Journal ArticleDOI
On the path integral for diffusion in curved spaces
TLDR
The Onsager-Machlup Lagrangian for diffusion processes in curved spaces is determined by evaluating the covariant path integral by means of a spectral analysis of smooth trajectories in Riemannian normal coordinates as mentioned in this paper.Abstract:
The Onsager-Machlup Lagrangian for diffusion processes in curved spaces is determined by evaluating the covariant path integral by means of a spectral analysis of smooth trajectories in Riemannian normal coordinates. The Lagrangian involves a novel curvature scalar potential term v=− ( 1 8 ) R . The present treatment replaces an earlier one.read more
Citations
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Statistical mechanics of neocortical interactions. I. Basic formulation
TL;DR: In this article, an approach to collective aspects of the neocortical system is formulated by methods of modern nonlinear nonequilibrium statistical mechanics, which are first spatially averaged over columnar domains.
Journal ArticleDOI
The path integral for a particle in curved spaces and Weyl anomalies
TL;DR: In this paper, a path integral for a particle moving in curved spaces is analyzed in a manifestly covariant way and by making use of ghost fields, which allows us to represent the path-integral measure in a form suitable for performing the perturbative expansion.
Journal ArticleDOI
Loop calculations in quantum mechanical non-linear sigma models with fermions and applications to anomalies
TL;DR: In this paper, the path integral for one-dimensional sigma models, starting from a given Hamiltonian operator and states in a Hilbert space, is constructed and the correct Feynman rules are derived by explicit evaluation of the discretized propagators and vertices.
Journal ArticleDOI
Geometric momentum: The proper momentum for a free particle on a two-dimensional sphere
TL;DR: In this article, the authors show that the well-known canonical momentum of a free particle on a two-dimensional sphere or a spherical top breaks one of the relations, while three components of the momentum expressed in the three-dimensional Cartesian system of axes as ${p}_{i}$ $(i=1,2,3)$ are satisfactory all around.
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Proper dirac quantization of a free particle on a d-dimensional sphere
TL;DR: In this paper, it was shown that an unambiguous and correct quantization of the second-class constrained system of a free particle on a sphere in D dimensions is possible only by converting the constraints to Abelian gauge constraints, which are of first class in Dirac's classification scheme.
References
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Book
Quantum Mechanics and Path Integrals
TL;DR: Au sommaire as discussed by the authors developed the concepts of quantum mechanics with special examples and developed the perturbation method in quantum mechanics and the variational method for probability problems in quantum physics.