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The role of topology in elementary quantum physics is discussed in detail. It is argued that attributes of classical spatial topology emerge from properties of state vectors with suitably smooth time evolution. Equivalently, they emerge…
Quantum mechanics is able to predict challenging behaviors even in the simplest physical scenarios. These behaviors are possible because of the important dynamical role that phase plays in the evolution of quantum systems, and are very…
Symmetries and transformations are explored in the framework of entropic quantum dynamics. Two conditions arise that are required for any transformation to qualify as a symmetry. The heart of this work lies in the application of these…
A simple algebraic model for charged particle moving in two dimensional space under influence of singular magnetic field is given. The fundamental assumption for the model is that every charged particle coupled to the magnetic field is…
Excitations of a relativistic geometry are used to represent the theory of quantum electrodynamics. The connection excitations and the frame excitations reduce, respectively, to the electromagnetic field operator and electron field…
The quantum dynamics of an atom with a magnetic quadrupole moment that interacts with an external field subject to a harmonic and a linear confining potentials is investigated. It is shown that the interaction between the magnetic…
It is offered to consider monopoles in Abelian Projection as quantum excitations which are solutions of the quantized Yang-Mills equations. According to the Heisenberg quantization method these equations are equivalent an infinite set of…
We establish a quantum dynamics framework for curved submanifolds embedded in higher-dimensional spaces. Through rigorous dimensional reduction, we derive the first complete Schr\"{o}dinger and Klein-Gordon equations incorporating…
Quantum Hamiltonian Computing is a recent approach that uses quantum systems, in particular a single molecule, to perform computational tasks. Within this approach, we present explicit methods to construct logic gates using two different…
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…
A formal symmetry between generalized coordinates and momenta is postulated to formulate classical and quantum theories of a particle coupled to an Abelian gauge field. It is shown that the symmetry (a) requires the field to have dynamic…
The behavior of a massive scalar particle on the spacetime surrounding a monopole is studied from a quantum mechanical point of view. All the boundary conditions necessary to turn into self-adjoint the spatial portion of the wave operator…
Motivated by group-theoretical questions that arise in the context of asymptotic symmetries in gravity, we study model spaces and their quantization from the viewpoint of constrained Hamiltonian systems. More precisely, we propose that a…
Simple constructions and protocols are demonstrated to allow the implementation of universal quantum computation on an arbitrarily large quantum system by controlling a fixed number of spins, vastly reducing the engineering requirements in…
Simulating magnetic effects with cold gases of neutral atoms is a challenge. Since these atoms have no charge, one needs to create artificial gauge fields by taking advantage of the geometric phases that can result for instance from…
The collective dynamics of a many-body system is described as a special case of low-energy quantum dynamics, occurring when the ground state breaks a continuous symmetry of the Hamiltonian. This approach is applied to the spontaneous…
The Hamiltonian action of a Lie group on a symplectic manifold induces a momentum map generalizing Noether's conserved quantity occurring in the case of a symmetry group. Then, when a Hamiltonian function can be written in terms of this…
In this paper, we address a foundational challenge in quantum field theory on curved spacetime by developing a consistent framework within loop quantum gravity. We introduce a methodology for defining meaningful superpositions of quantum…
Absolute confinement of its color charges is a natural property of gauge theories such as quantum chromodynamics. On the one hand, it can be attributed to the existence of color-magnetic monopoles, a topological feature of the theory, but…
Systems of interacting charges and fields are ubiquitous in physics. Recently, it has been shown that Hamiltonians derived using different gauges can yield different physical results when matter degrees of freedom are truncated to a few…