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Real spinors and real Dirac equation
We reexamine the minimal coupling procedure in the Hestenes' geometric algebra formulation of the Dirac equation, where spinors are identified with the even elements of the real Clifford algebra of…
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Tsallis thermostatics as a statistical physics of random chains.
In this paper we point out that the generalized statistics of Tsallis-Havrda-Charvát can be conveniently used as a conceptual framework for statistical treatment of random chains. In particular, we…
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Local-time representation of path integrals.
TLDR
A local-time path-integral representation for a generic one-dimensional time-independent system is derived and it is argued that the results obtained represent a powerful alternative to the traditional Feynman-Kac formula, particularly in the high- and low-temperature regimes.
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Green function of the double-fractional Fokker-Planck equation: path integral and stochastic differential equations.
The statistics of rare events, the so-called black-swan events, is governed by non-Gaussian distributions with heavy power-like tails. We calculate the Green functions of the associated Fokker-Planck…
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Local time of Lévy random walks: A path integral approach.
TLDR
This work focuses on the local times of Lévy random walks (Lévy flights), which correspond to fractional diffusion equations and uses the phase-space path-integral representation of random walk transition probabilities to quantify the properties of the local time.
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Quantum walks with non-Abelian anyons.
TLDR
It is found that asymptotically a mobile Ising model anyon becomes so entangled with its environment that its statistical dynamics reduces to a classical random walk with linear dispersion in contrast to particles with Abelian statistics which have quadratic dispersion.
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Path-integral approach to the Wigner-Kirkwood expansion.
TLDR
A functional representation of the Wigner-Kirkwood perturbation expansion for quantum Boltzmann densities is derived from the Feynman-Kac formula and applied to obtain basic thermodynamic functions of the one-dimensional anharmonic oscillator.
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Hamiltonian Constraint Formulation of Classical Field Theories
Classical field theory is considered as a theory of unparametrized surfaces embedded in a configuration space, which accommodates, in a symmetric way, spacetime positions and field values. Dynamics…
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Classical Field Theories from Hamiltonian Constraint: Local Symmetries and Static Gauge Fields
We consider the Hamiltonian constraint formulation of classical field theories, which treats spacetime and the space of fields symmetrically, and utilizes the concept of momentum multivector. The…
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Transport properties of anyons in random topological environments
The quasi-one-dimensional transport of Abelian and non-Abelian anyons is studied in the presence of a random topological background. In particular, we consider the quantum walk of an anyon that…
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