Covariant Schrodinger Equation via Path Integrals

Rigorous Covariant Path Integrals

Our rigorous path integral is extended to quantum evolution on metricaffine manifolds. 1 Path Integrals on Euclidean Spaces. Consider the evolution operator U [ψ(t, q)] = ψ(t, q), t ≥ t, of the quantum evolution equation on L(R): h̄ i ∂ψ(t, q)/∂t+ f(t, q, h̄ i ∂/∂q)ψ(t, q) = 0. Here the operator f(t, q, h̄ i ∂/∂q) is the standard quantization of a classical timedependent quasi-Hamiltonian f(t, q, ...

Covariant path integrals and black holes

The thermal nature of the propagator in a collapsed black-hole spacetime is shown to follow from the non-trivial topology of the configuration space in tortoise coordinates by using the path integral formalism. The path integral (PI) formalism is useful to calculate propagators in configuration spaces (CS) endowed with a non-trivial topology, such as in curved spacetimes. Moreover, even if the ...

Exact quantum master equation via the calculus on path integrals.

An exact quantum master equation formalism is constructed for the efficient evaluation of quantum non-Markovian dissipation beyond the weak system-bath interaction regime in the presence of time-dependent external field. A novel truncation scheme is further proposed and compared with other approaches to close the resulting hierarchically coupled equations of motion. The interplay between system...

Path Integrals Without Integrals∗

Recently, we have developed an efficient recursive approach for analytically calculating the short-time expansion of the propagator to extremely high orders for a general many-body quantum system. Here we give brief overview of this approach and then demonstrate application of this technique by numerically studying the thermodynamical properties of a rotating ideal Bose gas of Rb atoms in an an...

Schrodinger Equation and Quantum Chemistry