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J. Kowalski-Glikman

Publications and source records attributed to J. Kowalski-Glikman.

At least 37 records · Page 2Linked to original sources
arXiv2009

A bound on Planck-scale modifications of the energy-momentum composition rule from atomic interferometry

High sensitivity measurements in atomic spectroscopy were recently used in Amelino-Camelia et. al. to constraint the form of possible modifications of the energy-momentum dispersion relation resulting from Lorentz invariance violation (LIV). In this letter we show that the same data can be used successfully to set experimental bounds on deformations of the energy-momentum composition rule. Such modifications are natural in models of deformed Lorentz symmetry which are relevant in certain quantum gravity scenarios. We find the bound for the deformation parameter $κ$ to be a few orders of magnitude below the Planck scale and of the same magnitude as the next-to-leading order effect found in Amelino-Camelia et. al. We briefly discuss how it would be possible to distinguish between these two scenarios.

hep-th↗
arXiv2009

Supergravity as a constrained BF theory

In this paper we formulate ${\cal N}=1$ supergravity as a constrained $BF$ theory with $OSp(4|1)$ gauge superalgebra. We derive the modified supergravity Lagrangian that, apart from the standard supergravity with negative cosmological constant, contains terms proportional to the (inverse of) Immirzi parameter. Although these terms do not change classical field equations, they might be relevant in quantum theory. We briefly discuss the perturbation theory around the supersymmetric topological vacuum.

hep-th↗
arXiv2009

Lorentz invariant field theory on kappa-Minkowski space

It is by now well established that the momentum space dual to the non-commutative $κ$-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 $κ$-deformed complex quantum field.

hep-th↗
arXiv2009

$κ$--Rindler space

In this paper we construct, and investigate some thermal properties of, the non-commutative counterpart of Rindler space, which we call $κ$--Rindler space. This space is obtained by changing variables in the defining commutators of $κ$--Minkowski space. We then re-derive the commutator structure of $κ$--Rindler space with the help of an appropriate star product, obtained from the $κ$--Minkowski one. Using this star product, following the idea of Padmanabhan, we find the leading order, $1/κ$ correction to the Hawking thermal spectrum.

hep-th↗
arXiv2009

Star product and interacting fields on $κ$-Minkowski space

In this note we extend the methods developed by Freidel et al. [arXiv:hep-th/0612170] to derive the form of $ϕ^4$ interaction term in the case of scalar field theory on $κ$-Minkowski space, defined in terms of star product. We present explicit expressions for the $κ$-Minkowski star product. Having obtained the the interaction term we use the resulting deformed conservation rules to investigate if they lead to any threshold anomaly, and we find that in the leading order they do not, as expected.

hep-th↗
arXiv2007

Field theory on $κ$--Minkowski space revisited: Noether charges and breaking of Lorentz symmetry

This paper is devoted to detailed investigations of free scalar field theory on $κ$-Minkowski space. After reviewing necessary mathematical tools we discuss in depth the Lagrangian and solutions of field equations. We analyze the spacetime symmetries of the model and construct the conserved charges associated with translational and Lorentz symmetry. We show that the version of the theory usually studied breaks Lorentz invariance in a subtle way: There is an additional trans-Planckian mode present, and an associated conserved charge (the number of such modes) is not a Lorentz scalar.

hep-th↗
arXiv2006

Can we see gravitational collapse in (quantum) gravity perturbation theory?

In this paper, by making use of the perturbative expansion around topological field theory we are trying to understand why the standard perturbation theory for General Relativity, which starts with linearized gravity does not see gravitational collapse. We start with investigating classical equations of motion. For zero Immirzi parameter the ambiguity of the standard perturbative expansion is reproduced. This ambiguity is related to the appearance of the linearized diffeomorphism symmetry, which becomes unlinked from the original diffeomorphism symmetry. Introducing Immirzi parameter makes it possible to restore the link between these two symmetries and thus removes the ambiguity, but at the cost of making classical perturbation theory rather intractable. Then we argue that the two main sources of complexity of perturbation theory, infinite number of degrees of freedom and non-trivial curvature of the phase space of General Relativity could be disentangled when studying {\it quantum} amplitudes. As an illustration we consider zero order approximation in quantum perturbation theory. We identify relevant observables, and sketch their quantization. We find some indications that this zero order approximation might be described by Doubly Special Relativity.

gr-qc↗
arXiv2005

The Free Particle in Deformed Special Relativity

The phase space of a classical particle in DSR contains de Sitter space as the space of momenta. We start from the standard relativistic particle in five dimensions with an extra constraint and reduce it to four dimensional DSR by imposing appropriate gauge fixing. We analyze some physical properties of the resulting theories like the equations of motion, the form of Lorentz transformations and the issue of velocity. We also address the problem of the origin and interpretation of different bases in DSR.

