1,139 research outputs found
Some comments on the universal constant in DSR
Deformed Special Relativity is usually presented as a deformation of Special
Relativity accommodating a new universal constant, the Planck mass, while
respecting the relativity principle. In order to avoid some fundamental
problems (e.g. soccer ball problem), we argue that we should switch point of
view and consider instead the Newton constant as the universal constant.Comment: 12 pages, Proceedings of DICE2006 (Piombino, Italy
Non-Commutativity of Effective Space-Time Coordinates and the Minimal Length
Considering that a position measurement can effectively involve a
momentum-dependent shift and rescaling of the "true" space-time coordinates, we
construct a set of effective space-time coordinates which are naturally
non-commutative. They lead to a minimum length and are shown to be related to
Snyder's coordinates and the five-dimensional formulation of Deformed Special
Relativity. This effective approach then provides a natural physical
interpretation for both the extra fifth dimension and the deformed momenta
appearing in this context.Comment: 5 page
Physics of Deformed Special Relativity
In many different ways, Deformed Special Relativity (DSR) has been argued to
provide an effective limit of quantum gravity in almost-flat regime.
Unfortunately DSR is up to now plagued by many conceptual problems (in
particular how it describes macroscopic objects) which forbids a definitive
physical interpretation and clear predictions. Here we propose a consistent
framework to interpret DSR. We extend the principle of relativity: the same way
that Special Relativity showed us that the definition of a reference frame
requires to specify its speed, we show that DSR implies that we must also take
into account its mass. We further advocate a 5-dimensional point of view on DSR
physics and the extension of the kinematical symmetry from the Poincare group
to the Poincare-de Sitter group (ISO(4,1)). This leads us to introduce the
concept of a pentamomentum and to take into account the renormalization of the
DSR deformation parameter kappa. This allows the resolution of the "soccer ball
problem" (definition of many-particle-states) and provides a physical
interpretation of the non-commutativity and non-associativity of the addition
the relativistic quadrimomentum.Comment: 8 pages, short version of gr-qc/0412004, Proceedings of the Second
International Workshop DICE2004 (Castello di Piombino, Tuscany) "From
Decoherence and Emergent Classicality to Emergent Quantum Mechanics
Physics of Deformed Special Relativity: Relativity Principle revisited
In many different ways, Deformed Special Relativity (DSR) has been argued to
provide an effective limit of quantum gravity in almost-flat regime. Some
experiments will soon be able to test some low energy effects of quantum
gravity, and DSR is a very promising candidate to describe these latter.
Unfortunately DSR is up to now plagued by many conceptual problems (in
particular how it describes macroscopic objects) which forbids a definitive
physical interpretation and clear predictions. Here we propose a consistent
framework to interpret DSR. We extend the principle of relativity: the same way
that Special Relativity showed us that the definition of a reference frame
requires to specify its speed, we show that DSR implies that we must also take
into account its mass. We further advocate a 5-dimensional point of view on DSR
physics and the extension of the kinematical symmetry from the Poincare group
to the Poincare-de Sitter group (ISO(4,1)). This leads us to introduce the
concept of a pentamomentum and to take into account the renormalization of the
DSR deformation parameter kappa. This allows the resolution of the "soccer ball
problem" (definition of many-particle-states) and provides a physical
interpretation of the non-commutativity and non-associativity of the addition
the relativistic quadrimomentum. In particular, the coproduct of the
kappa-Poincare algebra is interpreted as defining the law of change of
reference frames and not the law of scattering. This point of view places DSR
as a theory, half-way between Special Relativity and General Relativity,
effectively implementing the Schwarzschild mass bound in a flat relativistic
context.Comment: 24 pages, Revtex
Scalar field theory in Snyder space-time: alternatives
We construct two types of scalar field theory on Snyder space-time. The first
one is based on the natural momenta addition inherent to the coset momentum
space. This construction uncovers a non-associative deformation of the
Poincar\'e symmetries. The second one considers Snyder space-time as a subspace
of a larger non-commutative space. We discuss different possibilities to
restrict the extra-dimensional scalar field theory to a theory living only on
Sndyer space-time and present the consequences of these restrictions on the
Poincar\'e symmetries. We show moreover how the non-associative approach and
the Doplicher-Fredenhagen-Roberts space can be seen as specific approximations
of the extra-dimensional theory. These results are obtained for the 3d
Euclidian Snyder space-time constructed from \SO(3,1)/\SO(3), but our results
extend to any dimension and signature.Comment: 24 pages
And what if gravity is intrinsically quantic ?
Since the early days of search for a quantum theory of gravity the attempts
have been mostly concentrated on the quantization of an otherwise classical
system. The two most contentious candidate theories of gravity, sting theory
and quantum loop gravity are based on a quantum field theory - the latter is a
quantum field theory of connections on a SU(2) group manifold and former a
quantum field theory in two dimensional spaces. Here we argue that there is a
very close relation between quantum mechanics and gravity. Without gravity
quantum mechanics becomes ambiguous. We consider this observation as the
evidence for an intrinsic relation between these fundamental laws of nature. We
suggest a quantum role and definition for gravity in the context of a quantum
universe, and present a preliminary formulation for gravity in a system with a
finite number of particles.Comment: 8 pages, 1 figure. To appear in the proceedings of the DICE2008
conference, Castiglioncello, Tuscany, Italy, 22-26 Sep. 2008. V2: some typos
remove
Field theories with homogenous momentum space
We discuss the construction of a scalar field theory with momentum space
given by a coset. By introducing a generalized Fourier transform, we show how
the dual scalar field theory actually lives in Snyder's space-time. As a
side-product we identify a star product realization of Snyder's non-commutative
space, but also the deformation of the Poincare symmetries necessary to have
these symmetries realized in Snyder's space-time. A key feature of the
construction is that the star product is non-associative.Comment: 9 pages, To appear in the Proceedings of the XXV Max Born Symposium,
"The Planck Scale", Wroclaw, Poland, July 200
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