130 citations · 896 across the 43 of their papers we have counts for
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Path Integral Quantization and Riemannian-Symplectic Manifolds
Sergei V. Shabanov, John R. Klauder
We develop a mathematically well-defined path integral formalism for general symplectic manifolds. We argue that in order to make a path integral quantization covariant under gener…
An Introduction to Coordinate-free Quantization and its Application to Constrained Systems
John R. Klauder, Sergei V. Shabanov
Canonical quantization entails using Cartesian coordinates, and Cartesian coordinates exist only in flat spaces. This situation can either be questioned or accepted. In this paper…
Supersymmetry in Stochastic Processes with Higher-Order Time Derivatives
Hagen Kleinert, Sergei V. Shabanov
A supersymmetric path integral representation is developed for stochastic processes whose Langevin equation contains any number N of time derivatives, thus generalizing the Langevi…
Proper Dirac Quantization of Free Particle on D-Dimensional Sphere
Hagen Kleinert, Sergei V. Shabanov
We show that an unambiguous and correct quantization of the second-class constrained system of a free particle on a sphere in dimensions is possible only by converting the cons…
q-oscillators, (non-)Kaehler manifolds and constrained dynamics
Sergei V. Shabanov
It is shown that q-deformed quantum mechanics (systems with q-deformed Heisenberg commutation relations) can be interpreted as an ordinary quantum mechanics on Kaehler manifolds, o…
Path Integral in Holomorphic Representation without Gauge Fixation
Sergei V. Shabanov
A method of path integral construction without gauge fixing in the holomorphic representation is proposed for finite-dimensional gauge models. This path integral determines a manif…