hep-th↗
arXiv2005

Scalar field theory on $κ$-Minkowski space-time and Doubly Special Relativity

In this paper we recall the construction of scalar field action on $κ$-Minkowski space-time and investigate its properties. In particular we show how the co-product of $κ$-Poincaré algebra of symmetries arises from the analysis of the symmetries of the action, expressed in terms of Fourier transformed fields. We also derive the action on commuting space-time, equivalent to the original one. Adding the self-interaction $Φ^4$ term we investigate the modified conservation laws. We show that the local interactions on $κ$-Minkowski space-time give rise to 6 inequivalent ways in which energy and momentum can be conserved at four-point vertex. We discuss the relevance of these results for Doubly Special Relativity.

hep-th↗
arXiv2004

Quantum $κ$-Poincaré Algebra from de Sitter Space of Momenta

There is a growing number of physical models, like point particle(s) in 2+1 gravity or Doubly Special Relativity, in which the space of momenta is curved, de Sitter space. We show that for such models the algebra of space-time symmetries possesses a natural Hopf algebra structure. It turns out that this algebra is just the quantum $κ$-Poincaré algebra.

hep-th↗
arXiv2004

Triply Special Relativity

We describe an extension of special relativity characterized by {\it three} invariant scales, the speed of light, $c$, a mass, $κ$ and a length $R$. This is defined by a non-linear extension of the Poincare algerbra, $\cal A$, which we describe here. For $R\to \infty$, $\cal A$ becomes the Snyder presentation of the $κ$-Poincare algebra, while for $κ\to \infty$ it becomes the phase space algebra of a particle in deSitter spacetime. We conjecture that the algebra is relevant for the low energy behavior of quantum gravity, with $κ$ taken to be the Planck mass, for the case of a nonzero cosmological constant $Λ= R^{-2}$. We study the modifications of particle motion which follow if the algebra is taken to define the Poisson structure of the phase space of a relativistic particle.

hep-th↗
arXiv2003

Phase spaces of Doubly Special Relativity

We show that depending on the direction of deformation of $κ$-Poincaré algebra (time-like, space-like, or light-like) the associated phase spaces of single particle in Doubly Special Relativity theories have the energy-momentum spaces of the form of de Sitter, anti-de Sitter, and flat space, respectively.

hep-th↗
arXiv2003

Velocity of particles in Doubly Special Relativity

Doubly Special Relativity (DSR) is a class of theories of relativistic motion with two observer-independent scales. We investigate the velocity of particles in DSR, defining velocity as the Poisson bracket of position with the appropriate hamiltonian, taking care of the non-trivial structure of the DSR phase space. We find the general expression for four-velocity, and we show further that the three-velocity of massless particles equals 1 for all DSR theories. The relation between the boost parameter and velocity is also clarified.

hep-th↗
arXiv2003

Doubly Special Relativity with light-cone deformation

We propose a new Doubly Special Relativity theory based on the generalization of the $κ$-deformation of the Poincaré algebra acting along one of the null directions. We recall the quantum Hopf structure of such deformed Poincaré algebra and use it to derive the phase space commutation relations. As in the DSR based on the standard quantum $κ$-Poincaré algebra we find that the space time is non-commutative. We investigate the fate of the properties of Special Relativity in the null basis: the split of the algebra of Lorentz and momentum generators into kinematical and dynamical parts, the action of the kinematical boost $M^{+-}$, and the emergence of the two dimensional Galilean symmetry.

hep-th↗
arXiv2002

Doubly Special Relativity theories as different bases of $κ$--Poincaré algebra

Doubly Special Relativity (DSR) theory is a theory with two observer-independent scales, of velocity and mass (or length). Such a theory has been proposed by Amelino--Camelia as a kinematic structure which may underline quantum theory of relativity. Recently another theory of this kind has been proposed by Magueijo and Smolin. In this paper we show that both these theories can be understood as particular bases of the $κ$--Poincaré theory based on quantum (Hopf) algebra. This observation makes it possible to construct the space-time sector of Magueijo and Smolin DSR. We also show how this construction can be extended to the whole class of DSRs. It turns out that for all such theories the structure of space-time commutators is the same. This results lead us to the claim that physical predictions of properly defined DSR theory should be independent of the choice of basis.

hep-th↗
arXiv2001

Doubly special quantum and statistical mechanics from quantum $κ$-Poincaré algebra

Recently Amelino--Camelia proposed a ``Doubly Special Relativity'' theory with two observer independent scales (of speed and mass) that could replace the standard Special Relativity at energies close to the Planck scale. Such a theory might be a starting point in construction of quantum theory of space-time. In this paper we investigate the quantum and statistical mechanical consequences of such a proposal. We construct the generalized Newton--Wigner operator and find relations between energy/momentum and frequency/wavevector for position eigenstates of this operator. These relations indicate the existence of a minimum length scale. Next we analyze the statistical mechanics of the corresponding systems. We find that depending on the value of a parameter defining the canonical commutational algebra one has to do either with system with maximal possible temperature or with the one, which in the high temperature limit becomes discrete.

hep-th↗