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Classical Mechanics: Hamiltonian and Lagrangian Formalism
Sketch of Lagrangian Formalism.- Hamiltonian Formalism.- Canonical Transformations of Two-Dimensional Phase Space.- Properties of Canonical Transformations.- Integral Invariants.- Potential Motion inExpand
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Noncommutative relativistic particle on the electromagnetic background
Abstract A noncommutative version of D-dimensional relativistic particle is proposed. We consider the particle interacting with the configuration space variable θμν(τ) instead of the numericalExpand
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World-line geometry probed by fast spinning particle
Interaction of spin with electromagnetic field yields an effective metric along the world line of spinning particle. If we insist to preserve the usual special-relativity definitions of time andExpand
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Noncommutative version of an arbitrary nondegenerated mechanics
A procedure to obtain noncommutative version for any nondegenerated dynamical system is proposed and discussed. The procedure is as follow. Let $S=\int dt L(q^A, ~ \dot q^A)$ is action of someExpand
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Ultrarelativistic Spinning Particle and a Rotating Body in External Fields
We use the vector model of spinning particle to analyze the influence of spin-field coupling on the particle’s trajectory in ultrarelativistic regime. The Lagrangian with minimal spin-gravityExpand
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Frenkel electron on an arbitrary electromagnetic background and magnetic Zitterbewegung
Abstract We present Lagrangian which implies both necessary constraints and dynamical equations for position and spin of relativistic spin one-half particle. The model is consistent for any value ofExpand
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Mathisson–Papapetrou–Tulczyjew–Dixon equations in ultra-relativistic regime and gravimagnetic moment
Mathisson–Papapetrou–Tulczyjew–Dixon (MPTD) equations in the Lagrangian formulation correspond to the minimal interaction of spin with gravity. Due to the interaction, in the Lagrangian equationsExpand
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Rigid particle revisited: Extrinsic curvature yields the Dirac equation
Abstract We reexamine the model of relativistic particle with higher-derivative linear term on the first extrinsic curvature (rigidity). The passage from classical to quantum theory requires a numberExpand
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On singular Lagrangian underlying the Schrödinger equation
Abstract We analyze the properties that manifest Hamiltonian nature of the Schrodinger equation and show that it can be considered as originating from singular Lagrangian action (with two secondExpand
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Three-loop β-function for the two-dimensional non-linear σ-model with a Wess-Zumino-Witten term
Abstract The three-loop β-function for the two-dimensional non-linear σ-model with a Wess- Zumino-Witten term is computed by using the covariant background field method. The β-function is proved toExpand
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