477 research outputs found
On the Structure of Lie Pseudo-Groups
We compare and contrast two approaches to the structure theory for Lie
pseudo-groups, the first due to Cartan, and the second due to the first two
authors. We argue that the latter approach offers certain advantages from both
a theoretical and practical standpoint
Generalized Symmetries of Massless Free Fields on Minkowski Space
A complete and explicit classification of generalized, or local, symmetries
of massless free fields of spin is carried out. Up to equivalence,
these are found to consists of the conformal symmetries and their duals, new
chiral symmetries of order , and their higher-order extensions obtained by
Lie differentiation with respect to conformal Killing vectors. In particular,
the results yield a complete classification of generalized symmetries of the
Dirac-Weyl neutrino equation, Maxwell's equations, and the linearized gravity
equations.Comment: This is a contribution to the Proc. of the Seventh International
Conference ''Symmetry in Nonlinear Mathematical Physics'' (June 24-30, 2007,
Kyiv, Ukraine), published in SIGMA (Symmetry, Integrability and Geometry:
Methods and Applications) at http://www.emis.de/journals/SIGMA
Variational Principles for Natural Divergence-free Tensors in Metric Field Theories
Let be a system of differential equations for the
components of a metric tensor on . Suppose that transforms
tensorially under the action of the diffeomorphism group on metrics and that
the covariant divergence of vanishes. We then prove that is
the Euler-Lagrange expression some Lagrangian density provided that is
of third order. Our result extends the classical works of Cartan, Weyl,
Vermeil, Lovelock, and Takens on identifying field equations for the metric
tensor with the symmetries and conservation laws of the Einstein equations
Conserved currents of massless fields of spin s>0
A complete and explicit classification of all locally constructed conserved
currents and underlying conserved tensors is obtained for massless linear
symmetric spinor fields of any spin s>0 in four dimensional flat spacetime.
These results generalize the recent classification in the spin s=1 case of all
conserved currents locally constructed from the electromagnetic spinor field.
The present classification yields spin s>0 analogs of the well-known
electromagnetic stress-energy tensor and Lipkin's zilch tensor, as well as a
spin s>0 analog of a novel chiral tensor found in the spin s=1 case. The chiral
tensor possesses odd parity under a duality symmetry (i.e., a phase rotation)
on the spin s field, in contrast to the even parity of the stress-energy and
zilch tensors. As a main result, it is shown that every locally constructed
conserved current for each s>0 is equivalent to a sum of elementary linear
conserved currents, quadratic conserved currents associated to the
stress-energy, zilch, and chiral tensors, and higher derivative extensions of
these currents in which the spin s field is replaced by its repeated
conformally-weighted Lie derivatives with respect to conformal Killing vectors
of flat spacetime. Moreover, all of the currents have a direct, unified
characterization in terms of Killing spinors. The cases s=2, s=1/2 and s=3/2
provide a complete set of conserved quantities for propagation of gravitons
(i.e., linearized gravity waves), neutrinos and gravitinos, respectively, on
flat spacetime. The physical meaning of the zilch and chiral quantities is
discussed.Comment: 26 pages; final version with minor changes, accepted in Proc. Roy.
Soc. A (London
Generalized Symmetries of Massless Free Fields on Minkowski Space
A complete and explicit classification of generalized, or local, symmetries of massless free fields of spin s ≥ 1/2 is carried out. Up to equivalence, these are found to consists of the conformal symmetries and their duals, new chiral symmetries of order 2s, and their higher-order extensions obtained by Lie differentiation with respect to conformal Killing vectors. In particular, the results yield a complete classification of generalized symmetries of the Dirac-Weyl neutrino equation, Maxwell's equations, and the linearized gravity equations
On the Structure of Lie Pseudo-Groups
We compare and contrast two approaches to the structure theory for Lie pseudo-groups, the first due to Cartan, and the second due to the first two authors. We argue that the latter approach offers certain advantages from both a theoretical and practical standpoint
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