相关论文: Twist-related geometries on q-Minkowski space

We present a short introductory overview of the non-commutative extensions of several classical physical theories. After a general discussion of the reasons that suggest that the non-commutativity is a major issue that will eventually lead…

Doubly special relativity has been studied for the last twenty years as a way to go beyond the special relativistic kinematics, trying to capture residual effects of a quantum gravity theory. In particular, in doubly special relativity the…

We establish global existence and derive sharp pointwise decay estimates of solutions to cubic Dirac and Dirac-Klein-Gordon systems on a curved background, close to the Minkowski spacetime. By squaring the Dirac operator, we reduce the…

Multidimensional Heisenberg algebras, whose creation and annihilation operators are the N-dimensional vectors, can be injected into simple Lie algebras g. It is demonstrated that the spectrum of their deformations can be investigated using…

Quantization of relativistic point particles coupled to three-dimensional Einstein gravity naturally leads to field theories living on the Lorentz group in their momentum representation. The Lie group structure of momentum space can be…

We review the main features of models where relativistic symmetries are deformed at the Planck scale. We cover the motivations and links to other quantum gravity approaches. We describe in some detail the most studied theoretical…

Without a complete theory of quantum gravity, the question of how quantum fields and quantum particles behave in a superposition of spacetimes seems beyond the reach of theoretical and experimental investigations. Here we use an extension…

Over the last two years, the canonical approach to quantum gravity based on connections and triads has been put on a firm mathematical footing through the development and application of a new functional calculus on the space of gauge…

We investigate deformed superconformal symmetries on non(anti)commutative (super)spaces from the point of view of the Drinfel'd twisted symmetries. We classify all possible twist elements derived from an abelian subsector of the…

In this work we apply the Drinfel'd twist of Hopf algebras to the study of deformed quantum theories. We prove that, by carefully considering the role of the central extension, it is indeed possible to construct the universal enveloping…

We investigate several problems in relativity and particle physics where symmetries play a central role; in all cases geometric properties of Lie groups and their quotients are related to physical effects. The first part is concerned with…

Finsler geometry is a natural and fundamental generalization of Riemann geometry. The Finsler structure depends on both coordinates and velocities. It is defined as a function on tangent bundle of a manifold. We use the Bianchi identities…

In this paper, we introduce the concept of N-dimensional generalized Minkowski space, i.e. a space endowed with a (in general non-diagonal) metric tensor, whose coefficients do depend on a set of non-metrical coodinates. This is the first…

In any attempt to build a quantum theory of gravity, a central issue is to unravel the structure of space-time at the smallest scale. Of particular relevance is the possible definition of coordinate functions within the theory and the study…

Each approach to the quantum-gravity problem originates from expertise in one or another area of theoretical physics. The particle-physics perspective encourages one to attempt to reproduce in quantum gravity as much as possible of the…

In this article, spatially-structured gravitational waves are investigated. Drawing upon analogies between electrodynamics and general relativity, a new gauge is found. We investigate the polarization and degrees of freedom of the resulting…

By virtue of the Noether theorems, the vast gauge redundancy of general relativity provides us with a rich algebra of boundary charges that generate physical symmetries. These charges are located at codimension-2 entangling surfaces called…

We construct the differential geometry of smooth manifolds equipped with an algebraic curvature map acting as an area measure. Area metric geometry provides a spacetime structure suitable for the discussion of gauge theories and strings,…

The covariant form of the field equations for two--dimensional $R^2$--gravity with torsion as well as its Hamiltonian formulation are shown to suggest the choice of the light--cone gauge. Further a one--to--one correspondence between the…

The issue of the transformations of units is treated, mainly, in a geometrical context. It is shown that Weyl-integrable geometry is a consistent framework for the formulation of the gravitational laws since the basic law on which this…