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the Hamiltonian of an even anharmonic oscillator is defined as

[itex] H_N(g) = - \frac{1}{2} ∂_q^2 + \frac{1}{2} q^2 + g q^N [/itex] (N even).

In a paper (PRl 102, 011601) I found that to determine the eigenenergies of this system the Euclidean path integral formalism is used. They concluded that they have to use instanton configurations.

Since some googling of this term gave me only explanations in terms of Yang-Mills theories or string theory stuff and nothing else, my first question is: How are these instanton configurations defined for a given Hamiltonian.

From the Hamiltonian they further conclude that instanton configurations only exist for negative g. To find then the configurations they scale [itex] q(t) = (-g)^{-1/(N-2)} ζ(t). [/itex]. Maybe it will be obvious once I know the exact definition of instanton configuration, but why do they then scale q(t) with this prefactor?

Many thanks in advance for your answers!

Greetings, Syrius

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# Instanton configurations of an even anharmonic oscillator

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