Ciprian Acatrinei

Path integral formulation of noncommutative quantum mechanics

We propose a phase-space path integral formulation of noncommutative quantum mechanics, and prove its equivalence to the operatorial formulation. As an illustration, the partition function of a noncommutative two-dimensional harmonic oscillator is calculated.

A SIMPLE SIGNAL OF NONCOMMUTATIVE SPACE

We propose a simple low-energy classical experiment in which the effects of noncommutativity can be clearly separated from commutative physics. The ensuing bound on the noncommutative scale is remarkable, especially in view of its elementary derivation.

A Note on the decay of noncommutative solitons

We propose an ansatz for the equations of motion of the noncommutative model of a tachyonic scalar field interacting with a gauge field, which allows one to find time-dependent solutions describing decaying solitons. These correspond to the collapse of lower dimensional branes obtained through tachyon condensation of unstable brane systems in string theory.

A path integral leading to higher order Lagrangians

We consider a simple modification of standard phase-space path integrals and show that it leads in configuration space to Lagrangians depending also on accelerations.

Canonical quantization of noncommutative field theory

A simple method to canonically quantize noncommutative field theories is proposed. As a result, the elementary excitations of a (2n+1)-dimensional scalar field theory are shown to be bilocal objects living in an (n+1)-dimensional space-time. Feynman rules for their scattering are derived canonically. They agree, upon suitable redefinitions, with the rules obtained via star-product methods. The IR/UV connection is interpreted within this framework.

Noncommutative radial waves

We study radial waves in a (2+1)-dimensional noncommutative scalar field theory, using operatorial methods. The waves propagate along a discrete radial coordinate and are described by finite series deformations of Bessel-type functions. At radius much larger than the noncommutativity scale , one recovers the usual commutative behaviour. At small distances, classical divergences are smoothed out by noncommutativity.

Lagrangian versus quantization

We discuss examples of systems which can be quantized consistently, although they do not admit a Lagrangian description.