76 research outputs found
Physical Constraints on Quantum Deformations of Spacetime Symmetries
In this work we study the deformations into Lie bialgebras of the three
relativistic Lie algebras: de Sitter, Anti-de Sitter and Poincar\'e, which
describe the symmetries of the three maximally symmetric spacetimes. These
algebras represent the centrepiece of the kinematics of special relativity (and
its analogue in (Anti-)de Sitter spacetime), and provide the simplest framework
to build physical models in which inertial observers are equivalent. Such a
property can be expected to be preserved by Quantum Gravity, a theory which
should build a length/energy scale into the microscopic structure of spacetime.
Quantum groups, and their infinitesimal version `Lie bialgebras', allow to
encode such a scale into a noncommutativity of the algebra of functions over
the group (and over spacetime, when the group acts on a homogeneous space). In
2+1 dimensions we have evidence that the vacuum state of Quantum Gravity is one
such `noncommutative spacetime' whose symmetries are described by a Lie
bialgebra. It is then of great interest to study the possible Lie bialgebra
deformations of the relativistic Lie algebras. In this paper, we develop a
classification of such deformations in 2, 3 and 4 spacetime dimensions, based
on physical requirements based on dimensional analysis, on various degrees of
`manifest isotropy' (which implies that certain symmetries, i.e. Lorentz
transformations or rotations, are `more classical'), and on discrete symmetries
like P and T. On top of a series of new results in 3 and 4 dimensions, we find
a no-go theorem for the Lie bialgebras in 4 dimensions, which singles out the
well-known `-deformation' as the only one that depends on the first
power of the Planck length, or, alternatively, that possesses `manifest'
spatial isotropy.Comment: 13 pages, 1 table, matches version published on Nuclear Physics
Light Cone in a Quantum Spacetime
Noncommutative spacetimes are a proposed effective description of the
low-energy regime of Quantum Gravity. Defining the microcausality relations of
a scalar quantum field theory on the -Minkowski noncommutative
spacetime allows us to define for the first time a notion of light-cone in a
quantum spacetime. This allows us to reach two conclusions. First, the majority
of the literature on -Minkowski suggests that this spacetime allows
superluminal propagation of particles. The structure of the light-cone we
introduced allows to rule this out, thereby excluding the possibility of
constraining the relevant models with observations of in-vacuo dispersion of
Gamma Ray Burst photons. Second, we are able to reject a claim made in [Phys.
Rev. Lett. 105, 211601 (2010)], according to which the light-cone of the
-Minkowski spacetime has a "blurry" region of Planck-length thickness,
independently of the distance of the two events considered. Such an effect
would be hopeless to measure. Our analysis reveals that the thickness of the
region where the notion of timelike and spacelike separations blurs grows like
the square root of the distance. This magnifies the effect, e.g. in the case of
cosmological distances, by 30 orders of magnitude.Comment: 7 pages, 3 figures, matches version accepted by Phys. Lett.
Extended noncommutative Minkowski spacetimes and hybrid gauge symmetries
We study the Lie bialgebra structures that can be built on the
one-dimensional central extension of the Poincar\'e and (A)dS algebras in (1+1)
dimensions. These central extensions admit more than one interpretation, but
the simplest one is that they describe the symmetries of (the noncommutative
deformation of) an Abelian gauge theory, or on the (1+1)
dimensional Minkowski or (A)dS spacetime. We show that this highlights the
possibility that the algebra of functions on the gauge bundle becomes
noncommutative. This is a new way in which the Coleman-Mandula theorem could be
circumvented by noncommutative structures, and it is related to a mixing of
spacetime and gauge symmetry generators when they act on tensor-product states.
We obtain all Lie bialgebra structures on centrally-extended Poincar\'e and
(A)dS which are coisotropic w.r.t. the Lorentz algebra, and therefore all of
them admit the construction of a noncommutative principal gauge bundle on a
quantum homogeneous Minkowski spacetime. It is shown that several different
types of hybrid noncommutativity between the spacetime and gauge coordinates
are allowed by introducing quantum extended Poincar\'e symmetries. In one of
these cases, an alternative interpretation of the central extension leads to a
new description of the well-known canonical noncommutative spacetime as the
quantum homogeneous space of a quantum Poincar\'e algebra of symmetries.Comment: 18 page
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