Albert Much

Quantum mechanical effects from deformation theory

We consider deformations of quantum mechanical operators by using the novel construction tool of warped convolutions. The deformation enables us to obtain several quantum mechanical effects where electromagnetic and gravitomagnetic fields play a role. Furthermore, a quantum plane can be defined by using the deformation techniques. This in turn gives an experimentally verifiable effect.

Wedge-Local Quantum Fields on a Nonconstant Noncommutative Spacetime

Within the framework of warped convolutions we deform the massless free scalar field. The deformation is performed by using the generators of the special conformal transformations. The investigation shows that the deformed field turns out to be wedge-local. Furthermore, it is shown that the spacetime induced by the deformation with the special conformal operators is nonconstant noncommutative. The noncommutativity is obtained by calculating the deformed commutator of the coordinates.

Self-adjointness of deformed unbounded operators

We consider deformations of unbounded operators by using the novel construction tool of warped convolutions. By using the Kato-Rellich theorem, we show that unbounded self-adjoint deformed operators are self-adjoint if they satisfy a certain condition. This condition proves itself to be necessary for the oscillatory integral to be well-defined. Moreover, different proofs are given for self-adjointness of deformed unbounded operators in the context of quantum mechanics and quantum field theory.

Relativistic corrections to the Moyal-Weyl spacetime

We use the framework of quantum field theory to obtain by deformation the Moyal-Weyl spacetime. This idea is extracted from recent progress in deformation theory concerning the emergence of the quantum plane of the Landau-quantization. The quantum field theoretical emerging spacetime is not equal to the standard Moyal-Weyl plane, but terms resembling relativistic corrections occur.

Curving flat space-time by deformation quantization?

We use a deformed differential structure to obtain a curved metric by a deformation quantization of the flat space-time. In particular, by setting the deformation parameters to be equal to physical constants, we obtain the Friedmann-Robertson-Walker (FRW) model for inflation and a deformed version of the FRW space-time. By calculating classical Einstein-equations for the extended space-time, we obtain non-trivial solutions. Moreover, in this framework, we obtain the Moyal-Weyl, i.e., a constant non-commutative space-time, as a consistency condition.

Noncommutative Riemannian geometry from quantum spacetime generated by twisted Poincaré group

We investigate a quantum geometric space in the context of what could be considered an emerging effective theory from quantum gravity. Specifically we consider a two-parameter class of twisted Poincare algebras, from which Lie-algebraic noncommutativities of the translations are derived as well as associative star-products, deformed Riemannian geometries, Lie-algebraic twisted Minkowski spaces, and quantum effects that arise as noncommutativities. Starting from a universal differential algebra of forms based on the above-mentioned Lie-algebraic noncommutativities of the translations, we construct the noncommutative differential forms and inner and outer derivations, which are the noncommutative equivalents of the vector fields in the case of commutative differential geometry. Having established the essentials of this formalism, we construct a bimodule, which is required to be central under the action of the inner derivations in order to have well-defined contractions and from where the algebraic dependenc...