# q‐deformed relativistic wave equations

@article{Pillin1993qdeformedRW, title={q‐deformed relativistic wave equations}, author={M. Pillin}, journal={Journal of Mathematical Physics}, year={1993}, volume={35}, pages={2804-2817} }

Based on the representation theory of the q‐deformed Lorentz and Poincare symmetries q‐deformed relativistic wave equation are constructed. The most important cases of the Dirac, Proca, Rarita–Schwinger, and Maxwell equations are treated explicitly. The q‐deformed wave operators look structurally like the undeformed ones but they consist of the generators of a noncommutative Minkowski space. The existence of the q‐deformed wave equations together with previous results on the representation… Expand

#### 31 Citations

Free q-deformed relativistic wave equations by representation theory

- Physics, Mathematics
- 2001

Abstract.In a representation theoretic approach a free q-relativistic wave equation must have the property that the space of solutions is an irreducible representation of the q-Poincaré algebra. It… Expand

h-deformed Lorentz relativistic invariant equations

- Physics
- 1998

After a brief report on theh-deformations of the Lorentz group and their associated spacetimes, we discuss the Klein-Gordon operator. It is found that theh-deformed d’Alembertian has plane wave… Expand

2 q-Spinor Wave Functions 2 . 1 General q-Wave Equations

In a representation theoretic approach a free q-relativistic wave equation must be such, that the space of solutions is an irreducible representation of the q-Poincaré algebra. It is shown how this… Expand

On representations of the q-deformed Lorentz and Poincare algebras

- Physics
- 1994

We construct explicitly all finite-dimensional representations of the quantum Lorentz group SLq(2,C). Based on this we prove that the q-deformed Lorentz algebra which was recently introduced can be… Expand

Deformed field equations

- Physics
- 1995

Abstract A q-deformed Klein—Gordon equation describing nonlinear corrections to the usual linear equation is given introducing a dependence of the frequency of mode vibrations on their amplitudes.… Expand

The influence of the κ-Poincaré- and q-deformations of the energy of the Klein-Gordon Coulomb system

- Physics
- 1994

Abstract Proofs are given that the κ-Poincare Klein-Gordon Coulomb system with a trigonometric like deformation can be solved, to first 1 N - order , for selected values of the deformation parameter.… Expand

Conservation Laws for Linear Equations on Quantum Minkowski Spaces

- Mathematics, Physics
- 1998

Abstract:The general, linear equations with constant coefficients on quantum Minkowski spaces are considered and the explicit formulae for their conserved currents are given. The proposed procedure… Expand

q-conformally covariant q-Minkowski space-time and invariant equations

- Mathematics
- 1997

We present explicitly the covariant action of the q-conformal algebra on the q-Minkowski space we proposed earlier. We also present some q-conformally invariant equations, namely a hierarchy of… Expand

Conservation Laws for Linear Equations on Quantum

- Mathematics
- 1998

The general, linear equations with constant coefficients on quantum Minkowski spaces are considered and the explicit formulae for their conserved cur- rents are given. The proposed procedure can be… Expand

Generalized q‐exponentials related to orthogonal quantum groups and Fourier transformations of noncommutative spaces

- Mathematics, Physics
- 1995

Essential prerequisites for the study of q‐deformed physics are particle states in position and momentum representation. In order to relate x and p space by Fourier transformations the appropriate… Expand

#### References

SHOWING 1-10 OF 38 REFERENCES

q-Deformed relativistic one-particle states

- Physics
- 1993

Abstract Hilbert space representations of the q -deformed Poincare algebra are constructed. The states of these representations can be interpreted as q -deformed relativistic one-particle states with… Expand

A QUANTUM LORENTZ GROUP

- Physics
- 1991

We examine the properties of the quantum Lorentz group SOq(3, 1) using the matrix given in Ref. 14. We show that this matrix together with the q-deformed metric C provide a representation of a BWM… Expand

q-Deformed Poincaré algebra

- Mathematics
- 1992

Theq-differential calculus for theq-Minkowski space is developed. The algebra of theq-derivatives with theq-Lorentz generators is found giving theq-deformation of the Poincaré algebra. The reality… Expand

New quantum Poincaré algebra and κ-deformed field theory

- Physics
- 1992

Abstract We derive a new real quantum Poincare algebra with standard real structure, obtained by contraction of Uq(O(3,2)) (q real), which is a standard real Hopf algebra, depending on a… Expand

Six generatorq-deformed Lorentz algebra

- Mathematics
- 1991

The six generator deformation of the Lorentz algebra is presented. The Hopf algebra structure and the reality conditions are found. The chiral decomposition of SL(2, C) is generalized to theq-case.… Expand

Realizations of the Unitary Representations of the Inhomogeneous Space-Time Groups II. Covariant Realizations of the Poincaré Group

- Mathematics, Physics
- 1974

The aim of Part I1 of this paper is to try to give a unified, systematic description of the different covariant wave-functions (Dirac, Fierz, Bargmann-Wigner etc.) which can be used to carry the same… Expand

On Unitary Representations of the Inhomogeneous Lorentz Group

- Mathematics
- 1939

It is perhaps the most fundamental principle of Quantum Mechanics that the system of states forms a linear manifold,1 in which a unitary scalar product is defined.2 The states are generally… Expand

Low-dimensional topology and quantum field theory

- Mathematics
- 1993

Combinatorial Recoupling Theory and 3Manifold Invariants L.H. Kauffman. Quantum Field Theory and A,B,C,D, IRF Model Invariants O.J. Backofen. On Combinatorial 3-Manifold Invariants G. Felder.… Expand

FEYNMAN RULES FOR ANY SPIN

- Physics
- 1964

The explicit Feynman rules are given for massive particles of any spin j, in both a 2j+1-component and a 2(2j+l)-component formalism. The propagators involve matrices which transform like symmetric… Expand

Representations of the quantum group SUq(2) and the little q-Jacobi polynomials

- Mathematics
- 1991

Abstract In this paper, we study the finite dimensional unitary representations of the quantum group SUq(2). Then we obtain the Peter-Weyl theorem for SUq(2) and the matrix elements of these unitary… Expand