Large-N phase-integral approximation for SU(1,1) coherent states

Large-N expansions in quantum mechanics, atomic physics and some O(N) invariant systems

We elaborate on Abelian complex scalar models, which are dictated by natural actions (all couplings are of order one), at fixed and large global U(1) charge in an arbitrary number of dimensions. The ground state v is coherently constructed by the zero modes and the appearance of a centrifugal potential is quantum mechanically verified. Using the path integral formulation we systematically analyze the quantum fluctuations around v in order to derive an effective action for the Goldstone mode, which becomes perturbatively meaningful when the charge is large. In this regime we explicitly show, by computing the first few loop corrections, that the whole construction is stable against quantum effects, in the sense that any higher derivative couplings to Goldstone's tree-level action are suppressed by appropriate powers of the large charge.

Abelian scalar theory at large global charge

SU(1,1) coherent-state dynamics: A path-integral approach.

Nonlinear pseudospin dynamics on a noncompact manifold.

A phase integral approximation, based on the notion that large N is a semiclassical limit, is presented for spherically symmetric systems of the Coulomb type. Since the dynamical group SO(2,1) is the spectrum generating group for the radial point Coulomb problem and the Casimir operators of O(N) and SO(2,1) are coupled, the authors write a path integral expression of the Green function in terms of SO(2,1) coherent states. The resulting phase integral approximation is applied to the Yukawa potential and the Coulomb plus linear r confining potential.

Large-N phase-integral approximation for SU(1,1) coherent states

Citations

Large-N expansions in quantum mechanics, atomic physics and some O(N) invariant systems

Abelian scalar theory at large global charge

SU(1,1) coherent-state dynamics: A path-integral approach.

Nonlinear pseudospin dynamics on a noncompact manifold.

A large-N phase integral approximation of Coulomb-type systems using SO(2,1) coherent states

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