Volkmar Putz

Space/time non-commutative field theories and causality

Abstract. As argued previously, amplitudes of quantum field theories on non-commutative space and time cannot be computed using naïve path integral Feynman rules. One of the proposals is to use the Gell-Mann-Low formula with time-ordering applied before performing the integrations. We point out that the previously given prescription should rather be regarded as an interaction-point time-ordering. Causality is explicitly violated inside the region of interaction. It is nevertheless a consistent procedure, which seems to be related to the interaction picture of quantum mechanics. In this framework we compute the one-loop self-energy for a space/time non-commutative

Perturbative Chern-Simons theory on noncommutative Bbb R3

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THE ENERGY–MOMENTUM TENSOR IN NONCOMMUTATIVE GAUGE FIELD MODELS

theory. Although in all intermediate steps only three-momenta play a rôle, the final result is manifestly Lorentz covariant and agrees with the naïve calculation. Deriving the Feynman rules for general graphs, we show, however, that such a picture holds for tadpole lines only.

Towards UV finite quantum field theoriesfrom non-local field operators

A U(N) Chern-Simons theory on non-commutative 3 is constructed as a θ-deformed field theory. The model is characterized by two symmetries: the BRST-symmetry and the topological linear vector supersymmetry. It is shown that the theory is finite and θ-independent at the one-loop level and that the calculations respect the restriction of the topological supersymmetry. Thus the topological θ-deformed Chern-Simons theory is an example of a model which is non singular in the limit θ→0.

Quantum electrodynamics in the squeezed vacuum state: Electron mass shift

We discuss the different possibilities of constructing the various energy–momentum tensors for noncommutative gauge field models. We use Jackiws method in order to get symmetric and gauge invariant stress tensors — at least for commutative gauge field theories. The noncommutative counterparts are analyzed with the same methods. The issues for the noncommutative cases are worked out.

Quantum music

Abstract.A non-local toy model whose interaction consists of smeared, non-local field operators is presented. We work out the Feynman rules and propose a power counting formula for arbitrary graphs. Explicit calculations for one loop graphs show that their contribution is finite for sufficient smearing and agree with the power counting formula. UV/IR mixing does not occur.

Consistent construction of perturbation theoryon non-commutative spaces

Due to the non-vanishing average photon population of the squeezed vacuum state. finite corrections to the scattering matrix are obtained. The lowest-order contribution to the electron mass shift for a one-mode squeezed vacuum state is given by δm(Ω,s)/m = α(2/π)(Ω/m) 2 sinh 2 (s), where Ω and s stand for the mode frequency and the squeeze parameter and α for the fine-structure constant, respectively.

Can a Computer be "Pushed" to Perform Faster-Than-Light?

We consider ways of conceptualizing, rendering and perceiving quantum music and quantum art in general. Thereby, we give particular emphasis to its non-classical aspects, such as coherent superposition and entanglement.

Can a computer be

Abstract.We examine the effect of non-local deformations on the applicability of interaction point time ordered perturbation theory (IPTOPT) based on the free Hamiltonian of local theories. The usual argument for the case of quantum field theory on a non-commutative space (based on the fact that the introduction of star products in bilinear terms does not alter the action) is not applicable to IPTOPT due to several discrepancies compared to the naive path integral approach when non-commutativity involves time. These discrepancies are explained in detail. Besides scalar models, gauge fields are also studied. For both cases, we discuss the free Hamiltonian with respect to non-local deformations.