Related papers: Quantum Theory and Galois Fields
Given the impending timeline of developing good-quality quantum processing units, it is time to rethink the approach to advance quantum computing research. Rather than waiting for quantum hardware technologies to mature, we need to start…
The formalism of quantum mechanics is presented in a way that its interpretation as a classical field theory is emphasized. Two coupled real fields are defined with given equations of motion. Densities and currents associated to the fields…
We prove the Galois correspondence between the subgroups of a finite automorphism group G of a simple vertex operator algebra V and the vertex operator subalgebras of V containing the set V^G of G-invariants.
Quantum information science and engineering (QISE) is a rapidly developing field that leverages the skills of experts from many disciplines to utilize the potential of quantum systems in a variety of applications. It requires talent from a…
"All men by nature desire to know," states Aristotle in the famous first sentence of his Metaphysics. Knowledge about fundamental particles and interactions, that is, knowledge about the deepest aspects of matter, is certainly high if not…
This paper is a commentary on the foundational significance of the Clifton-Bub-Halvorson theorem characterizing quantum theory in terms of three information-theoretic constraints (Foundations of Physics 33, 1561-1591 (2003);…
Quantum theory describes our universe incredibly successfully. To our classically-inclined brains, however, it is a bizarre description that requires a re-imagining of what fundamental reality, or "ontology", could look like. This thesis…
We argue that a clear view on quantum mechanics is obtained by considering that the unicity of the macroscopic world is a fundamental postulate of physics, rather than an issue that must be mathematically justified or demonstrated. This…
In this paper we discuss the problem of performing elementary finite field arithmetic on a quantum computer. Of particular interest, is the controlled-multiplication operation, which is the only group-specific operation in Shor's algorithms…
Intense field quantum field theory (IFQFT) is used to determine new phenomenological predictions arising from Compton scattering and pair production in a strong laser field. This theory utilizes exact solutions of fermions embedded in…
These lecture notes cover the basics of Quantum Field Theory (QFT) and peculiarities in the construction of the Electroweak (EW) sector of the Standard Model (SM). In addition, the present status, issues, and prospects of the SM are…
We consider the quantum Hall effect in terms of an effective field theory formulation of the edge states, providing a natural common framework for the fractional and integral effects.
Quantum gauge theories with finite-dimensional representation spaces are constructed that can have canonical gauge field theories as singular limits. They describe nature as a recursive quantum assembly by iterating Fermi-Dirac…
We outline the solution of a fundamental problem in quantum theory which has hitherto lacked a proper solution, namely finding the requisite quantum theoretical framework guaranteeing that the calculated inverse spontaneous emission rate of…
We review some recent progress in quantum field theory in non-commutative space, focusing onto the fuzzy sphere as a non-perturbative regularisation scheme. We first introduce the basic formalism, and discuss the limits corresponding to…
The quest for a consistent theory which describes the quantum microstructure of spacetime seems to require some departure from the paradigms that have been followed in the construction of quantum theories for the other fundamental…
Gravitational decoherence (GD) refers to the effects of gravity in actuating the classical appearance of a quantum system. Because the underlying processes involve issues in general relativity (GR), quantum field theory (QFT) and quantum…
Many attempts have been made to provide Quantum Field Theory with conceptually clear and mathematically rigorous foundations; remarkable examples are the Bohmian and the algebraic perspectives respectively. In this essay we introduce the…
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…
Lattice field theory, along with its algorithmic and hardware ecosystems, has been at the forefront of computational particle and nuclear physics. It continues to deliver impressive results on the hadronic spectrum, structure, decays, and…