Related papers: Canonical Quantization of Cylindrical Waveguides: …
The unitary Clifford algebras are described here for the first time, and arise from the intersection of the orthogonal and common symplectic (Weyl) Clifford algebras of the complexification of the canonical phase space. The convergence of…
We study the quantum-classical correspondence in terms of coherent wave functions of a charged particle in two-dimensional central-scalar-potentials as well as the gauge field of a magnetic flux in the sense that the probability clouds of…
A midi-superspace model is a field theory obtained by symmetry reduction of a parent gravitational theory. Such models have proven useful for exploring the classical and quantum dynamics of the gravitational field. I present 3 recent…
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…
We extend the notion of quantum information flow defined by Danos and Kashefi for the one-way model and present a necessary and sufficient condition for the deterministic computation in this model. The generalized flow also applied in the…
The symmetry studies of Maxwell equations gave new insight on the nature of electromagnetic (EM) field. It has in general case quaternion single structure, consisting of four independent field constituents, which differ with each other by…
The description of the $T\bar{T}$ deformation in terms of two-dimensional gravity is analyzed from the Hamiltonian point of view, in a manner analogous to the ADM description of general relativity. We find that the Hamiltonian constraints…
Partial differential equations (PDEs) are central to computational electromagnetics (CEM) and photonic design, but classical solvers face high costs for large or complex structures. Quantum Hamiltonian simulation provides a framework to…
The canonical quantization of the essentially nonlinear midisuperspace model describing cylindrically symmetric gravitational waves with two polarizations is presented. A Fock space type representation is constructed. It is based on a…
The method of geometric quantization is applied to a particle moving on an arbitrary Riemannian manifold $Q$ in an external gauge field, that is a connection on a principal $H$-bundle $N$ over $Q$. The phase space of the particle is a…
The canonical quantization on a single light front is performed for the Abelian gauge fields with the Weyl gauge coupled with fermion field currents. The analysis is carried separately for 1+1 dimensions and for higher dimensions. The Gauss…
We develop a systematic procedure to quantise canonically Hamiltonians of light-matter models of transmission lines coupled through lumped linear lossless ideal nonreciprocal elements, that break time-reversal symmetry, in a circuit QED…
We study the transformation leading from Arnowitt, Deser, Misner (ADM) Hamiltonian formulation of General Relativity (GR) to the $\Gamma\Gamma$ metric Hamiltonian formulation derived from the Lagrangian density which was firstly proposed by…
Classical phasor analysis is fundamentally limited to sinusoidal single-frequency conditions, which poses challenges when working in the presence of harmonics. Furthermore, the conventional solution, which consists of decomposing signals…
We canonically quantize a Poisson manifold to a Lie 2-groupoid, complete with a quantization map, and show that it relates geometric and deformation quantization: the perturbative expansion in $\hbar$ of the (formal) convolution of two…
The Standard Model of particle physics stands as one of the most profound and successful frameworks for describing the fundamental workings of nature. The global form of the Standard Model gauge group, however, remains an open question: it…
We develop a unified categorical framework for gauging both continuous and finite symmetries in arbitrary spacetime dimensions. Our construction applies to geometric categories i.e. categories internal to stacks. This generalizes the…
In this paper a class of classical Hamiltonian systems is geometrically formulated. This class is such that a Hamiltonian can be written as the sum of a kinetic energy function and a potential energy function. In addition, these energy…
In this article we give a universal model for geometric quantization associated to a real polarization given by an integrable system with non-degenerate singularities. This universal model goes one step further than the previous cotangent…
In this first of a series of four articles, it is shown how a hamiltonian quantum dynamics can be formulated based on a generalization of classical probability theory using the notion of quasi-invariant measures on the classical phase space…