786 research outputs found
Topological Background Fields as Quantum Degrees of Freedom of Compactified Strings
It is shown that background fields of a topological character usually
introduced as such in compactified string theories correspond to quantum
degrees of freedom which parametrise the freedom in choosing a representation
of the zero mode quantum algebra in the presence of non-trivial topology. One
consequence would appear to be that the values of such quantum degrees of
freedom, in other words of the associated topological background fields, cannot
be determined by the nonperturbative string dynamics.Comment: 1+10 pages, no figure
Topologically Massive Gauge Theories and their Dual Factorised Gauge Invariant Formulation
There exists a well-known duality between the Maxwell-Chern-Simons theory and
the self-dual massive model in 2+1 dimensions. This dual description has been
extended to topologically massive gauge theories (TMGT) in any dimension. This
Letter introduces an unconventional approach to the construction of this type
of duality through a reparametrisation of the master theory action. The dual
action thereby obtained preserves the same gauge symmetry structure as the
original theory. Furthermore, the dual action is factorised into a propagating
sector of massive gauge invariant variables and a sector with gauge variant
variables defining a pure topological field theory. Combining results obtained
within the Lagrangian and Hamiltonian formulations, a new completed structure
for a gauge invariant dual factorisation of TMGT is thus achieved.Comment: 1+7 pages, no figure
Spectrum of the non-commutative spherical well
We give precise meaning to piecewise constant potentials in non-commutative
quantum mechanics. In particular we discuss the infinite and finite
non-commutative spherical well in two dimensions. Using this, bound-states and
scattering can be discussed unambiguously. Here we focus on the infinite well
and solve for the eigenvalues and eigenfunctions. We find that time reversal
symmetry is broken by the non-commutativity. We show that in the commutative
and thermodynamic limits the eigenstates and eigenfunctions of the commutative
spherical well are recovered and time reversal symmetry is restored
Finite Euler Hierarchies And Integrable Universal Equations
Recent work on Euler hierarchies of field theory Lagrangians iteratively
constructed {}from their successive equations of motion is briefly reviewed. On
the one hand, a certain triality structure is described, relating arbitrary
field theories, {\it classical\ts} topological field theories -- whose
classical solutions span topological classes of manifolds -- and
reparametrisation invariant theories -- generalising ordinary string and
membrane theories. On the other hand, {\it finite} Euler hierarchies are
constructed for all three classes of theories. These hierarchies terminate with
{\it universal\ts} equations of motion, probably defining new integrable
systems as they admit an infinity of Lagrangians. Speculations as to the
possible relevance of these theories to quantum gravity are also suggested.Comment: (replaces previous unprintable version corrupted mailer) 13 p.,
(Plain TeX), DTP-92/3
Switching to nonhyperbolic cycles from codim 2 bifurcations of equilibria in ODEs
The paper provides full algorithmic details on switching to the continuation
of all possible codim 1 cycle bifurcations from generic codim 2 equilibrium
bifurcation points in n-dimensional ODEs. We discuss the implementation and the
performance of the algorithm in several examples, including an extended
Lorenz-84 model and a laser system.Comment: 17 pages, 7 figures, submitted to Physica
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