569 research outputs found
Canonical and Lie-algebraic twist deformations of -Poincare and contractions to -Galilei algebras
We propose canonical and Lie-algebraic twist deformations of
-deformed Poincare Hopf algebra which leads to the generalized
-Minkowski space-time relations. The corresponding deformed
-Poincare quantum groups are also calculated. Finally, we perform the
nonrelativistic contraction limit to the corresponding twisted Galilean
algebras and dual Galilean quantum groups.Comment: 16 pages, no figures, v3: few changes provided - version for journal,
v2: submitted incidentally, v4: the page numbers for all references in
preprint version are provide
Field theory on --Minkowski space revisited: Noether charges and breaking of Lorentz symmetry
This paper is devoted to detailed investigations of free scalar field theory
on -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.Comment: 22 pages, 1 figure, formulas in sect. III correcte
-Deformation of Poincar\'e Superalgebra with Classical Lorentz Subalgebra and its Graded Bicrossproduct Structure
The -deformed Poincar{\'e} superalgebra written in Hopf
superalgebra form is transformed to the basis with classical Lorentz subalgebra
generators. We show that in such a basis the -deformed Poincare
superalgebra can be written as graded bicrossproduct. We show that the
-deformed superalgebra acts covariantly on -deformed
chiral superspace.Comment: 13 pages, late
Scalar field propagation in the phi^4 kappa-Minkowski model
In this article we use the noncommutative (NC) kappa-Minkowski phi^4 model
based on the kappa-deformed star product, ({*}_h). The action is modified by
expanding up to linear order in the kappa-deformation parameter a, producing an
effective model on commutative spacetime. For the computation of the tadpole
diagram contributions to the scalar field propagation/self-energy, we
anticipate that statistics on the kappa-Minkowski is specifically
kappa-deformed. Thus our prescription in fact represents hybrid approach
between standard quantum field theory (QFT) and NCQFT on the kappa-deformed
Minkowski spacetime, resulting in a kappa-effective model. The propagation is
analyzed in the framework of the two-point Green's function for low,
intermediate, and for the Planckian propagation energies, respectively.
Semiclassical/hybrid behavior of the first order quantum correction do show up
due to the kappa-deformed momentum conservation law. For low energies, the
dependence of the tadpole contribution on the deformation parameter a drops out
completely, while for Planckian energies, it tends to a fixed finite value. The
mass term of the scalar field is shifted and these shifts are very different at
different propagation energies. At the Planckian energies we obtain the
direction dependent kappa-modified dispersion relations. Thus our
kappa-effective model for the massive scalar field shows a birefringence
effect.Comment: 23 pages, 2 figures; To be published in JHEP. Minor typos corrected.
Shorter version of the paper arXiv:1107.236
Scalar field theory on -Minkowski space-time and Doubly Special Relativity
In this paper we recall the construction of scalar field action on
-Minkowski space-time and investigate its properties. In particular we
show how the co-product of -Poincar\'e 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 term we
investigate the modified conservation laws. We show that the local interactions
on -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.Comment: 17 pages; some editing done, final version to be published in Int. J.
Mod. Phys.
Generalized Weyl systems and kappa-Minkowski space
We introduce the notion of generalized Weyl system, and use it to define
*-products which generalize the commutation relations of Lie algebras. In
particular we study in a comparative way various *-products which generalize
the k-Minkowski commutation relations.Comment: 21 pages, minor corrections and references adde
Newtonian Gravity and the Bargmann Algebra
We show how the Newton-Cartan formulation of Newtonian gravity can be
obtained from gauging the Bargmann algebra, i.e., the centrally extended
Galilean algebra. In this gauging procedure several curvature constraints are
imposed. These convert the spatial (time) translational symmetries of the
algebra into spatial (time) general coordinate transformations, and make the
spin connection gauge fields dependent. In addition we require two independent
Vielbein postulates for the temporal and spatial directions. In the final step
we impose an additional curvature constraint to establish the connection with
(on-shell) Newton-Cartan theory. We discuss a few extensions of our work that
are relevant in the context of the AdS-CFT correspondence.Comment: Latex, 20 pages, typos corrected, published versio
Braided algebras and the kappa-deformed oscillators
Recently there were presented several proposals how to formulate the binary
relations describing kappa-deformed oscillator algebras. In this paper we shall
consider multilinear products of kappa-deformed oscillators consistent with the
axioms of braided algebras. In general case the braided triple products are
quasi-associative and satisfy the hexagon condition depending on the
coassociator . We shall consider only the products
of kappa-oscillators consistent with co-associative braided algebra, with Phi
=1. We shall consider three explicite examples of binary kappa-deformed
oscillator algebra relations and describe briefly their multilinear
coassociative extensions satisfying the postulates of braided algebras. The
third example, describing kappa-deformed oscillators in group manifold approach
to kappa-deformed fourmomenta, is a new result.Comment: v2, 13 pages; Proc. of 2-nd Corfu School on Quantum Gravity and
Quantum Geometry, September 2009, Corfu; Gen. Rel. Grav. (2011),special
Proceedings issue; version in pres
Coproduct and star product in field theories on Lie-algebra non-commutative space-times
We propose a new approach to field theory on -Minkowski
non-commutative space-time, a popular example of Lie-algebra space-time. Our
proposal is essentially based on the introduction of a star product, a
technique which is proving to be very fruitful in analogous studies of
canonical non-commutative space-times, such as the ones recently found to play
a role in the description of certain string-theory backgrounds. We find to be
incorrect the expectation, previously reported in the literature, that the lack
of symmetry of the -Poincare' coproduct should lead to interaction
vertices that are not symmetric under exchanges of the momenta of identical
particles entering the relevant processes. We show that in -Minkowski
the coproduct and the star product must indeed treat momenta in a non-symmetric
way, but the overall structure of interaction vertices is symmetric under
exchange of identical particles. We also show that in -Minkowski field
theories it is convenient to introduce the concepts of "planar" and
"non-planar" Feynman loop-diagrams, again in close analogy with the
corresponding concepts previously introduced in the study of field theories in
canonical non-commutative space-times.Comment: LaTex, 16 pages. Some remarks on the differences between planar and
nonplanar diagrams have been adde
Doubly Special Relativity and de Sitter space
In this paper we recall the construction of Doubly Special Relativity (DSR)
as a theory with energy-momentum space being the four dimensional de Sitter
space. Then the bases of the DSR theory can be understood as different
coordinate systems on this space. We investigate the emerging geometrical
picture of Doubly Special Relativity by presenting the basis independent
features of DSR that include the non-commutative structure of space-time and
the phase space algebra. Next we investigate the relation between our geometric
formulation and the one based on quantum -deformations of the
Poincar\'e algebra. Finally we re-derive the five-dimensional differential
calculus using the geometric method, and use it to write down the deformed
Klein-Gordon equation and to analyze its plane wave solutions.Comment: 26 pages, one formula (67) corrected; some remarks adde
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