Related papers: A Deformed Poincar\'e Algebra On A Cubic Lattice
We propose a definition of a Poincar\'e algebra for a two dimensional space--time with one discretized dimension. This algebra has the structure of a Hopf algebra. We use the link between Onsager's uniformization of the Ising model and the…
We examine a two-parameter ($\hbar ,$ $\lambda $) deformation of the Poincar\`e algebra which is covariant under the action of $SL_q(2,C).$ When $\lambda \rightarrow 0$ it yields the Poincar\`e algebra, while in the $\hbar\rightarrow 0$…
In this essay we present evidence suggesting that loop quantum gravity leads to deformation of the local Poincar\'e algebra within the limit of high energies. This deformation is a consequence of quantum modification of effective off-shell…
We investigate spin as algebraic structure within the q-deformed Poincare algebra, proceeding in the same manner as in the undeformed case. The q-Pauli-Lubanski vector, the q-spin Casimir, and the q-little algebras for the massless and the…
In the present paper we construct deformations of the Poincar\'e algebra as representations on a noncommutative spacetime with canonical commutation relations. These deformations are obtained by solving a set of conditions by an appropriate…
We analyze the decomposition of the enveloping algebra of the conformal algebra in arbitrary dimension with respect to the mass-squared operator. It emerges that the subalgebra that commutes with the mass-squared is generated by its…
In this letter we derive a deformed Dirac equation invariant under the k-Poincare` quantum algebra. A peculiar feature is that the square of the k-Dirac operator is related to the second Casimir (the k-deformed squared Pauli-Lubanski…
We find a one parameter family of quadratic Poisson structures on ${\bf R}^4\times SL(2,C)$ which satisfies the property {\it a)} that it is preserved under the Lie-Poisson action of the Lorentz group, as well as {\it b)} that it reduces to…
We present Lie-algebraic deformations of Minkowski space with undeformed Poincar\'{e} algebra. These deformations interpolate between Snyder and $\kappa$-Minkowski space. We find realizations of noncommutative coordinates in terms of…
A classical deformation procedure, based on universal enveloping algebras, Casimirs and curvatures of symmetrical homogeneous spaces, is applied to several cases of physical relevance. Starting from the (3+1)D Galilei algebra, we describe…
We examine deformed Poincar\'e algebras containing the exact Lorentz algebra. We impose constraints which are necessary for defining field theories on these algebras and we present simple field theoretical examples. Of particular interest…
We describe the deformed Poincare-conformal symmetries implying the covariance of the noncommutative space obeying Snyder's algebra. Relativistic particle models invariant under these deformed symmetries are presented. A gauge…
Contracting the $h$-deformation of $\SL(2,\Real)$, we construct a new deformation of two dimensional Poincar\'e algebra, the algebra of functions on its group and its differential structure. It is also shown that the Hopf algebra is…
A tensor extension of the Poincar\'e algebra is proposed for the arbitrary dimensions. Casimir operators of the extension are constructed. A possible supersymmetric generalization of this extension is also found in the dimensions $D=2,3,4$.
A new quantum deformation, which we call null-plane, of the (3+1) Poincar\'e algebra is obtained. The algebraic properties of the classical null-plane description are generalized to this quantum deformation. In particular, the classical…
We propose a regular way to construct lattice versions of $W$-algebras, both for quantum and classical cases. In the classical case we write the algebra explicitly and derive the lattice analogue of Boussinesq equation from the Hamiltonian…
A systematic study of non-trivial cubic extensions of the four-dimensional Poincar\'e algebra is undertaken. Explicit examples are given with various techniques (Young tableau, characters etc).
Deformed special relativity is embedded in deformed general relativity using the methods of canonical relativity and loop quantum gravity. Phase-space dependent deformations of symmetry algebras then appear, which in some regimes can be…
Quantum mechanical fluctuations in an interval give rise to the Casimir effect, which destabilizes the size of the interval. This can be problematic in constructing Kaluza-Klein theories. We consider the possibility that a breakdown of the…
We investigate a systematic approach to include curvature corrections to the isometry algebra of flat space-time order-by-order in the curvature scale. The Poincar\'e algebra is extended to a free Lie algebra, with generalised boosts and…