We establish existence and stability results for solitons in noncommutative scalar field theories in even space dimension 2d. In particular, for any finite rank spectral projection P of the number operator N of the d-dimensional harmonic oscillator and sufficiently large noncommutativity parameter θ we prove the existence of a rotationally invariant soliton which depends smoothly on θ and converges to a multiple of P as θ →∞ . In the two-dimensional case we prove that these solitons are stable at large θ ,i f P = PN , where PN projects onto the space spanned by the N + 1 lowest eigenstates of N , and otherwise they are unstable. We also discuss the generalisation of the stability re- sults to higher dimensions. In particular, we prove stability of the soliton corresponding to P = P0 for all θ in its domain of existence. Finally, for arbitrary d and small values of θ , we prove without assuming rotational invariance that there do not exist any solitons depending smoothly on θ .
Ryszard Nest hasn't uploaded this paper.
Let Ryszard know you want this paper to be uploaded.
