Multitime propagators and the consistency condition

Theoretical and Mathematical Physics - For a nonrelativistic quantum system of $$N$$ particles, the wave function is a function of $$3N$$ spatial coordinates and one temporal coordinate. The...     

The impedance function of a confined polaron and bipolaron: The single-path-integral approach

We use the single-path-integral to calculate the impedance function of the polaron and bipolaron in quantum confinement with the presence of the external fields. The expectation values of the classical equation of motion is considered in order to obtain the impedance function. The mobility of the polaron and bipolaron in quantum confinement is also calculated in the direction parallel and perpendicular to the magnetic field. Without trapping, we also calculate the effective mass of the bipolaron in the magnetic field.     

Multiplicative form of the Lagrangian

We obtain an alternative class of Lagrangians in the so-called the multiplicative form for a system with one degree of freedom in the nonrelativistic and the relativistic cases. This new form of the Lagrangian can be regarded as a one-parameter class with the parameter λ obtained using an extension of the standard additive form of the Lagrangian because both forms yield the same equation of motion. We note that the multiplicative form of the Lagrangian can be regarded as a generating function for obtaining an infinite hierarchy of Lagrangians that yield the same equation of motion. This nontrivial set of Lagrangians confirms that the Lagrange function is in fact nonunique.