TY - JOUR

T1 - The existence and stability of noncommutative scalar solitons

AU - Durhuus, Bergfinnur

AU - Jonsson, Thordur

AU - Nest, Ryszard

PY - 2003/2/1

Y1 - 2003/2/1

N2 - 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, if 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 results 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.

AB - 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, if 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 results 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.

UR - http://www.scopus.com/inward/record.url?scp=0037330001&partnerID=8YFLogxK

U2 - 10.1007/s00220-002-0721-4

DO - 10.1007/s00220-002-0721-4

M3 - Journal article

AN - SCOPUS:0037330001

VL - 233

SP - 49

EP - 78

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 1

ER -