4,699 research outputs found
Faddeev-Jackiw approach to gauge theories and ineffective constraints
The general conditions for the applicability of the Faddeev-Jackiw approach
to gauge theories are studied. When the constraints are effective a new proof
in the Lagrangian framework of the equivalence between this method and the
Dirac approach is given. We find, however, that the two methods may give
different descriptions for the reduced phase space when ineffective constraints
are present. In some cases the Faddeev-Jackiw approach may lose some
constraints or some equations of motion. We believe that this inequivalence can
be related to the failure of the Dirac conjecture (that says that the Dirac
Hamiltonian can be enlarged to an Extended Hamiltonian including all first
class constraints, without changes in the dynamics) and we suggest that when
the Dirac conjecture fails the Faddeev-Jackiw approach fails to give the
correct dynamics. Finally we present some examples that illustrate this
inequivalence.Comment: 21 pages, Latex. To be published in Int. J. Mod. Phys.
Equivalence of Faddeev-Jackiw and Dirac approaches for gauge theories
The equivalence between the Dirac method and Faddeev-Jackiw analysis for
gauge theories is proved. In particular we trace out, in a stage by stage
procedure, the standard classification of first and second class constraints of
Dirac's method in the F-J approach. We also find that the Darboux
transformation implied in the F-J reduction process can be viewed as a
canonical transformation in Dirac approach. Unlike Dirac's method the F-J
analysis is a classical reduction procedure, then the quantization can be
achieved only in the framework of reduce and then quantize approach with all
the know problems that this type of procedures presents. Finally we illustrate
the equivalence by means of a particular example.Comment: Latex v2.09, 15 pages, to appear in Int. J. Mod. Phys.
Three-forms in Supergravity and Flux Compactifications
We present a duality procedure that relates conventional four-dimensional
matter-coupled N=1 supergravities to dual formulations in which auxiliary
fields are replaced by field-strengths of gauge three-forms. The duality
promotes specific coupling constants appearing in the superpotential to vacuum
expectation values of the field-strengths. We then apply this general duality
to type IIA string compactifications on Calabi-Yau orientifolds with RR fluxes.
This gives a new supersymmetric formulation of the corresponding effective
four-dimensional theories which includes gauge three-forms.Comment: 37 pages, v3: minor correction
Boundary Terms, Variational Principles and Higher Derivative Modified Gravity
We discuss the criteria that must be satisfied by a well-posed variational
principle. We clarify the role of Gibbons-Hawking-York type boundary terms in
the actions of higher derivative models of gravity, such as F(R) gravity, and
argue that the correct boundary terms are the naive ones obtained though the
correspondence with scalar-tensor theory, despite the fact that variations of
normal derivatives of the metric must be fixed on the boundary. We show in the
case of F(R) gravity that these boundary terms reproduce the correct ADM energy
in the hamiltonian formalism, and the correct entropy for black holes in the
semi-classical approximation.Comment: 54 pages, 2 figures. Several typos corrected, references added.
Version appearing in PR
Gauge invariant approach to low-spin anomalous conformal currents and shadow fields
Conformal low-spin anomalous currents and shadow fields in flat space-time of
dimension greater than or equal to four are studied. Gauge invariant
formulation for such currents and shadow fields is developed. Gauge symmetries
are realized by involving Stueckelberg and auxiliary fields. Gauge invariant
differential constraints for anomalous currents and shadow fields and
realization of global conformal symmetries are obtained. Gauge invariant
two-point vertices for anomalous shadow fields are also obtained. In
Stueckelberg gauge frame, these gauge invariant vertices become the standard
two-point vertices of CFT. Light-cone gauge two-point vertices of the anomalous
shadow fields are derived. AdS/CFT correspondence for anomalous currents and
shadow fields and the respective normalizable and non-normalizable solutions of
massive low-spin AdS fields is studied. The bulk fields are considered in
modified de Donder gauge that leads to decoupled equations of motion. We
demonstrate that leftover on-shell gauge symmetries of bulk massive fields
correspond to gauge symmetries of boundary anomalous currents and shadow
fields, while the modified (Lorentz) de Donder gauge conditions for bulk
massive fields correspond to differential constraints for boundary anomalous
currents and shadow fields.Comment: 28 pages, RevTeX4, v2: Sections 9C and 10C extended. Typos correcte
Shadows, currents and AdS fields
Conformal totally symmetric arbitrary spin currents and shadow fields in flat
space-time of dimension greater than or equal to four are studied. Gauge
invariant formulation for such currents and shadow fields is developed. Gauge
symmetries are realized by involving the Stueckelberg fields. Realization of
global conformal boost symmetries is obtained. Gauge invariant differential
constraints for currents and shadow fields are obtained. AdS/CFT correspondence
for currents and shadow fields and the respective normalizable and
non-normalizable solutions of massless totally symmetric arbitrary spin AdS
fields is studied. The bulk fields are considered in modified de Donder gauge
that leads to decoupled equations of motion. We demonstrate that leftover
on-shell gauge symmetries of bulk fields correspond to gauge symmetries of
boundary currents and shadow fields, while the modified de Donder gauge
conditions for bulk fields correspond to differential constraints for boundary
conformal currents and shadow fields. Breaking conformal symmetries, we find
interrelations between the gauge invariant formulation of the currents and
shadow fields and the gauge invariant formulation of massive fields.Comment: v3: 31 pages, RevTeX4. Appendix D devoted to modified de Donder gauge
in AdS(d+1) x S(d+1) added. Footnotes 10, 21 added. Typos correcte
Faddeev-Jackiw Hamiltonian Reduction for Free and Gauged Rarita-Schwinger Theories
We study the Faddeev-Jackiw symplectic Hamiltonian reduction for
3+1-dimensional free and Abelian gauged Rarita-Schwinger theories that comprise
Grassmannian fermionic fields. We obtain the relevant fundamental brackets and
find that they are in convenient forms for quantization. The brackets are
independent of whether the theories contain mass or gauge fields, and the
structure of constraints and symplectic potentials largely determine
characteristic behaviors of the theories. We also note that, in contrast to the
free massive theory, the Dirac field equations for free massless
Rarita-Schwinger theory cannot be obtained in a covariant way.Comment: 17 pages, minor corrections made, reference and appendix added,
discussions amplifie
Superconformal theories from Pseudoparticle Mechanics
We consider a one-dimensional Osp() pseudoparticle mechanical model
which may be written as a phase space gauge theory. We show how the
pseudoparticle model naturally encodes and explains the two-dimensional zero
curvature approach to finding extended conformal symmetries. We describe a
procedure of partial gauge fixing of these theories which leads generally to
theories with superconformally extended -algebras. The pseudoparticle
model allows one to derive the finite transformations of the gauge and matter
fields occurring in these theories with extended conformal symmetries. In
particular, the partial gauge fixing of the Osp() pseudoparticle
mechanical models results in theories with the SO() invariant -extended
superconformal symmetry algebra of Bershadsky and Knizhnik. These algebras are
nonlinear for We discuss in detail the cases of and
giving two new derivations of the superschwarzian derivatives. Some comments
are made in the case on how twisted and topological theories represent a
significant deformation of the original particle model. The particle model also
allows one to interpret superconformal transformations as deformations of flags
in super jet bundles over the associated super Riemann surface.Comment: 36 pages, UTTG-93-00
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