375 research outputs found
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.
Solutions of Quantum Gravity Coupled to the Scalar Field
We consider the Wheeler-De Witt equation for canonical quantum gravity
coupled to massless scalar field. After regularizing and renormalizing this
equation, we find a one-parameter class of its solutions.Comment: 8 pages, LaTe
2+1 gravity and Doubly Special Relativity
It is shown that gravity in 2+1 dimensions coupled to point particles
provides a nontrivial example of Doubly Special Relativity (DSR). This result
is obtained by interpretation of previous results in the field and by
exhibiting an explicit transformation between the phase space algebra for one
particle in 2+1 gravity found by Matschull and Welling and the corresponding
DSR algebra. The identification of 2+1 gravity as a system answers a
number of questions concerning the latter, and resolves the ambiguity of the
basis of the algebra of observables.
Based on this observation a heuristic argument is made that the algebra of
symmetries of ultra high energy particle kinematics in 3+1 dimensions is
described by some DSR theory.Comment: 8 pages Latex, no figures, typos correcte
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
Lorentz invariant field theory on kappa-Minkowski space
It is by now well established that the momentum space dual to the
non-commutative -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
-deformed complex quantum field.Comment: 10 pages, no figure
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