Kinematics of a relativistic particle with de Sitter momentum space

We discuss kinematical properties of a free relativistic particle with deformed phase space in which momentum space is given by (a submanifold of) de Sitter space. We provide a detailed derivation of the action, Hamiltonian structure and equations of motion for such free particle. We study the action of deformed relativistic symmetries on the phase space and derive explicit formulas for the action of the deformed Poincare' group. Finally we provide a discussion on parametrization of the particle worldlines stressing analogies and differences with ordinary relativistic kinematics.Comment: RevTeX, 12 pages, no figure

Free vacuum for loop quantum gravity

We linearize extended ADM-gravity around the flat torus, and use the associated Fock vacuum to construct a state that could play the role of a free vacuum in loop quantum gravity. The state we obtain is an element of the gauge-invariant kinematic Hilbert space and restricted to a cutoff graph, as a natural consequence of the momentum cutoff of the original Fock state. It has the form of a Gaussian superposition of spin networks. We show that the peak of the Gaussian lies at weave-like states and derive a relation between the coloring of the weaves and the cutoff scale. Our analysis indicates that the peak weaves become independent of the cutoff length when the latter is much smaller than the Planck length. By the same method, we also construct multiple-graviton states. We discuss the possible use of these states for deriving a perturbation series in loop quantum gravity.Comment: 30 pages, 3 diagrams, treatment of phase factor adde

Revisiting the Simplicity Constraints and Coherent Intertwiners

In the context of loop quantum gravity and spinfoam models, the simplicity constraints are essential in that they allow to write general relativity as a constrained topological BF theory. In this work, we apply the recently developed U(N) framework for SU(2) intertwiners to the issue of imposing the simplicity constraints to spin network states. More particularly, we focus on solving them on individual intertwiners in the 4d Euclidean theory. We review the standard way of solving the simplicity constraints using coherent intertwiners and we explain how these fit within the U(N) framework. Then we show how these constraints can be written as a closed u(N) algebra and we propose a set of U(N) coherent states that solves all the simplicity constraints weakly for an arbitrary Immirzi parameter.Comment: 28 page

Comparison of relativity theories with observer-independent scales of both velocity and length/mass

We consider the two most studied proposals of relativity theories with observer-independent scales of both velocity and length/mass: the one discussed by Amelino-Camelia as illustrative example for the original proposal (gr-qc/0012051) of theories with two relativistic invariants, and an alternative more recently proposed by Magueijo and Smolin (hep-th/0112090). We show that these two relativistic theories are much more closely connected than it would appear on the basis of a naive analysis of their original formulations. In particular, in spite of adopting a rather different formal description of the deformed boost generators, they end up assigning the same dependence of momentum on rapidity, which can be described as the core feature of these relativistic theories. We show that this observation can be used to clarify the concepts of particle mass, particle velocity, and energy-momentum-conservation rules in these theories with two relativistic invariants.Comment: 21 pages, LaTex. v2: Andrea Procaccini (contributing some results from hia Laurea thesis) is added to the list of authors and the paper provides further elements of comparison between DSR1 and DSR2, including the observation that both lead to the same formula for the dependence of momentum on rapidit

CaloCube: a novel calorimeter for high-energy cosmic rays in space

In order to extend the direct observation of high-energy cosmic rays up to the PeV region, highly performing calorimeters with large geometrical acceptance and high energy resolution are required. Within the constraint of the total mass of the apparatus, crucial for a space mission, the calorimeters must be optimized with respect to their geometrical acceptance, granularity and absorption depth. CaloCube is a homogeneous calorimeter with cubic geometry, to maximise the acceptance being sensitive to particles from every direction in space; granularity is obtained by relying on small cubic scintillating crystals as active elements. Different scintillating materials have been studied. The crystal sizes and spacing among them have been optimized with respect to the energy resolution. A prototype, based on CsI(Tl) cubic crystals, has been constructed and tested with particle beams. Some results of tests with different beams at CERN are presented.Comment: Seven pages, seven pictures. Proceedings of INSTR17 Novosibirs

Quantum symmetry, the cosmological constant and Planck scale phenomenology

We present a simple algebraic argument for the conclusion that the low energy limit of a quantum theory of gravity must be a theory invariant, not under the Poincare group, but under a deformation of it parameterized by a dimensional parameter proportional to the Planck mass. Such deformations, called kappa-Poincare algebras, imply modified energy-momentum relations of a type that may be observable in near future experiments. Our argument applies in both 2+1 and 3+1 dimensions and assumes only 1) that the low energy limit of a quantum theory of gravity must involve also a limit in which the cosmological constant is taken very small with respect to the Planck scale and 2) that in 3+1 dimensions the physical energy and momenta of physical elementary particles is related to symmetries of the full quantum gravity theory by appropriate renormalization depending on Lambda l^2_{Planck}. The argument makes use of the fact that the cosmological constant results in the symmetry algebra of quantum gravity being quantum deformed, as a consequence when the limit \Lambda l^2_{Planck} -> 0 is taken one finds a deformed Poincare invariance. We are also able to isolate what information must be provided by the quantum theory in order to determine which presentation of the kappa-Poincare algebra is relevant for the physical symmetry generators and, hence, the exact form of the modified energy-momentum relations. These arguments imply that Lorentz invariance is modified as in proposals for doubly special relativity, rather than broken, in theories of quantum gravity, so long as those theories behave smoothly in the limit the cosmological constant is taken to be small.Comment: LaTex, 19 page

Symmetries and observables in topological gravity

After a brief review of topological gravity, we present a superspace approach to this theory. This formulation allows us to recover in a natural manner various known results and to gain some insight into the precise relationship between different approaches to topological gravity. Though the main focus of our work is on the vielbein formalism, we also discuss the metric approach and its relationship with the former formalism.Comment: 34 pages; a few explanations added in subsection 2.2.1, published version of pape

Ponzano-Regge model revisited III: Feynman diagrams and Effective field theory

We study the no gravity limit G_{N}-> 0 of the Ponzano-Regge amplitudes with massive particles and show that we recover in this limit Feynman graph amplitudes (with Hadamard propagator) expressed as an abelian spin foam model. We show how the G_{N} expansion of the Ponzano-Regge amplitudes can be resummed. This leads to the conclusion that the dynamics of quantum particles coupled to quantum 3d gravity can be expressed in terms of an effective new non commutative field theory which respects the principles of doubly special relativity. We discuss the construction of Lorentzian spin foam models including Feynman propagatorsComment: 46 pages, the wrong file was first submitte

Doubly Special Relativity and de Sitter space

In this paper we recall the construction of Doubly Special Relativity (DSR) as a theory with energy-momentum space being the four dimensional de Sitter space. Then the bases of the DSR theory can be understood as different coordinate systems on this space. We investigate the emerging geometrical picture of Doubly Special Relativity by presenting the basis independent features of DSR that include the non-commutative structure of space-time and the phase space algebra. Next we investigate the relation between our geometric formulation and the one based on quantum $\kappa$-deformations of the Poincar\'e algebra. Finally we re-derive the five-dimensional differential calculus using the geometric method, and use it to write down the deformed Klein-Gordon equation and to analyze its plane wave solutions.Comment: 26 pages, one formula (67) corrected; some remarks adde