Related papers: Gauge invariance of parametrized systems and path …
We discuss the time-continuous path integration in the coherent states basis in a way that is free from inconsistencies. Employing this notion we reproduce known and exact results working directly in the continuum. Such a formalism can set…
This report concerns the inverse problem of estimating a spacially dependent coefficient of a partial differential equation from observations of the solution at the boundary. Such a problem can be formulated as an optimal control problem…
The problem of extracting the work from a quantum-thermodynamic system driven by slowly varying external parameters is discussed. It is shown that there naturally emerges a gauge-theoretic structure. The field strength identically vanishes…
Theories that contain first class constraints possess gauge invariance which results in the necessity of altering the measure in the associated quantum mechanical path integral. If the path integral is derived from the canonical structure…
Scalar field systems containing higher derivatives are studied and quantized by Hamiltonian path integral formalism. A new point to previous quantization methods is that field functions and their derivatives with time are considered as…
We study the periodic homogenization problem of state-constraint Hamilton--Jacobi equations on perforated domains in the convex setting and obtain the optimal convergence rate. We then consider a dilute situation in which the holes'…
We consider cosmological perturbations around homogeneous and isotropic spacetimes minimally coupled to a scalar field and present a formulation which is designed to preserve covariance. We truncate the action at quadratic perturbative…
The additional information within a Hamilton-Jacobi representation of quantum mechanics is extra, in general, to the Schr\"odinger representation. This additional information specifies the microstate of $\psi$ that is incorporated into the…
The path integral approach offers not only an exact expression for the non- equilibrium dynamics of dissipative quantum systems, but is also a convenient starting point for perturbative treatments. An alternative way to explore the…
Quantum systems with constraints are often considered in modern theoretical physcics. All realistic field models based on the idea of gauge symmetry are of this type. A partial case of constraints being linear in coordinate and momenta…
We present a novel geometric approach for determining the unique structure of a Hamiltonian and establishing an instability criterion for quantum quadratic systems. Our geometric criterion provides insights into the underlying geometric…
Measurement incompatibility is a cornerstone of quantum mechanics. In the context of estimating multiple parameters of a quantum system, this manifests as a fundamental trade-off between the precisions with which different parameters can be…
This mini-course provides a presentation of the method of characteristics to initial/boundary-value problems for systems of first-order partial differential equations and to Hamilton-Jacobi variational inequalities. In particular, these…
We pursue the view that quantum theory may be an emergent structure related to large space-time scales. In particular, we consider classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a…
Systems with singular higher order- Lagrangians are investigated by using the extended form of the canonical method. Besides, the canonical path integral formulation is generalized using the Hamilton- jacobi formulation to investigate…
The precise implementation and manipulation of quantum gates is key to extracting advantages from future quantum technologies. Achieving this requires very accurate control over the quantum system. If one has complete knowledge about a…
Found all equivalence classes for electromagnetic potentials and space-time metrics of Stackel spaces, provided that the equations of motion of the classical charged test particles are integrated by the method of complete separation of…
Motivated by the Hamilton$-$Jacobi approach of fields with constraints, we analyse the classical structure of three different constrained field systems: (i) the scalar field coupled to two flavors of fermions through Yukawa couplings (ii)…
A number of many-body problems can be formulated using Hamiltonians that are quadratic in the creation and annihilation operators. Here, we show how such quadratic Hamiltonians can be efficiently estimated indirectly, employing very few…
The rarely used Hamilton-Jacobi equation has been utilized as an elegant way to find the trajectories of mechanical systems and to derive symplectic maps. Further, the exact solution in kick approximation of Hamilton's equations of motion…