coupled to
gravity. Nevertherless we include a direct compact Hamiltonian proof of these
properties, which is based on the surface-deformation algebra. The symmetry in
the dependence of the action on the electric and magnetic variables is
manifest, since they appear as canonical conjugates. Spacetime covariance,
although present, is not manifest.Comment: Version to appear in Phys. Rev.
Asymptotic symmetries of three-dimensional higher-spin gravity: the metric approach
The asymptotic structure of three-dimensional higher-spin anti-de Sitter
gravity is analyzed in the metric approach, in which the fields are described
by completely symmetric tensors and the dynamics is determined by the standard
Einstein-Fronsdal action improved by higher order terms that secure gauge
invariance. Precise boundary conditions are given on the fields. The asymptotic
symmetries are computed and shown to form a non-linear W-algebra, in complete
agreement with what was found in the Chern-Simons formulation. The W-symmetry
generators are two-dimensional traceless and divergenceless rank-s symmetric
tensor densities of weight s (s = 2, 3, ...), while asymptotic symmetries
emerge at infinity through the conformal Killing vector and conformal Killing
tensor equations on the two-dimensional boundary, the solution space of which
is infinite-dimensional. For definiteness, only the spin 3 and spin 4 cases are
considered, but these illustrate the features of the general case: emergence of
the W-extended conformal structure, importance of the improvement terms in the
action that maintain gauge invariance, necessity of the higher spin gauge
transformations of the metric, role of field redefinitions.Comment: 74 pages. References amended and typos corrected. Version to appear
in JHE
Kac-Moody and Borcherds Symmetries of Six-Dimensional Chiral Supergravity
We investigate the conjectured infinite-dimensional hidden symmetries of
six-dimensional chiral supergravity coupled to two vector multiplets and two
tensor multiplets, which is known to possess the symmetry upon
dimensional reduction to three spacetime dimensions. Two things are done. (i)
First, we analyze the geodesic equations on the coset space
using the level decomposition associated with
the subalgebra of and
show their equivalence with the bosonic equations of motion of six-dimensional
chiral supergravity up to the level where the dual graviton appears. In
particular, the self-duality condition on the chiral -form is automatically
implemented in the sense that no dual potential appears for that -form, in
contradistinction with what occurs for the non chiral -forms. (ii) Second,
we describe the -form hierarchy of the model in terms of its -duality
Borcherds superalgebra, of which we compute the Cartan matrix.Comment: 31 pages. v2: Error in section 6.3 corrected, Dynkin diagram now
appears correctly, minor typo
Oscillatory Behaviour in Homogeneous String Cosmology Models
Some spatially homogeneous Bianchi type I cosmological models filled with
homogeneous ``electric'' -form fields are shown to mimic the never-ending
oscillatory behaviour of generic string cosmologies established recently. The
validity of the ``Kasner-free-flights plus collisions-on-potential-walls''
picture is also illustrated in the case of known, non-chaotic, superstring
solutions.Comment: 12 pages, latex, submitted to Phys. Lett.
BMS Group at Spatial Infinity: the Hamiltonian (ADM) approach
New boundary conditions for asymptotically flat spacetimes are given at
spatial infinity. These boundary conditions are invariant under the BMS group,
which acts non trivially. The boundary conditions fulfill all standard
consistency requirements: (i) they make the symplectic form finite; (ii) they
contain the Schwarzchild solution, the Kerr solution and their Poincar\'e
transforms, (iii) they make the Hamiltonian generators of the asymptotic
symmetries integrable and well-defined (finite). The boundary conditions differ
from the ones given earlier in the literature in the choice of the parity
conditions. It is this different choice of parity conditions that makes the
action of the BMS group non trivial. Our approach is purely Hamiltonian and
off-shell throughout.Comment: 26 page
Comments on Unitarity in the Antifield Formalism
It is shown that the local completeness condition introduced in the analysis
of the locality of the gauge fixed action in the antifield formalism plays also
a key role in the proof of unitarity.Comment: 15 pages, Latex error corrected, otherwise unchange
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