Related papers: Extending Hamilton's principle to quantize classic…
Hamilton's principle is extended to have compatible initial conditions to the strong form. To use a number of computational and theoretical benefits for dynamical systems, the mixed variational formulation is preferred in the systems other…
Classical physics is reformulated as a constrained Hamiltonian system in the history phase space. Dynamics, i.e. the Euler-Lagrange equations, play the role of first-class constraints. This allows us to apply standard methods from the…
Constrained Hamiltonian description of the classical limit is utilized in order to derive consistent dynamical equations for hybrid quantum-classical systems. Starting with a compound quantum system in the Hamiltonian formulation conditions…
We discuss the transition from a quantum to a classical domain for a model where a separation into environment and system is explicitely not given. Utilizing the coarse graining procedure for free quantum fields we also apply the projection…
These lectures are an introduction to formal semiclassical quantization of classical field theory. First we develop the Hamiltonian formalism for classical field theories on space time with boundary. It does not have to be a cylinder as in…
Hamilton's principle of stationary action lies at the foundation of theoretical physics and is applied in many other disciplines from pure mathematics to economics. Despite its utility, Hamilton's principle has a subtle pitfall that often…
Despite the widely-held premise that initial boundary conditions (BCs) corresponding to measurements/interactions can fully specify a physical subsystem, a literal reading of Hamilton's principle would imply that both initial and final BCs…
It is argued that the massive non-Abelian gauge field theory without involving Higgs bosons may be well established on the basis of gauge-invariance principle because the dynamics of the field is gauge-invariant in the physical space…
Many quantization schemes rely on analogs of classical mechanics where the connections with classical mechanics are indirect. In this work I propose a new and direct connection between classical mechanics and quantum mechanics where the…
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 is defined by a (Hamiltonian) constraint…
We present and contrast two distinct ways of including extremal black holes in a Lorentzian Hamiltonian quantization of spherically symmetric Einstein-Maxwell theory. First, we formulate the classical Hamiltonian dynamics with boundary…
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 is defined via the (Hamiltonian)…
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 gauge field is introduced to compensate for…
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…
The technique of "extension" allows to build $(n+1)$-dimensional Hamiltonian systems with a non-trivial polynomial in the momenta first integral of any given degree starting from a $n$-dimensional Hamiltonian satisfying some additional…
It is shown how to extend the formal variational calculus in order to incorporate integrals of divergences into it. Such a generalization permits to study nontrivial boundary problems in field theory on the base of canonical formalism.
In this paper we consider a generalized classical mechanics with fractional derivatives. The generalization is based on the time-clock randomization of momenta and coordinates taken from the conventional phase space. The fractional…
We study how the classical Hamilton's principal and characteristic functions are generated from the solutions of the quantum Hamilton-Jacobi equation. While in the classically forbidden regions these quantum quantities directly tend to the…
If the gravitational field is quantized, then a solution of Einstein's field equations is a valid cosmological model only if it corresponds to a classical limit of a quantum cosmology. To determine which solutions are valid requires looking…
The quantization of classical theories that admit more than one Hamiltonian description is considered. This is done from a geometrical viewpoint, both at the quantization level (geometric quantization) and at the level of the dynamics of…