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31
Analogue Gravity
- Living Rev. Rel
"... Analogue models of (and for) gravity have a long and distinguished history dating back to the earliest years of general relativity. In this review article we will discuss the history, aims, results, and future prospects for the various analogue models. We start the discussion by presenting a particu ..."
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Cited by 70 (27 self)
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Analogue models of (and for) gravity have a long and distinguished history dating back to the earliest years of general relativity. In this review article we will discuss the history, aims, results, and future prospects for the various analogue models. We start the discussion by presenting a particularly simple example of an analogue model, before exploring the rich history and complex tapestry of models discussed in the literature. The last decade in particular has seen a remarkable and sustained development of analogue gravity ideas, leading to some hundreds of published articles, a workshop, two books, and this review article. Future prospects for the analogue gravity programme also look promising, both on the experimental front (where technology is rapidly advancing) and on the theoretical front (where variants of analogue models can be used as a springboard for radical attacks on the problem
Modern tests of Lorentz invariance
- Living Rev. Rel
"... Motivated by ideas about quantum gravity, a tremendous amount of effort over the past decade has gone into testing Lorentz invariance in various regimes. This review summarizes both the theoretical frameworks for tests of Lorentz invariance and experimental advances that have made such high precisio ..."
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Cited by 55 (1 self)
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Motivated by ideas about quantum gravity, a tremendous amount of effort over the past decade has gone into testing Lorentz invariance in various regimes. This review summarizes both the theoretical frameworks for tests of Lorentz invariance and experimental advances that have made such high precision tests possible. The current constraints on Lorentz violating effects from both terrestrial experiments and astrophysical observations are presented.
Free q-deformed relativistic wave equations by representation theory
- Eur. Phys. J. C
"... In a representation theoretic approach a free q-relativistic wave equation must be such, that the space of solutions is an irreducible representation of the q-Poincaré algebra. It is shown how this requirement uniquely determines the q-wave equations. As examples, the q-Dirac equation (including q-g ..."
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Cited by 11 (1 self)
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In a representation theoretic approach a free q-relativistic wave equation must be such, that the space of solutions is an irreducible representation of the q-Poincaré algebra. It is shown how this requirement uniquely determines the q-wave equations. As examples, the q-Dirac equation (including q-gamma matrices which satisfy a q-Clifford algebra), the q-Weyl equations, and the q-Maxwell equations are computed explicitly. 1
2003 On the Lorentz transformations of momentum and energy
- A 18 2019 (Preprint hep-th/0301153
"... Motivated by ultra-high-energy cosmic ray physics, we discuss all the possible alternatives to the familiar Lorentz transformations of the momentum and the energy of a particle. Starting from natural physical requirements, we exclude all the possibilities, apart from the ones which arise from the us ..."
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Cited by 4 (1 self)
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Motivated by ultra-high-energy cosmic ray physics, we discuss all the possible alternatives to the familiar Lorentz transformations of the momentum and the energy of a particle. Starting from natural physical requirements, we exclude all the possibilities, apart from the ones which arise from the usual four-vector transformations by means of a change of coordinates in the mass-shell. This result confirms the remark, given in a preceding paper, that, in a theory without preferred inertial frames, one can always define a linearly transforming energy parameter to which the GZK cutoff argument can be applied. We also discuss the connections between the conservation and the transformation properties of energy-momentum and the relation between energy-momentum and velocity.
Electric Chern-Simons term, enlarged exotic Galilei symmetry and noncommutative plane
, 2005
"... The extended exotic planar model for a charged particle is constructed. It includes a Chern-Simons-like term for a dynamical electric field, but produces usual equations of motion for the particle in background constant uniform electric and magnetic fields. The electric Chern-Simons term is responsi ..."
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Cited by 3 (0 self)
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The extended exotic planar model for a charged particle is constructed. It includes a Chern-Simons-like term for a dynamical electric field, but produces usual equations of motion for the particle in background constant uniform electric and magnetic fields. The electric Chern-Simons term is responsible for the non-commutativity of the boost generators in the ten-dimensional enlarged exotic Galilei symmetry algebra of the extended system. The model admits two reduction schemes by the integrals of motion, one of which reproduces the usual formulation for the charged particle in external constant electric and magnetic fields with associated field-deformed Galilei symmetry, whose commuting boost generators are identified with the nonlocal in time Noether charges reduced on-shell. Another reduction scheme, in which electric field transmutes into the commuting space translation generators, extracts from the model a free particle on the noncommutative plane described by the two-fold centrally extended Galilei group of the non-relativistic anyons.
Scalar field theory on κ-Minkowski space-time and Doubly Special Relativity
, 2008
"... In this paper we recall the construction of scalar field action on κ-Minkowski spacetime 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 fi ..."
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In this paper we recall the construction of scalar field action on κ-Minkowski spacetime 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. 1
Twisted (2+1) κ-AdS Algebra, Drinfel’d Doubles and Non-Commutative Spacetimes?
"... Abstract. We construct the full quantum algebra, the corresponding Poisson–Lie structure and the associated quantum spacetime for a family of quantum deformations of the isometry algebras of the (2+1)-dimensional anti-de Sitter (AdS), de Sitter (dS) and Minkowski spaces. These deformations correspon ..."
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Abstract. We construct the full quantum algebra, the corresponding Poisson–Lie structure and the associated quantum spacetime for a family of quantum deformations of the isometry algebras of the (2+1)-dimensional anti-de Sitter (AdS), de Sitter (dS) and Minkowski spaces. These deformations correspond to a Drinfel’d double structure on the isometry algebras that are motivated by their role in (2+1)-gravity. The construction includes the cosmological constant Λ as a deformation parameter, which allows one to treat these cases in a common framework and to obtain a twisted version of both space- and time-like κ-AdS and dS quantum algebras; their flat limit Λ → 0 leads to a twisted quantum Poincare ́ algebra. The resulting non-commutative spacetime is a nonlinear Λ-deformation of the κ-Minkowski one plus an additional contribution generated by the twist. For the AdS case, we relate this quantum deformation to two copies of the standard (Drinfel’d–Jimbo) quantum deformation of the Lorentz group in three dimensions, which allows one to determine the impact of the twist. Key words: (2+1)-gravity; deformation; non-commutative spacetime; anti-de Sitter; cosmo-logical constant; quantum groups; Poisson–Lie groups; contraction 2010 Mathematics Subject Classification: 16T20; 81R50; 81R60 1
Observable Algebra
, 2008
"... A physical applicability of normed split-algebras, such as hyperbolic numbers, split-quaternions and split-octonions is considered. We argue that the observable geometry can be described by the algebra of split-octonions, which is naturally equipped by zero divisors (the elements of split-algebras c ..."
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A physical applicability of normed split-algebras, such as hyperbolic numbers, split-quaternions and split-octonions is considered. We argue that the observable geometry can be described by the algebra of split-octonions, which is naturally equipped by zero divisors (the elements of split-algebras corresponding to zero norm). In such a picture physical phenomena are described by the ordinary elements of chosen algebra, while the zero divisors give raise the coordinatization and two fundamental constants, namely velocity of light and Planck constant. It turns to be possible that uncertainty principle appears from the condition of positively defined norm, and has the same geometrical meaning as the existence of the maximal value of speed. The property of non-associativity of octonions could correspond to the appearance of fundamental probabilities in physics. Grassmann elements and a non-commutativity of space coordinates, which are widely used in various physical theories, appear naturally in our approach. PACS numbers: 01.55.+b; 02.10.De; 11.10.Kk 1
