Related papers: Kramers equation and supersymmetry
A geometric approach to integrability and reduction of dynamical system is developed from a modern perspective. The main ingredients in such analysis are the infinitesimal symmetries and the tensor fields that are invariant under the given…
Supersymmetry is one of the most important and indispensable ingredients of modern theoretical physics. However, the absence, at least at the time of publishing this review, of experimental verification of supersymmetry in elementary…
The Hamilton function is a powerful tool for studying the classical limit of quantum systems, which remains meaningful in background-independent systems. In quantum gravity, it clarifies the physical interpretation of the transitions…
A novel theory of hybrid quantum-classical systems is developed, utilizing the mathematical framework of constrained dynamical systems on the quantum-classical phase space. Both, the quantum and the classical descriptions of the respective…
Hamiltonian dynamics can be used to produce distant proposals for the Metropolis algorithm, thereby avoiding the slow exploration of the state space that results from the diffusive behaviour of simple random-walk proposals. Though…
We describe a method for analyzing the phase space structures of Hamiltonian systems. This method is based on a time-frequency decomposition of a trajectory using wavelets. The ridges of the time-frequency landscape of a trajectory, also…
One method to overcome the notorious problem of time in the quantisation of gravity is the identification of a physically preferred time parameter, a promising candidate being so-called `York time'. The dynamical equations for matter and…
An effective mathematical framework based on Presymplectic Geometry for dealing with the "phase space picture" of timeless dynamics in General Relativity is presented. In General Relativity, the presence of the scalar Hamiltonian constraint…
Ideal fluid dynamics is studied as a relativistic field theory with particular importance on its hamiltonian structure. The Schwinger condition, whose integrated version yields the stress tensor conservation, is explicitly verified both in…
It is shown that the Hamilton equations in supersymmetric quantum mechanics can be presented in nonassociative form, where the Hamiltonian is decomposed into two nonassociative factors.
We consider a Hamiltonian system of particles, interacting through of a smooth pair potential. We look at the system on a space scale of order {\epsilon}^1, times of order {\epsilon}^2, and mean velocities of order {\epsilon}, with…
We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…
Hidden symmetries in a covariant Hamiltonian formulation are investigated involving gauge covariant equations of motion. The special role of the Stackel-Killing tensors is pointed out. A reduction procedure is used to reduce the original…
The expansion of a classical Hamilton formalism consisting in adaptation of it to describe the nonequilibrium systems is offered. Expansion is obtained by construction of formalism on the basis of the dynamics equation of the equilibrium…
Among theoretical issues in General Relativity the problem of constructing its Hamiltonian formulation is still of interest. The most of attempts to quantize Gravity are based upon Dirac generalization of Hamiltonian dynamics for system…
Using Hamilton-Jacobi theory, we develop a formalism for solving semi-classical cosmological perturbations which does not require an explicit choice of time-hypersurface. The Hamilton-Jacobi equation for gravity interacting with matter…
We apply the Dirac procedure for constrained systems to the Arnowitt-Deser-Misner formalism linearized around the Friedmann-Lemaitre universe. We explain and employ some basic concepts such as Dirac observables, Dirac brackets, gauge-fixing…
Relations between Hamiltonian mechanics and quantum mechanics are studied. It is stressed that classical mechanics possesses all the specific features of quantum theory: operators, complex variables, probabilities (in case of ergodic…
Hamilton's equations of motion form a fundamental framework in various branches of physics, including astronomy, quantum mechanics, particle physics, and climate science. Classical numerical solvers are typically employed to compute the…
It is shown that a well-known theory of random stationary processes contain contradictions. Integral representations of correlation functions and random stationary processes are investigated further. The new method of struggle with…