Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets

Hagen M. Kleinert

Hagen M. Kleinert

Hagen M. Kleinert

Hagen M. Kleinert

Fundamentals Path Integrals - Elementary Properties and Simple Solutions External Sources, Correlations, and Perturbation Theory Semiclassical Time Evolution Amplitude Variational Perturbation Theory Path Integrals with Topological Constrainsts Many Particle Orbits - Statistics and Second Quantization Path Integrals in Spherical Coordinates Fixed-Energy Amplitude and Wave Functions Spaces with Curvature and Torsion Schrodinger Equation in General Metric-Affine Spaces New Path Integral Formula for Singular Potentials Path Integral of Coulomb System Solution of Further Path Integrals by the Duru-Kleinert Method Path Integrals in Polymer Physics Polymers and Particle Orbits in Multiply Connected Spaces Tunneling Nonequilibrium Quantum Statistics Relativistic Particle Orbits Path Integrals and Financial Markets.

Osamu Tsuchiya

Ijiris Journal Division, Lester Ingber

The author previously developed a numerical multivariate path-integral algorithm, PATHINT, which was applied to several classical physics systems, including statistical mechanics of neocortical interactions, options in financial markets, and other nonlinear systems including chaotic systems. A quantum version, qPATHINT, has the ability to take into account time dependent modifications of an evolving system. qPATHINT is shown to be useful to study some aspects of serial changes to systems. Potential applications in neuroscience and financial markets are discussed.