730 research outputs found
Moyal Brackets, Star Products and the Generalised Wigner Function
The Wigner-Weyl- Moyal approach to Quantum Mechanics is recalled, and
similarities to classical probability theory emphasised. The Wigner
distribution function is generalised and viewed as a construction of a bosonic
object, a target space co-ordinate, for example, in terms of a bilinear
convolution of two fermionic objects, e.g. a quark antiquark pair. This
construction is essentially non-local, generalising the idea of a local
current. Such Wigner functions are shown to solve a BPS generalised Moyal-Nahm
equation.Comment: 7 pages, LaTeX, to appear in special issue of the J. of Chaos,
Solitons and Fractal
Study of Quommutators of Quantum Variables and Generalized Derivatives
A general deformation of the Heisenberg algebra is introduced with two
deformed operators instead of just one. This is generalised to many variables,
and permits the simultaneous existence of coherent states, and the
transposition of creation operators.Comment: 17 pages (Previous version was truncated in transmission
Lagrange Brackets and U(1) fields
The idea of a companion Lagrangian associated with -Branes is extended to
include the presence of U(1) fields. The Brane Lagrangians are constructed with
represented in terms of Lagrange Brackets, which make manifest the
reparametrisation invariance of the theory; these are replaced by Poisson
Brackets in the companion Lagrangian, which is now covariant under field
redefinition. The ensuing Lagrangians possess a similar formal structure to
those in the absence of an anti-symmetric field tensor.Comment: 7 pages, LaTeX, reference correcte
Moyal Brackets in M-Theory
The infinite limit of Matrix Theory in 4 and 10 dimensions is described in
terms of Moyal Brackets. In those dimensions there exists a Bogomol'nyi bound
to the Euclideanized version of these equations, which guarantees that
solutions of the first order equations also solve the second order Matrix
Theory equations. A general construction of such solutions in terms of a
representation of the target space co-ordinates as non-local spinor bilinears,
which are generalisations of the standard Wigner functions on phase space, is
given.Comment: 10 pages, Latex, no figures. References altered, typos correcte
Moyal Nahm Equations
Various aspects of the Nahm equations in 3 and 7 dimensions are investigated.
The residues of the variables at simple poles in the 7-dimensional case form an
algebra. A large class of matrix representations of this algebra is
constructed. The large limit of these equations is taken by replacing the
commutators by Moyal Brackets, and a set of non trivial solutions in a
generalised form of Wigner distribution functions is obtained.Comment: 15 pages, latex, no figure
Morphing quantum mechanics and fluid dynamics
We investigate the effects of given pressure gradients on hydrodynamic flow
equations. We obtain results in terms of implicit solutions and also in the
framework of an extra-dimensional formalism involving the diffusion/Schrodinger
equation.Comment: Examples involving shocks and references adde
Multi-Field Generalisations of the Klein-Gordon Theory associated with p-Branes
The purpose of this article is to initiate a study of a class of Lorentz
invariant, yet tractable, Lagrangian Field Theories which may be viewed as an
extension of the Klein-Gordon Lagrangian to many scalar fields in a novel
manner. These Lagrangians are quadratic in the Jacobians of the participating
fields with respect to the base space co-ordinates. In the case of two fields,
real valued solutions of the equations of motion are found and a phenomenon
reminiscent of instanton behaviour is uncovered; an ansatz for a subsidiary
equation which implies a solution of the full equations yields real solutions
in three-dimensional Euclidean space. Each of these is associated with a
spherical harmonic function.Comment: 13 pages, Late
Euler Incognito
The nonlinear flow equations discussed recently by Bender and Feinberg are
all reduced to the well-known Euler equation after change of variables.Comment: 2 page
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