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For any massless, irreducible representation of the covering of the proper, orthochronous Poincar\'e group we construct covariant, free quantum fields that generate the representation space from the vacuum and are localized in semi-infinite…
Electromagnetism is the paradigm case of a theory that satisfies relativistic locality. This can be proven by demonstrating that, once the theory's laws are imposed, what is happening within a region fixes what will happen in the…
The principal goal of this paper is to pass all quantum probability formulas to the projective space associated to the complex Hilbert space of a given quantum system, providing a more complete geometrization of quantum theory. Quantum…
We illustrate an isomorphic representation of the observable algebra for quantum mechanics in terms of the functions on the projective Hilbert space, and its Hilbert space analog, with a noncommutative product in terms of explicit…
Due to the existence of incompatible observables, the propositional calculus of a quantum system does not form a Boolean algebra but an orthomodular lattice. Such lattice can be realised as a lattice of subspaces on a real, complex or…
Familiar formulations of classical and quantum mechanics are shown to follow from a general theory of mechanics based on pure states with an intrinsic probability structure. This theory is developed to the stage where theorems from quantum…
Goal of this review is to introduce the algebraic approach to quantum field theory on curved backgrounds. Based on a set of axioms, first written down by Haag and Kastler, this method consists of a two-step procedure. In the first one, a…
We consider a matrix space based on the spin degree of freedom, describing both a Hilbert state space, and its corresponding symmetry operators. Under the requirement that the Lorentz symmetry be kept, at given dimension, scalar symmetries,…
Analytical and numerical methods are developed to analyze the quantum nature of the big bang in the setting of loop quantum cosmology. They enable one to explore the effects of quantum geometry both on the gravitational and matter sectors…
The extended algebra of the free electromagnetic fields, including infrared singular fields, and the almost radial gauge, both introduced earlier, are postulated for the construction of the quantum electrodynamics in a Hilbert space (no…
The problems which arise for a relativistic quantum mechanics are reviewed and critically examined in connection with the foundations of quantum field theory. The conflict between the quantum mechanical Hilbert space structure, the locality…
It is shown that adopting the \emph{Quantum Field} ---extended entity in space-time build by dynamic appearance propagation and annihilation of virtual particles--- as the primary ontology the astonishing features of quantum mechanics can…
Well defined quantum field theory (QFT) for the electroweak force including quantum electrodynamics (QED) and the weak force is obtained by considering natural unitary representations of a group $K\subset U(2,2)$, where $K$ is locally…
We compute the electromagnetic field created by an ultrarelativistic charged particle in vacuum at distances comparable to the particle Compton wavelength. The wave function of the particle is governed by the Klein-Gordon equation, for a…
A formulation of Covariant Canonical Quantization is discussed, which works on an extended Hilbert space and reduces to conventional canonical quantization when constraining to the solution of the field equation a priori. From the formal…
Entanglement is often regarded as an inherently quantum feature. We show that this does not have to be the case: under restricted operational access, classical correlations can appear nonseparable when expressed in the formalism of quantum…
The quantization of the electromagnetic field in vacuum is presented without reference to lagrangean quantum field theory. The equal time commutators of the fields are calculated from basic principles. A physical discussion of the…
Hamiltonian light-front dynamics of quantum fields may provide a useful approach to systematic non-perturbative approximations to quantum field theories. We investigate inequivalent Hilbert-space representations of the light-front field…
We consider an approach in which the usual wave function in the quadrature representation of mode j of the electromagnetic field is further quantized to produce a field operator. Since the electromagnetic field is already second quantized,…
Classical surfaces in phase space correspond to quantum states in Hilbert space. Subsystems specify factor spaces of the Hilbert space. An entangled state corresponds semiclassically to a surface that cannot be decomposed into a product of…