# Deformed oscillator algebras and QFT in κ-Minkowski spacetime

@article{Govindarajan2009DeformedOA, title={Deformed oscillator algebras and QFT in $\kappa$-Minkowski spacetime}, author={T. R. Govindarajan and Kumar S. Gupta and E. Harikumar and Stjepan Meljanac and Daniel Meljanac}, journal={Physical Review D}, year={2009}, volume={80}, pages={025014} }

In this paper, we study the deformed statistics and oscillator algebras of quantum fields defined in $\ensuremath{\kappa}$-Minkowski spacetime. The twisted flip operator obtained from the twist associated with the star product requires an enlargement of the Poincar\'e algebra to include the dilatation generators. Here we propose a novel notion of a fully covariant flip operator and show that to the first order in the deformation parameter it can be expressed completely in terms of the Poincar…

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## 64 References

### kappa-Minkowski spacetime as the result of Jordanian twist deformation

- Mathematics
- 2009

Two one-parameter families of twists providing {kappa}-Minkowski * product deformed spacetime are considered: Abelian and Jordanian. We compare the derivation of quantum Minkowski space from two…

### Towards quantum noncommutative κ-deformed field theory

- Physics, Mathematics
- 2008

We introduce a new {kappa}-star product describing the multiplication of quantized {kappa}-deformed free fields. The {kappa} deformation of local free quantum fields originates from two sources:…

### Deformed special relativity and deformed symmetries in a canonical framework

- Mathematics
- 2007

In this paper we have studied the nature of kinematical and dynamical laws in $\ensuremath{\kappa}$-Minkowski spacetime from a new perspective: the canonical phase space approach. We discuss a…

### Classical and Quantum Mechanics of Free κ-Relativistic Systems

- Physics
- 1993

We consider the Hamiltonian and Lagrangian formalism describing free κ-relativistic particles with their four-momenta constrained to the κ-deformed mass shell. We study the formalism with commuting…

### Twisted gauge and gravity theories on the Groenewold-Moyal plane

- Mathematics
- 2007

Recent work indicates an approach to the formulation of diffeomorphism invariant quantum field theories (qft's) on the Groenewold-Moyal plane. In this approach to the qft's, statistics gets twisted…

### κ-Minkowski spacetime and the star product realizations

- Mathematics
- 2008

We investigate a Lie algebra-type κ-deformed Minkowski spacetime with undeformed Lorentz algebra and mutually commutative vector-like Dirac derivatives. There are infinitely many realizations of…

### Coproduct and star product in field theories on Lie-algebra noncommutative space-times

- Mathematics
- 2002

We propose a new approach to field theory on $\kappa$-Minkowski non-commutative space-time, a popular example of Lie-algebra space-time. Our proposal is essentially based on the introduction of a…

### Noncommutative differential forms on the kappa-deformed space

- Mathematics
- 2009

We construct a differential algebra of forms on the kappa-deformed space. For a given realization of noncommutative coordinates as formal power series in the Weyl algebra we find an infinite family…

### A gravity theory on noncommutative spaces

- Mathematics
- 2005

A deformation of the algebra of diffeomorphisms is constructed for canonically deformed spaces with constant deformation parameter θ. The algebraic relations remain the same, whereas the…