454 research outputs found
Spacetime algebraic skeleton
The cosmological constant Lambda, which has seemingly dominated the primaeval
Universe evolution and to which recent data attribute a significant
present-time value, is shown to have an algebraic content: it is essentially an
eigenvalue of a Casimir invariant of the Lorentz group which acts on every
tangent space. This is found in the context of de Sitter spacetimes but, as
every spacetime is a 4-manifold with Minkowski tangent spaces, the result
suggests the existence of a "skeleton" algebraic structure underlying the
geometry of general physical spacetimes. Different spacetimes come from the
"fleshening" of that structure by different tetrad fields. Tetrad fields, which
provide the interface between spacetime proper and its tangent spaces, exhibit
to the most the fundamental role of the Lorentz group in Riemannian spacetimes,
a role which is obscured in the more usual metric formalism.Comment: 13 page
Closed Expressions for Lie Algebra Invariants and Finite Transformations
A simple procedure to obtain complete, closed expressions for Lie algebra
invariants is presented. The invariants are ultimately polynomials in the group
parameters. The construction of finite group elements require the use of
projectors, whose coefficients are invariant polynomials. The detailed general
forms of these projectors are given. Closed expressions for finite Lorentz
transformations, both homogeneous and inhomogeneous, as well as for Galilei
transformations, are found as examples.Comment: 34 pages, ps file, no figure
Primeval symmetries
A detailed examination of the Killing equations in Robertson-Walker
coordinates shows how the addition of matter and/or radiation to a de Sitter
Universe breaks the symmetry generated by four of its Killing fields. The
product U = (a^2)(dH/dt) of the squared scale parameter by the time-derivative
of the Hubble function encapsulates the relationship between the two cases: the
symmetry is maximal when U is a constant, and reduces to the six-parameter
symmetry of a generic Friedmann-Robertson-Walker model when it is not. As the
fields physical interpretation is not clear in these coordinates, comparison is
made with the Killing fields in static coordinates, whose interpretation is
made clearer by their direct relationship to the Poincare group generators via
Wigner-Inonu contractions.Comment: 16 pages, 2 tables; published versio
Free field representation of Toda field theories
We study the following problem: can a classical Toda field theory be
represented by means of free bosonic oscillators through a Drinfeld--Sokolov
construction? We answer affirmatively in the case of a cylindrical space--time
and for real hyperbolic solutions of the Toda field equations. We establish in
fact a one--to--one correspondence between such solutions and the space of free
left and right bosonic oscillators with coincident zero modes. We discuss the
same problem for real singular solutions with non hyperbolic monodromy.Comment: 29 pages, Latex, SISSA-ISAS 210/92/E
A coordinate-dependent superspace deformation from string theory
Starting from a type II superstring model defined on in
a linear graviphoton background, we derive a coordinate dependent -deformed
, superspace. The chiral fermionic coordinates
satisfy a Clifford algebra, while the other coordinate algebra remains
unchanged. We find a linear relation between the graviphoton field strength and
the deformation parameter. The null coordinate dependence of the graviphoton
background allows to extend the results to all orders in .Comment: 14 pages, reference added, accepted for publication in JHE
Kinematics of a Spacetime with an Infinite Cosmological Constant
A solution of the sourceless Einstein's equation with an infinite value for
the cosmological constant \Lambda is discussed by using Inonu-Wigner
contractions of the de Sitter groups and spaces. When \Lambda --> infinity,
spacetime becomes a four-dimensional cone, dual to Minkowski space by a
spacetime inversion. This inversion relates the four-cone vertex to the
infinity of Minkowski space, and the four-cone infinity to the Minkowski
light-cone. The non-relativistic limit c --> infinity is further considered,
the kinematical group in this case being a modified Galilei group in which the
space and time translations are replaced by the non-relativistic limits of the
corresponding proper conformal transformations. This group presents the same
abstract Lie algebra as the Galilei group and can be named the conformal
Galilei group. The results may be of interest to the early Universe Cosmology.Comment: RevTex, 7 pages, no figures. Presentation changes, including a new
Title. Version to appear in Found. Phys. Let
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