ar X iv : h ep - t h / 04 05 01 3 v 1 3 M ay 2 00 4 Ladder operators for subtle hidden shape invariant potentials 1

ar X iv : h ep - t h / 04 05 01 3 v 1 3 M ay 2 00 4 Ladder operators for subtle hidden shape invariant potentials

Ladder operators can be constructed for all potentials that present the integrability condition known as shape invariance, satisfied by most of the exactly solvable potentials. Using the superalgebra of supersymmetric quantum mechanics we construct the ladder operators for two exactly solvable potentials that present a subtle hidden shape invariance. PACS No. 03.65.Fd, 11.30.Pb, 31.15.Pf

ar X iv : h ep - t h / 01 01 05 9 v 2 1 4 M ay 2 00 1

We consider the complex scalar field coupled to background NC U(1) YM and calculate the correlator of two gauge invariant composite operators. We show how the noncommutative gauge invariance is restored for higher correlators (though the Green's function itself is not invariant). It is interesting that the recently discovered noncommutative solitons appear in the calculation.

ar X iv : h ep - t h / 01 05 31 8 v 1 3 1 M ay 2 00 1 Trace anomaly for 4 D higher derivative scalar - dilaton theory

Trace anomaly for conformally invariant higher derivative 4D scalar-dilaton theory is obtained by means of calculating divergent part of one-loop effective action for such system. Its applications are briefly mentioned.

ar X iv : h ep - p h / 04 05 11 9 v 1 1 3 M ay 2 00 4 The Lorentz and CPT violating effects on the charged

ar X iv : h ep - p h / 04 05 03 9 v 1 5 M ay 2 00 4 η , η ′ → π + π − γ with coupled channels