29,648 research outputs found
Some Implications of the Cosmological Constant to Fundamental Physics
In the presence of a cosmological constant, ordinary Poincare' special
relativity is no longer valid and must be replaced by a de Sitter special
relativity, in which Minkowski space is replaced by a de Sitter spacetime. In
consequence, the ordinary notions of energy and momentum change, and will
satisfy a different kinematic relation. Such a theory is a different kind of a
doubly special relativity. Since the only difference between the Poincare' and
the de Sitter groups is the replacement of translations by certain linear
combinations of translations and proper conformal transformations, the net
result of this change is ultimately the breakdown of ordinary translational
invariance. From the experimental point of view, therefore, a de Sitter special
relativity might be probed by looking for possible violations of translational
invariance. If we assume the existence of a connection between the energy scale
of an experiment and the local value of the cosmological constant, there would
be changes in the kinematics of massive particles which could hopefully be
detected in high-energy experiments. Furthermore, due to the presence of a
horizon, the usual causal structure of spacetime would be significantly
modified at the Planck scale.Comment: 15 pages, lecture presented at the "XIIth Brazilian School of
Cosmology and Gravitation", Mangaratiba, Rio de Janeiro, September 10-23,
200
Cosmological Term and Fundamental Physics
A nonvanishing cosmological term in Einstein's equations implies a
nonvanishing spacetime curvature even in absence of any kind of matter. It
would, in consequence, affect many of the underlying kinematic tenets of
physical theory. The usual commutative spacetime translations of the Poincare'
group would be replaced by the mixed conformal translations of the de Sitter
group, leading to obvious alterations in elementary concepts such as time,
energy and momentum. Although negligible at small scales, such modifications
may come to have important consequences both in the large and for the
inflationary picture of the early Universe. A qualitative discussion is
presented which suggests deep changes in Hamiltonian, Quantum and Statistical
Mechanics. In the primeval universe as described by the standard cosmological
model, in particular, the equations of state of the matter sources could be
quite different from those usually introduced.Comment: RevTeX, 4 pages. Selected for Honorable Mention in the Annual Essay
Competition of the Gravity Research Foundation for the year 200
Generalized Euler-Lagrange equations for variational problems with scale derivatives
We obtain several Euler-Lagrange equations for variational functionals
defined on a set of H\"older curves. The cases when the Lagrangian contains
multiple scale derivatives, depends on a parameter, or contains higher-order
scale derivatives are considered.Comment: Submitted on 03-Aug-2009; accepted for publication 16-March-2010; in
"Letters in Mathematical Physics"
Replica-symmetric solutions of a dilute Ising ferromagnet in a random field
We use the replica method in order to obtain an expression for the
variational free energy of an Ising ferromagnet on a Viana-Bray lattice in the
presence of random external fields. Introducing a global order parameter, in
the replica-symmetric context, the problem is reduced to the analysis of the
solutions of a nonlinear integral equation. At zero temperature, and under some
restrictions on the form of the random fields, we are able to perform a
detailed analysis of stability of the replica-symmetric solutions. In contrast
to the behaviour of the Sherrington-Kirkpatrick model for a spin glass in a
uniform field, the paramagnetic solution is fully stable in a sufficiently
large random field
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