3,776 research outputs found
Free Differential Algebras: Their Use in Field Theory and Dual Formulation
The gauging of free differential algebras (FDA's) produces gauge field
theories containing antisymmetric tensors. The FDA's extend the Cartan-Maurer
equations of ordinary Lie algebras by incorporating p-form potentials (). We study here the algebra of FDA transformations. To every p-form in the
FDA we associate an extended Lie derivative generating a corresponding
``gauge" transformation. The field theory based on the FDA is invariant under
these new transformations. This gives geometrical meaning to the antisymmetric
tensors. The algebra of Lie derivatives is shown to close and provides the dual
formulation of FDA's.Comment: 10 pages, latex, no figures. Talk presented at the 4-th Colloquium on
"Quantum Groups and Integrable Sysytems", Prague, June 199
Super Quantum Mechanics in the Integral Form Formalism
We reformulate Super Quantum Mechanics in the context of integral forms. This
framework allows to interpolate between different actions for the same theory,
connected by different choices of Picture Changing Operators (PCO). In this way
we retrieve component and superspace actions, and prove their equivalence. The
PCO are closed integral forms, and can be interpreted as super Poincar\'e duals
of bosonic submanifolds embedded into a supermanifold.. We use them to
construct Lagrangians that are top integral forms, and therefore can be
integrated on the whole supermanifold. The and the
cases are studied, in a flat and in a curved supermanifold. In this formalism
we also consider coupling with gauge fields, Hilbert space of quantum states
and observables.Comment: 41 pages, no figures. Use birkjour.cls. Minor misprints, moved
appendix A and B in the main text. Version to be published in Annales H.
Poincar\'
The Geometry of Supermanifolds and New Supersymmetric Actions
We construct the Hodge dual for supermanifolds by means of the Grassmannian
Fourier transform of superforms. In the case of supermanifolds it is known that
the superforms are not sufficient to construct a consistent integration theory
and that the integral forms are needed. They are distribution-like forms which
can be integrated on supermanifolds as a top form can be integrated on a
conventional manifold. In our construction of the Hodge dual of superforms they
arise naturally. The compatibility between Hodge duality and supersymmetry is
exploited and applied to several examples. We define the irreducible
representations of supersymmetry in terms of integral and superforms in a new
way which can be easily generalised to several models in different dimensions.
The construction of supersymmetric actions based on the Hodge duality is
presented and new supersymmetric actions with higher derivative terms are
found. These terms are required by the invertibility of the Hodge operator.Comment: LateX2e, 51 pages. Corrected some further misprint
Non-linear conductivity and quantum interference in disordered metals
We report on a novel non-linear electric field effect in the conductivity of
disordered conductors. We find that an electric field gives rise to dephasing
in the particle-hole channel, which depresses the interference effects due to
disorder and interaction and leads to a non-linear conductivity. This
non-linear effect introduces a field dependent temperature scale and
provides a microscopic mechanism for electric field scaling at the
metal-insulator transition. We also study the magnetic field dependence of the
non-linear conductivity and suggest possible ways to experimentally verify our
predictions. These effects offer a new probe to test the role of quantum
interference at the metal-insulator transition in disordered conductors.Comment: 5 pages, 3 figure
Hidden Quantum Group Structure in Einstein's General Relativity
A new formal scheme is presented in which Einstein's classical theory of
General Relativity appears as the common, invariant sector of a one-parameter
family of different theories. This is achieved by replacing the Poincare` group
of the ordinary tetrad formalism with a q-deformed Poincare` group, the usual
theory being recovered at q=1. Although written in terms of noncommuting
vierbein and spin-connection fields, each theory has the same metric sector
leading to the ordinary Einstein-Hilbert action and to the corresponding
equations of motion. The Christoffel symbols and the components of the Riemann
tensor are ordinary commuting numbers and have the usual form in terms of a
metric tensor built as an appropriate bilinear in the vierbeins. Furthermore we
exhibit a one-parameter family of Hamiltonian formalisms for general
relativity, by showing that a canonical formalism a` la Ashtekar can be built
for any value of q. The constraints are still polynomial, but the Poisson
brackets are not skewsymmetric for q different from 1.Comment: LaTex file, 21 pages, no figure
Surviving on Mars: test with LISA simulator
We present the biological results of some experiments performed in the Padua
simulators of planetary environments, named LISA, used to study the limit of
bacterial life on the planet Mars. The survival of Bacillus strains for some
hours in Martian environment is shortly discussed.Comment: To be published on Highlights of Astronomy, Volume 15 XXVIIth IAU
General Assembly, August 2009 Ian F Corbett, ed. 2 pages, 1 figur
A note on quantum structure constants
The Cartan-Maurer equations for any -group of the
series are given in a convenient form, which allows their direct computation
and clarifies their connection with the case. These equations, defining
the field strengths, are essential in the construction of -deformed gauge
theories. An explicit expression \om ^i\we \om^j= -\Z {ij}{kl}\om ^k\we \om^l
for the -commutations of left-invariant one-forms is found, with \Z{ij}{kl}
\om^k \we \om^l \qonelim \om^j\we\om^i.Comment: 9 pp., LaTe
Comments on the Non-Commutative Description of Classical Gravity
We find a one-parameter family of Lagrangian descriptions for classical
general relativity in terms of tetrads which are not c-numbers. Rather, they
obey exotic commutation relations. These noncommutative properties drop out in
the metric sector of the theory, where the Christoffel symbols and the Riemann
tensor are ordinary commuting objects and they are given by the usual
expression in terms of the metric tensor. Although the metric tensor is not a
c-number, we argue that all measurements one can make in this theory are
associated with c-numbers, and thus that the common invariant sector of our
one--parameter family of deformed gauge theories (for the case of zero torsion)
is physically equivalent to Einstein's general relativity.Comment: Latex file, 13 pages, no figure
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