Related papers: Semiclassical Analysis of Constrained Quantum Syst…
The Dirac procedure for dealing with constraints is applied to the quantization of gauge theories on the light front. The light cone gauge is used in conjunction with the first class constraints that arise and the resulting Dirac brackets…
Systems under holonomic constraints are classified within the generalized Hamiltonian framework as second-class constraints systems. We show that each system of point particles with holonomic constraints has a hidden gauge symmetry which…
It has been found that quantum corrections can substantially affect the classical results of tracking for trajectories close to the separatrix. Hence the development of a basic formalism for obtaining the quantum maps for any particle beam…
In cosmology minisuperspace models are described by nonlinear time-reparametrization invariant systems with a finite number of degrees of freedom. Often these models are not explicitly integrable and cannot be quantized exactly. Having this…
We present a semiclassical analysis for Dirac fields on an arbitrary spacetime background and in the presence of a fixed electromagnetic field. Our approach is based on a Wentzel-Kramers-Brillouin approximation, and the results are analyzed…
Within the framework of loop quantum cosmology, there exists a semi-classical regime where spacetime may be approximated in terms of a continuous manifold, but where the standard Friedmann equations of classical Einstein gravity receive…
We develop a general canonical quantization scheme for $k$-essence cosmology in scalar-tensor theory. Utilizing the Dirac-Bergmann algorithm, we construct the Hamiltonian associated with the cosmological field equations and identify the…
Canonical quantisation of constrained systems with first class constraints via Dirac's operator constraint method proceeds by the thory of Rigged Hilbert spaces, sometimes also called Refined Algebraic Quantisation (RAQ). This method can…
The numerical treatment of quantum mechanics in the semi-classical regime is known to be computationally demanding, due to the highly oscillatory behaviour of the wave function and its large spatial extension. A recently proposed…
Stochastic quantisation is applied to the problem of calculating real-time evolution on a Minkowskian space-time lattice. We employ optimized updating using reweighting, or gauge fixing, respectively. These procedures do not affect the…
In this letter we give a systematic derivation and justification of the semiclassical model for the slow degrees of freedom in adiabatic slow-fast systems first found by Littlejohn and Flynn [5]. The classical Hamiltonian obtains a…
In this work we discuss the deformed relativistic wave equations, namely the Klein--Gordon and Dirac equations in a Doubly Special Relativity scenario. We employ what we call a geometric approach, based on the geometry of a curved momentum…
Useful relations describing arbitrary parameters of given quantum systems can be derived from simple physical constraints imposed on the vectors in the corresponding Hilbert space. This is well known and it usually proceeds by partitioning…
We study the theory of systems with constraints from the point of view of the formal theory of partial differential equations. For finite-dimensional systems we show that the Dirac algorithm completes the equations of motion to an…
Hamiltonian constraints feature in the canonical formulation of general relativity. Unlike typical constraints they cannot be associated with a reduction procedure leading to a non-trivial reduced phase space and this means the physical…
In this second paper on loop quantization of Gowdy model, we introduce the kinematical Hilbert space on which appropriate holonomies and fluxes are well represented. The quantization of the volume operator and the Gauss constraint is…
The development of emerging technologies in quantum optics demands accurate models that faithfully capture genuine quantum effects. Mature semiclassical approaches reach their limits when confronted with quantized electromagnetic fields,…
An initial coherent state is propagated exactly by a kicked quantum Hamiltonian and its associated classical stroboscopic map. The classical trajectories within the initial state are regular for low kicking strengths, then bifurcate and…
The Dirac method of quantizing Hamiltonian systems with constraints is applied to the massless Thirring model. We solve the quantum Hamiltonian equation for the energy-momentum tensor and obtain a violation of the classical conservation…
We present a method for constructing a consistent low energy canonical formalism for higher order time-derivative theories, extending the Dirac method to include perturbative Hamiltonian constraints. We apply it to two paradigmatic…