Related papers: The non-Abelian state-dependent gauge field in opt…
We present a general analytical formalism to determine the energy spectrum of a quantum particle in a cubic lattice subject to translationally invariant commensurate magnetic fluxes and in the presence of a general space-independent…
The modes of the electromagnetic field are solutions of Maxwell's equations taking into account the material boundary conditions. The field modes of classical optics - properly normalized - are also the mode functions of quantum optics.…
Efficient methods for describing non abelian charges in worldline approaches to QFT are useful to simplify calculations and address structural properties, as for example color/kinematics relations. Here we analyze in detail a method for…
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…
The standard lore in noncommutative physics is the use of first order variational description of a dynamical system to probe the space noncommutativity and its consequences in the dynamics in phase space. As the ultimate goal is to…
The dynamics of abelian vector and antisymmetric tensor gauge fields can be described in terms of twisted self-duality equations. These first-order equations relate the p-form fields to their dual forms by demanding that their respective…
Noncommutative quantum mechanics can be considered as a first step in the construction of quantum field theory on noncommutative spaces of generic form, when the commutator between coordinates is a function of these coordinates. In this…
Noncommutative duality for C*-dynamical systems is a vast generalization of Pontryagin duality for locally compact abelian groups. In this series of lectures, we give an introduction to the categorical aspects of this duality, focusing…
The space of states and operators for a large class of background independent theories of quantum spacetime dynamics is defined. The SU(2) spin networks of quantum general relativity are replaced by labelled compact two-dimensional…
We argue that higher dimensional classical, nonabelian gauge theory may lead to a lower dimensional quantum field theory due to its inherent chaotic dynamics which acts like stohastic quantization. The dimensional reduction is based upon…
The work is dedicated to the challenge: control and manipulation of the quantum state of a remote physical object. The goal is approached via the entanglement channel between the object and a local physical system - actuator - subjected to…
The algebraic formulation of the quantum group covariant noncommutative geometry in the framework of the $R$-matrix approach to the theory of quantum groups is given. We consider structure groups taking values in the quantum groups and…
A nonlocal mass operator can be consistently set in local form through the introduction of a set of additional fields with geometrical appropriated properties. A local and polynomial gauge invariant action is thus identified. Equations…
Noncommutative version of D-dimensional relativistic particle is proposed. We consider the particle interacting with the configuration space variable $\theta^{\mu\nu}(\tau)$ instead of the numerical matrix. The corresponding Poincare…
Results that illuminate the physical interpretation of states of nonperturbative quantum gravity are obtained using the recently introduced loop variables. It is shown that: i) While local operators such as the metric at a point may not be…
The Cartan control problem of the quantum circuits discussed from the differential geometry point of view. Abstract unitary transformations of $SU(2^n)$ are realized physically in the projective Hilbert state space $CP(2^n-1)$ of the…
We derive the interaction of fermions with a dynamical space-time based on the postulate that the description of physics should be independent of the reference frame, which means to require the form-invariance of the fermion action under…
We combine the "evolving constants" approach to the construction of observables in canonical quantum gravity with the Page--Wootters formulation of quantum mechanics with a relational time for generally covariant systems. This overcomes the…
We extend the "gauge choice" problem Lamb noticed to include a time-dependent relativistic non-perturbative Coulomb field, which can be produced by a cluster of relativistic charged particles. If adiabatic conditions are carefully…
The orbital angular momentum of light, unlike spin, is an infinite-dimensional discrete variable and may hence offer enhanced performances for encoding, transmitting, and processing information in the quantum regime. Hitherto, this degree…