Related papers: Hamiltonian Frenet-Serret dynamics
We formulate a Hamiltonian description of the orbital motion of a point particle in Kerr spacetime for generic (eccentric, inclined) orbits, which accounts for the effects of the conservative part of the gravitational self-force. This…
We argue that higher spin fields originate from Hamiltonian mechanics and play a role of gauge fields ensuring covariance of geometric observables such as length and volume with respect to canonical transformations in the same way as a…
How can we relate the constraint structure and constraint dynamics of the general gauge theory in the Hamiltonian formulation with specific features of the theory in the Lagrangian formulation, especially relate the constraint structure…
The link between the treatments of constrained systems with fractional derivatives by using both Hamiltonian and Lagrangian formulations is studied. It is shown that both treatments for systems with linear velocities are equivalent.
An algebraic procedure of getting of canonical variables in a rigid body dynamics is presented. The method is based on using a structure of an algebra of Lie-Poisson brackets with which a Hamiltonian dynamics is set. In a particular case of…
We derive the interaction of fermions with a dynamical space-time based on the postulate that the description of physics should be independent of the reference frame, which means to require the form-invariance of the fermion action under…
A relativistic Hamiltonian mechanical system is seen as a conservative Dirac constraint system on the cotangent bundle of a pseudo-Riemannian manifold. We provide geometric quantization of this cotangent bundle where the quantum constraint…
The Hamiltonian theory of a relativistic string is considered in a specific reference frame in terms the diffeo-invariant variables. The evolution parameter and energy invariant with respect to the time-coordinate transformations are…
A covariant approach towards a theory of deformations is developed to examine both the first and second variation of the Helfrich-Canham Hamiltonian -- quadratic in the extrinsic curvature -- which describes fluid vesicles at mesoscopic…
A detailed canonical treatment of a new action for a nonrelativistic particle coupled to background gravity, recently given by us, is performed both in the Lagrangian and Hamiltonian formulations. The equation of motion is shown to satisfy…
It is most common to construct the Hamiltonian function and Hamilton's canonical equations through a Legendre transformation of the Lagrangean function or through the central equation. These common perspectives, however, seem abstract and…
Doubly special relativity has been studied for the last twenty years as a way to go beyond the special relativistic kinematics, trying to capture residual effects of a quantum gravity theory. In particular, in doubly special relativity the…
The relationship between the Hamiltonian and Lagrangean functions in analytical mechanics is a type of duality. The two functions, while distinct, are both descriptive functions encoding the behavior of the same dynamical system. One…
A strengthened canonical quantization scheme for the constrained motion on a curved hypersurface is proposed with introduction of the second category of fundamental commutation relations between Hamiltonian and positions/momenta, whereas…
Recent results based on renormalization group approaches to Quantum Gravity suggest that the Newton's and cosmological constants should be treated as dynamical variables whose evolution depend on the characteristic energy scale of the…
Hamiltonian systems with functionally dependent constraints (irregular systems), for which the standard Dirac procedure is not directly applicable, are discussed. They are classified according to their behavior in the vicinity of the…
When a Hamiltonian system is subject to constraints which depend explicitly on time, difficulties can arise in attempting to reduce the system to its physical phase space. Specifically, it is non-trivial to restrict the system in such a way…
We develop a new, coordinate-free formulation of Hamiltonian mechanics on the dual of a Lie algebroid. Our approach uses a connection, rather than coordinates in a local trivialization, to obtain global expressions for the horizontal and…
Using well known Lagrangean techniques for uncovering the gauge symmetries of a Lagrangean, we derive the transformation laws for the phase space variables corresponding to local symmetries of the Hamilton equations of motion. These…
A Hamiltonian formalism is employed to elucidate the effects of the Stern-Gerlach force on beams of relativistic spin-polarized particles, for passage through a localized region with a static magnetic or electric field gradient. The problem…