Related papers: Introduction to a Quantum Theory over a Galois Fie…
This note is a development of our two previous papers, arXiv:1212.3392v1 and 1306.3660v1. The fundamental question is whether there exists a Galois theory, in which the Galois group is a quantum group. For a linear equations with respect to…
The usual formulation of quantum theory is rather abstract. In recent work I have shown that we can, nevertheless, obtain quantum theory from five reasonable axioms. Four of these axioms are obviously consistent with both classical…
The theory of quantum mechanics is examined using non-standard real numbers, called quantum real numbers (qr-numbers), that are constructed from standard Hilbert space entities. Our goal is to resolve some of the paradoxical features of the…
Gott spacetime has closed timelike curves, but no locally anomalous stress-energy. A complete orthonormal set of eigenfunctions of the wave operator is found in the special case of a spacetime in which the total deficit angle is $2\pi$. A…
It is commonly assumed that quantum field theory arises by applying ordinary quantum mechanics to the low energy effective degrees of freedom of a more fundamental theory defined at ultra-high-energy/short-wavelength scales. We shall argue…
Linearity allows several versions of reality to simultaneously exist in the state vector. But it implies that there is no interaction between versions, and that there will never be perception of more than one version. It also implies, in…
Quantum theory's irreducible empirical core is a probability calculus. While it presupposes the events to which (and on the basis of which) it serves to assign probabilities, and therefore cannot account for their occurrence, it has to be…
Since the quantum field theory treats a system of particles, there must be a distribution which is associated with the system of particles. It means that a meaningful quantity is adjoined in the system of particles. It seems that these…
For classical field theories with probabilistic initial conditions the classical field observables are an idealization. Their arbitrarily precise values poorly reflect the characteristic uncertainty in the presence of substantial…
The concept of a particle is ambiguous in quantum field theory. It is generally agreed that particles depend not only on spacetime, but also on coordinates used to parametrise spacetime points. One of us has in contrast proposed a…
Both statistics and quantum theory deal with prediction using probability. We will show that there can be established a connection between these two areas. This will at the same time suggest a new, less formalistic way of looking upon basic…
In this paper we derive the complex Hilbert space formalism of quantum theory from four simple information theoretic axioms. It is shown that quantum theory is the only non classical probabilistic theory satisfying the following axioms:…
We provide a mechanism by which, from a background independent model with no quantum mechanics, quantum theory arises in the same limit in which spatial properties appear. Starting with an arbitrary abstract graph as the microscopic model…
A quantum field theory formalism is reviewed that leads to a self-consistent, finite quantum gravity, Yang-Mills and Higgs theory, which is unitary and gauge invariant to all orders of perturbation theory. The gauge hierarchy problem is…
Quantum cosmology is the quantum theory of the entire universe. Although strange at first sight, it is appropriate because (1) our world appears to be fundamentally quantum, (2) the classical description of gravity breaks down at…
A realistic axiomatic formulation of Galilean Quantum Field Theories is presented, from which the most important theorems of the theory can be deduced. In comparison with others formulations, the formal aspect has been improved by the use…
Standard particle theory is based on quantized matter embedded in a classical geometry. Here, a complementary model is proposed, based on classical matter -- massive bodies, without quantum properties -- embedded in a quantum geometry. It…
Infinite statistics in which all representations of the symmetric group can occur is known as a special case of quon theory. Our previous work has built a relativistic quantum field theory which allows interactions involving infinite…
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 argue that the main reason of crisis in quantum theory is that nature, which is fundamentally discrete and even finite, is described by classical mathematics involving the notions of infinitely small, continuity etc. Moreover, since…