8 research outputs found
Ultraviolet singularities in classical brane theory
We construct for the first time an energy-momentum tensor for the
electromagnetic field of a p-brane in arbitrary dimensions, entailing finite
energy-momentum integrals. The construction relies on distribution theory and
is based on a Lorentz-invariant regularization, followed by the subtraction of
divergent and finite counterterms supported on the brane. The resulting
energy-momentum tensor turns out to be uniquely determined. We perform the
construction explicitly for a generic flat brane. For a brane in arbitrary
motion our approach provides a new paradigm for the derivation of the,
otherwise divergent, self-force of the brane. The so derived self-force is
automatically finite and guarantees, by construction, energy-momentum
conservation.Comment: 41 pages, no figures, minor change
Parent formulation at the Lagrangian level
The recently proposed first-order parent formalism at the level of equations
of motion is specialized to the case of Lagrangian systems. It is shown that
for diffeomorphism-invariant theories the parent formulation takes the form of
an AKSZ-type sigma model. The proposed formulation can be also seen as a
Lagrangian version of the BV-BRST extension of the Vasiliev unfolded approach.
We also discuss its possible interpretation as a multidimensional
generalization of the Hamiltonian BFV--BRST formalism. The general construction
is illustrated by examples of (parametrized) mechanics, relativistic particle,
Yang--Mills theory, and gravity.Comment: 26 pages, discussion of the truncation extended, typos corrected,
references adde
Local BRST cohomology in (non-)Lagrangian field theory
Some general theorems are established on the local BRST cohomology for not
necessarily Lagrangian gauge theories. Particular attention is given to the
BRST groups with direct physical interpretation. Among other things, the groups
of rigid symmetries and conservation laws are shown to be still connected,
though less tightly than in the Lagrangian theory. The connection is provided
by the elements of another local BRST cohomology group whose elements are
identified with Lagrange structures. This extends the cohomological formulation
of the Noether theorem beyond the scope of Lagrangian dynamics. We show that
each integrable Lagrange structure gives rise to a Lie bracket in the space of
conservation laws, which generalizes the Dickey bracket of conserved currents
known in Lagrangian field theory. We study the issues of existence and
uniqueness of the local BRST complex associated with a given set of field
equations endowed with a compatible Lagrange structure. Contrary to the usual
BV formalism, such a complex does not always exist for non-Lagrangian dynamics,
and when exists it is by no means unique. The ambiguity and obstructions are
controlled by certain cohomology classes, which are all explicitly identified.Comment: 37 pages, 1 figure, minor corrections, references adde