Fun from none: deformed symmetries and Fock space

We give a pedagogical introduction to the basics of deformations of relativistic symmetries and the Hilbert spaces of free quantum fields built as their representations. We focus in particular on the example of a $\kappa$-deformed scalar quantum field for which the generators of spatial translations that label the field modes act according to a deformed Leibnitz rule. We explore the richer structure of the $\kappa$-Fock space and point out possible physical consequences of the deformation.Comment: 7 pages, no figures. Invited talk at XXV Max Born Symposium, The Planck scale, Wroclaw (Poland), June 29 - July 3, 2009. To appear in the Proceeding

Dirac spinors for Doubly Special Relativity

We construct a Dirac equation that is consistent with one of the recently-proposed schemes for relativistic transformations with two observer-independent scales (a velocity scale, still naturally identified with the speed-of-light constant, and a length/momentum scale, possibly given by the Planck length/momentum). We exploit the fact that in the energy-momentum sector the transformation laws are governed by a nonlinear realization of the Lorentz group. We find that the nonlinearity, which is due to the introduction of the second observer-independent scale, only induces a mild deformation of the structure of Dirac spinors

HIDDEN ENTANGLEMENT AND UNITARITY AT THE PLANCK SCALE

Attempts to go beyond the framework of local quantum field theory include scenarios in which the action of external symmetries on the quantum fields Hilbert space is deformed. We show how the Fock spaces of such theories exhibit a richer structure in their multi-particle sectors. When the deformation scale is proportional to the Planck energy, such new structure leads to the emergence of a "planckian" mode-entanglement, invisible to an observer that cannot probe the Planck scale. To the same observer, certain unitary processes would appear non-unitary. We show how entanglement transfer to the additional degrees of freedom can provide a potential way out of the black hole information paradox

A glimpse at the flat-spacetime limit of quantum gravity using the Bekenstein argument in reverse

An insightful argument for a linear relation between the entropy and the area of a black hole was given by Bekenstein using only the energy-momentum dispersion relation, the uncertainty principle, and some properties of classical black holes. Recent analyses within String Theory and Loop Quantum Gravity describe black-hole entropy in terms of a dominant contribution, which indeed depends linearly on the area, and a leading log-area correction. We argue that, by reversing the Bekenstein argument, the log-area correction can provide insight on the energy-momentum dispersion relation and the uncertainty principle of a quantum-gravity theory. As examples we consider the energy-momentum dispersion relations that recently emerged in the Loop Quantum Gravity literature and the Generalized Uncertainty Principle that is expected to hold in String Theory.Comment: 7 pages, LaTex; this essay received an "honorable mention" in the 2004 Essay Competition of the Gravity Research Foundation; submitted to IJMPD on 23 June 2004; published as Int.J.Mod.Phys.D13:2337-2343,200

Lorentz invariant field theory on kappa-Minkowski space

It is by now well established that the momentum space dual to the non-commutative $\kappa$-Minkowski space is a submanifold of de Sitter space. It has been noticed recently that field theories built on such momentum space suffer from a subtle form of Lorentz symmetry breaking. Namely, for any negative energy mode the allowed range of rapidities is bounded above. In this paper we construct a complex scalar field theory with a modified action of Lorentz generators which avoids this problem. For such theory we derive conserved charges corresponding to translational and U(1) symmetries. We also discuss in some details the inner product and Hilbert space structure of the $\kappa$-deformed complex quantum field.Comment: 10 pages, no figure

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

On side refrigerant measurement of heat pump seasonal performances

International audienceHeat pump systems have become very popular for space heating in the residential sector in Europe. However, there is no data available on the in situ seasonal heating performances of air-to-air heat pumps. This is due to the difficulty of measuring their thermal capacity on field over a long period. Several methods relying on air flow rate and enthalpy measurements are being considered for in-situ measurement for air-to-air heat pumps. But accuracy and reliability of these methods are still unknown. In this paper, we show the results of a method based on intrusive measurements (on the refrigerant side) adapted to the dynamic behavior. This method uses Coriolis flow meters measures for the refrigerant flow rate and for enthalpies. Results confirm that the refrigerant density measurement with a Coriolis flow meter can help to predict the refrigerant vapor quality with a satisfying accuracy if the quality is not too high. The method is validated by testing an air-to-water heat pump in laboratory and by using the water enthalpy method as a reference. The experimental results show that the method is reliable in dynamic conditions (including during the defrosting periods). This internal method can be used as a reference to check the air enthalpy method for air-to-air heat pumps

Classical paradoxes of locality and their possible quantum resolutions in deformed special relativity

In deformed or doubly special relativity (DSR) the action of the lorentz group on momentum eigenstates is deformed to preserve a maximal momenta or minimal length, supposed equal to the Planck length. The classical and quantum dynamics of a particle propagating in kappa-Minkowski spacetime is discussed in order to examine an apparent paradox of locality which arises in the classical dynamics. This is due to the fact that the Lorentz transformations of spacetime positions of particles depend on their energies, so whether or not a local event, defined by the coincidence of two or more particles, takes place appears to depend on the frame of reference of the observer. Here it is proposed that the paradox arises only in the classical picture, and may be resolved when the quantum dynamics is taken into account. If so, the apparent paradoxes arise because it is inconsistent to study physics in which Planck's constant is zero but the Planck length is non-vanishing. This may be relevant for phenomenology such as observations by FERMI, because at leading order there is both a direct and a stochastic dependence of arrival time on energy, due to an additional spreading of wavepackets.Comment: LaTeX, 28 pages, no figures, substantially revise

On tunneling across horizons

The tunneling method for stationary black holes in the Hamilton-Jacobi variant is reconsidered in the light of various critiques that have been moved against. It is shown that once the tunneling trajectories have been correctly identified the method isfree from internal inconsistencies, it is manifestly covariant, it allows for the extension to spinning particles and it can even be used without solving the Hamilton-Jacobi equation. These conclusions borrow support on a simple analytic continuation of the classical action of a pointlike particle, made possible by the unique assumption that it should be analytic in complexified Schwarzschild or Kerr-Newman spacetimes. A more general version of the Parikh-Wilczek method will also be proposed along these lines.Comment: Latex Document, 5 pages, 2 figures, title changed, abstract changed, added references, results unchange

What kinds of coordinate can keep the Hawking temperature invariant for the static spherically symmetric black hole?

By studying the Hawking radiation of the most general static spherically symmetric black hole arising from scalar and Dirac particles tunnelling, we find the Hawking temperature is invariant in the general coordinate representation (\ref{arbitrary1}), which satisfies two conditions: a) its radial coordinate transformation is regular at the event horizon; and b) there is a time-like Killing vector.Comment: 10 page