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Investigating a class of models that is familiar in studies of cellular automata, we find that quantum operators can be employed to describe their long distance behavior. These operators span a Hilbert space that appears to turn such a…
Contrary to the conventional view point of quantization that breaks the gauge symmetry, a gauge invariant formulation of quantum electrodynamics is proposed. Instead of fixing the gauge, some frame is chosen to yield the locally invariant…
By modeling a dielectric medium with two independent reservoirs, i.e., electric and magnetic reservoirs, the electromagnetic field is quantized in a linear dielectric medium consistently. A Hamiltonian is proposed from which using the…
Linearized Einstein gravity (with possibly nonzero cosmological constant) is quantized in the framework of algebraic quantum field theory by analogy with Dimock's treatment of electromagnetism [Rev. Math. Phys. 4 (1992) 223--233]. To…
A nonlinear Wightman field is taken to be a nonlinear map from a linear space of test functions to a linear space of Hilbert space operators, with inessential modifications to other axioms only to the extent dictated by the introduction of…
Quantum fields are generally taken to be operator-valued distributions, linear functionals of test functions into an algebra of operators; here the effective dynamics of an interacting quantum field is taken to be nonlinearly modified by…
The purpose of this paper is to sketch an approach towards a reconciliation of quantum theory with relativity theory. It will actually be argued that these two theories ultimately rely on one another. A general operator-algebraic framework…
This note is an introduction to methods of construction for Hilbert space realizations of relativistic quantum physics. The realizations satisfy a revision to Wightman's functional analytic axioms and exhibit interaction in physical…
Quantum systems are viewed as emergent systems from the fundamental degrees of freedom. The laws and rules of quantum mechanics are understood as an effective description, valid for the emergent systems and specially useful to handle…
Non-Fock representations of the canonical commutation relations modeled over an infinite-dimensional nuclear space are constructed in an explicit form. The example of the nuclear space of smooth real functions of rapid decrease results in…
Algebraic quantum field theory is a general mathematical framework for relativistic quantum physics, based on the theory of operator algebras. It comprises all observable and operational aspects of a theory. In its framework the entire…
Polymer quantization is as a useful toy model for the mathematical aspects of loop quantum gravity and is interesting in its own right. Analyzing entropies of physically equivalent states in the standard Hilbert space and the polymer…
A preliminary model of meaningful quanta of information arising from the quantum vacuum, and giving rise to the elementary quantum fields, is presented. We attempt to establish an equivalence of information and physical action, with the…
We formulate the second quantization of a charged scalar field in homogeneous, time-dependent electromagnetic fields, in which the Hamiltonian is an infinite system of decoupled, time-dependent oscillators for electric fields, but it is…
The notion that the electromagnetic field is quantised is usually inferred from observations such as the photoelectric effect and the black-body spectrum. However accounts of the quantisation of this field are usually mathematically…
We discuss the quantization of an unstable field through the construction of a "one-particle Hilbert space." The system considered here is a neutral scalar field evolving over a globally hyperbolic static spacetime and subject to a…
The duality symmetry of free electromagnetic field is analyzed within an algebraic approach. To this end, the conformal $c(1,3)$ algebra generators are expressed as operators quadratic in some abstract operators $\kappa^\alpha$ and…
Background: The vacuum in the light-front representation of quantum field theory is trivial while vacuum in the equivalent canonical representation of the same theory is non-trivial. Purpose: Understand the relation between the vacuum in…
Mathematical tools related to coherence theory and classical-quantum equivalence, due to Wigner and Glauber, are essential to modern, practical and empirical understanding of electromagnetics in areas like quantum optics and…
It is shown that when the gauge-invariant Bohr-Rosenfeld commutators of the free electromagnetic field are applied to the expressions for the linear and angular momentum of the electromagnetic field interpreted as operators then, in the…