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Instanton calculations in semiclassical quantum mechanics rely on integration along trajectories which solve classical equations of motion. However in systems with higher dimensionality or complexified phase space these are rarely attainable. A prime example are spin-coherent states which are used e.g. to describe single molecule magnets (SMM). We use this example to develop instanton calculus which does not rely on explicit solutions of the classical equations of motion. Energy conservation restricts the complex phase space to a Riemann surface of complex dimension one, allowing to deform integration paths according to Cauchys integral theorem. As a result, the semiclassical actions can be evaluated without knowing actual classical paths. Furthermore we show that in many cases such actions may be solely derived from monodromy properties of the corresponding Riemann surface and residue values at its singular points. As an example, we consider quenching of tunneling processes in SMM by an applied magnetic field.
We present analytical implementation of conformal field theory on a compact Riemann surface. We consider statistical fields constructed from background charge modifications of the Gaussian free field and derive Ward identities which represent the Lie
We propose a new version of Wigner-Weyl calculus for tight-binding lattice models. It allows to express various physical quantities through Weyl symbols of operators and Greens functions. In particular, Hall conductivity in the presence of varying an
In this paper we compute gaugino and scalar condensates in N=1 supersymmetric gauge theories with and without massive adjoint matter, using localization formulae over the multi--instanton moduli space. Furthermore we compute the chiral ring relations
In this work we demonstrate a simple way to implement the quantum inverse scattering method to find eigenstates of spin-1/2 XXX Gaudin magnets in an arbitrarily oriented magnetic field. The procedure differs vastly from the most natural approach whic
To any differential system $dPsi=PhiPsi$ where $Psi$ belongs to a Lie group (a fiber of a principal bundle) and $Phi$ is a Lie algebra $mathfrak g$ valued 1-form on a Riemann surface $Sigma$, is associated an infinite sequence of correlators $W_n$ th