3,539 research outputs found
Gauge Symmetry and Consistent Spin-Two Theories
We study Lagrangians with the minimal amount of gauge symmetry required to
propagate spin-two particles without ghosts or tachyons. In general, these
Lagrangians also have a scalar mode in their spectrum. We find that, in two
cases, the symmetry can be enhanced to a larger group: the whole group of
diffeomorphisms or a enhancement involving a Weyl symmetry. We consider the
non-linear completions of these theories. The intuitive completions yield the
usual scalar-tensor theories except for the pure spin-two cases, which
correspond to two inequivalent Lagrangians giving rise to Einstein's equations.
A more constructive self-consistent approach yields a background dependent
Lagrangian.Comment: 7 pages, proceedings of IRGAC'06; typo correcte
Non-commutative solitons and strong-weak duality
Some properties of the non-commutative versions of the sine-Gordon model
(NCSG) and the corresponding massive Thirring theories (NCMT) are studied. Our
method relies on the NC extension of integrable models and the master
Lagrangian approach to deal with dual theories. The master Lagrangians turn out
to be the NC versions of the so-called affine Toda model coupled to matter
fields (NCATM) associated to the group GL(2), in which the Toda field belongs
to certain representations of either or corresponding
to the Lechtenfeld et al. (NCSG) or Grisaru-Penati (NCSG) proposals
for the NC versions of the sine-Gordon model, respectively. Besides, the
relevant NCMT models are written for two (four) types of Dirac fields
corresponding to the Moyal product extension of one (two) copy(ies) of the
ordinary massive Thirring model. The NCATM models share the same
one-soliton (real Toda field sector of model 2) exact solutions, which are
found without expansion in the NC parameter for the corresponding Toda
and matter fields describing the strong-weak phases, respectively. The
correspondence NCSG NCMT is promising since it is
expected to hold on the quantum level.Comment: 24 pages, 1 fig., LaTex. Typos in star products of eqs. (3.11)-(3.13)
and footnote 1 were corrected. Version to appear in JHE
Basic Properties and Stability of Fractional-Order Reset Control Systems
Reset control is introduced to overcome limitations of linear control. A
reset controller includes a linear controller which resets some of states to
zero when their input is zero or certain non-zero values. This paper studies
the application of the fractional-order Clegg integrator (FCI) and compares its
performance with both the commonly used first order reset element (FORE) and
traditional Clegg integrator (CI). Moreover, stability of reset control systems
is generalized for the fractional-order case. Two examples are given to
illustrate the application of the stability theorem.Comment: The 12th European Control Conference (ECC13), Switzerland, 201
Hybrid Systems and Control With Fractional Dynamics (I): Modeling and Analysis
No mixed research of hybrid and fractional-order systems into a cohesive and
multifaceted whole can be found in the literature. This paper focuses on such a
synergistic approach of the theories of both branches, which is believed to
give additional flexibility and help to the system designer. It is part I of
two companion papers and introduces the fundamentals of fractional-order hybrid
systems, in particular, modeling and stability analysis of two kinds of such
systems, i.e., fractional-order switching and reset control systems. Some
examples are given to illustrate the applicability and effectiveness of the
developed theory. Part II will focus on fractional-order hybrid control.Comment: 2014 International Conference on Fractional Differentiation and its
Application, Ital
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