Path Integral for Separable Hamiltonians of Liouville-type

On an exact path integral of the hydrogen atom

The path integral evaluation of the hydrogen atom by Duru and Kleinert is studied by recognizing it as a special case of the general treatment of the separable Hamiltonian of Liouville-type. The basic dynamical principle involved is identified as the Jacobi’s principle of least action for given energy which is reparametrization invariant, and thus the appearance of a gauge freedom is naturally ...

Integral Inequalities for h(x)-Riemann-Liouville Fractional Integrals

In this article, we obtain generalizations for Grüss type integral inequality by using h(x)-Riemann-Liouville fractional integral.

Path integral of the hydrogen atom, the Jacobi’s principle of least action and one-dimensional quantum gravity

A path integral evaluation of the Green’s function for the hydrogen atom initiated by Duru and Kleinert is studied by recognizing it as a special case of the general treatment of the separable Hamiltonian of Liouville-type. The basic dynamical principle involved is identified as the Jacobi’s principle of least action for given energy which is reparametrization invariant, and thus the appearance...

Integrability of Hamiltonian systems and transseries expansions

This paper studies analytic Liouville-non-integrable and C∞-Liouvilleintegrable Hamiltonian systems with two degrees of freedom. We will show that considerably general Hamiltonians than the one studied in [2] have the property. We also show that a certain monodromy property of an ordinary differential equation obtained as a subsystem of a given Hamiltonian and the transseries expansion of a fir...

Making the gravitational path integral more Lorentzian or Life beyond Liouville gravity