On Generalized Self-Duality Equations Towards Supersymmetric Quantum Field Theories Of Forms

We classify possible `self-duality' equations for p-form gauge fields in space-time dimension up to D=16, generalizing the pioneering work of Corrigan et al. (1982) on Yang-Mills fields (p=1) for D from 5 to 8. We impose two crucial requirements. First, there should exist a 2(p+1)-form T invariant under a sub-group H of SO(D). Second, the representation for the SO(D) curvature of the gauge field must decompose under H in a relevant way. When these criteria are fulfilled, the `self-duality' equations can be candidates as gauge functions for SO(D)-covariant and H-invariant topological quantum field theories. Intriguing possibilities occur for dimensions greater than 9, for various p-form gauge fields.Comment: 20 pages, Late

Administrative Powers of the President

Turning now to those particular branches of administration where the Constitution confers on the President special powers, we shall find that in these fields he has still more ample authority. Not only do the constitutional grants guard him from encroachment on the part of Congress, but they enable him at times to assume a large degree of legislative power

Integrable Generalisations of the 2-dimensional Born Infeld Equation

The Born-Infeld equation in two dimensions is generalised to higher dimensions whilst retaining Lorentz Invariance and complete integrability. This generalisation retains homogeneity in second derivatives of the field.Comment: 11 pages, Latex, DTP/93/3

Linearisation of Universal Field Equations

The Universal Field Equations, recently constructed as examples of higher dimensional dynamical systems which admit an infinity of inequivalent Lagrangians are shown to be linearised by a Legendre transformation. This establishes the conjecture that these equations describe integrable systems. While this construction is implicit in general, there exists a large class of solutions for which an explicit form may be written.Comment: 11pp., DTP-92/47, NI-92/01

Self-dual Yang-Mills fields in pseudoeuclidean spaces

The self-duality Yang-Mills equations in pseudoeuclidean spaces of dimensions $d\leq 8$ are investigated. New classes of solutions of the equations are found. Extended solutions to the D=10, N=1 supergravity and super Yang-Mills equations are constructed from these solutions.Comment: 9 pages, LaTeX, no figure

Physical Instances of Noncommuting Coordinates

Noncommuting spatial coordinates and fields can be realized in actual physical situations. Plane wave solutions to noncommuting photodynamics exhibit violaton of Lorentz invariance (special relativity).Comment: 13 pp., using sprocl and amsmath macros; Email correspondence to [email protected]; talk given at Feza Gursey Institute, Istanbul, Turkey -- June 2001; "Symmetry Methods in Physics", Yerevan, Armenia -- July 2001; "CPT and Lorentz Symmetry II", Bloomington, IN -- August 2001; "Particles and Strings", Trento, Italy -- September 2001; "VIII Adriatic Meeting", Dubrovnik, Croatia -- September 200

Testing Non-commutative QED, Constructing Non-commutative MHD

The effect of non-commutativity on electromagnetic waves violates Lorentz invariance: in the presence of a background magnetic induction field b, the velocity for propagation transverse to b differs from c, while propagation along b is unchanged. In principle, this allows a test by the Michelson-Morley interference method. We also study non-commutativity in another context, by constructing the theory describing a charged fluid in a strong magnetic field, which forces the fluid particles into their lowest Landau level and renders the fluid dynamics non-commutative, with a Moyal product determined by the background magnetic field.Comment: 14 pages, LaTeX; minor corrections, references adde

Properties of the Scalar Universal Equations

The variational properties of the scalar so--called ``Universal'' equations are reviewed and generalised. In particular, we note that contrary to earlier claims, each member of the Euler hierarchy may have an explicit field dependence. The Euler hierarchy itself is given a new interpretation in terms of the formal complex of variational calculus, and is shown to be related to the algebra of distinguished symmetries of the first source form.Comment: 15 pages, LaTeX articl

The Moyal bracket and the dispersionless limit of the KP hierarchy

A new Lax equation is introduced for the KP hierarchy which avoids the use of pseudo-differential operators, as used in the Sato approach. This Lax equation is closer to that used in the study of the dispersionless KP hierarchy, and is obtained by replacing the Poisson bracket with the Moyal bracket. The dispersionless limit, underwhich the Moyal bracket collapses to the Poisson bracket, is particularly simple.Comment: 9 pages, LaTe