531 research outputs found
Mapping the geometry of the E6 group
In this paper we present a construction for the compact form of the
exceptional Lie group E6 by exponentiating the corresponding Lie algebra e6,
which we realize as the the sum of f4, the derivations of the exceptional
Jordan algebra J3 of dimension 3 with octonionic entries, and the right
multiplication by the elements of J3 with vanishing trace. Our parametrization
is a generalization of the Euler angles for SU(2) and it is based on the
fibration of E6 via a F4 subgroup as the fiber. It makes use of a similar
construction we have performed in a previous article for F4. An interesting
first application of these results lies in the fact that we are able to
determine an explicit expression for the Haar invariant measure on the E6 group
manifold.Comment: 30 page
Symmetries of an Extended Hubbard Model
An extended Hubbard model with phonons is considered on a D-dimensional
lattice. The symmetries of the model are studied in various cases. It is shown
that for a certain choice of the parameters a superconducting SU_q(2) holds as
a true quantum symmetry - but only for D=1. In a natural basis the symmetry
requires vanishing local phonon coupling; a quantum symmetric Hubbard model
without phonons can then be obtained by a mean field approximation.Comment: plain tex, 7 page
q-Deformed Minkowski Space based on a q-Lorentz Algebra
The Hilbert space representations of a non-commutative q-deformed Minkowski
space, its momenta and its Lorentz boosts are constructed. The spectrum of the
diagonalizable space elements shows a lattice-like structure with accumulation
points on the light-cone.Comment: 31 pages, 1 figur
Some remarks on unilateral matrix equations
We briefly review the results of our paper hep-th/0009013: we study certain
perturbative solutions of left-unilateral matrix equations. These are algebraic
equations where the coefficients and the unknown are square matrices of the
same order, or, more abstractly, elements of an associative, but possibly
noncommutative algebra, and all coefficients are on the left. Recently such
equations have appeared in a discussion of generalized Born-Infeld theories. In
particular, two equations, their perturbative solutions and the relation
between them are studied, applying a unified approach based on the generalized
Bezout theorem for matrix polynomials.Comment: latex, 6 pages, 1 figure, talk given at the euroconference "Brane New
World and Noncommutative Geometry", Villa Gualino, Torino, Italy, Oct 2-7,
200
Il paesaggio e i gesti del sacro: i casi di Pontecagnano e Monte Vetrano (Salerno)
Pontecagnano and the site of Monte Vetrano in the Agro Picentino provide some interesting cases
for reconstructing cult practices and ritual actions integrated into the frame of the landscape: the
paper reports the results of the excavations carried out in the two settlements for the construction of
the third lane of the highway Salerno-Reggio Calabria and the WTE plant of Salerno
On the Euler angles for SU(N)
In this paper we reconsider the problem of the Euler parametrization for the
unitary groups. After constructing the generic group element in terms of
generalized angles, we compute the invariant measure on SU(N) and then we
determine the full range of the parameters, using both topological and
geometrical methods. In particular, we show that the given parametrization
realizes the group as a fibration of U(N) over the complex projective
space . This justifies the interpretation of the parameters as
generalized Euler angles.Comment: 16 pages, references adde
Una festa etrusca per Dioniso?
The paper aims to analyze the figurative program of an Etruscan black-figure amphora
in Dresden, decorated on one side with a scene of sacrifice in the presence of a satyr, and
on the other, with the representation of an armed dance.
The assumption is that the amphora is the product of a special commission to celebrate
a successful performance as a small triumph, using the mythical paradigm of the Gigantomachy
of Heracles as a model
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