相关论文: Introduction to a Quantum Theory over a Galois Fie…
A proposal of an algebraic model for the relation between a quantum environment and certain classical particle system is given. The quantum environment is described by a category of possible quantum states, the initial particle system is…
In the free case, it is possible to define quantum fields which describe particles with integer or half-integer spin larger than one. It is shown that particles with integer spin must have Bose statistic and particles with half-integer-spin…
We explore finite-field frameworks for quantum theory and quantum computation. The simplest theory, defined over unrestricted finite fields, is unnaturally strong. A second framework employs only finite fields with no solution to x^2+1=0,…
Practically measurable quantities resulting from quantum field theory are not described by hermitian operators, contradicting one of the cornerstone axioms of orthodox quantum theory. This could be a sign that some of the axioms of orthodox…
We describe how physical universes that are composed of gauge and gravitationally interacting bosonic and fermionic quantum fields arise from the generic discrete distribution of many quantifiable properties of arbitrary static entities.…
A unified conceptual foundation of classical and quantum physics is given, free of undefined terms. Ensembles are defined by extending the `probability via expectation' approach of Whittle to noncommuting quantities. This approach carries…
A gauge theory of quantum gravity is formulated, in which an internal, field dependent metric is introduced which non-linearly realizes the gauge fields on the non-compact group $SL(2,C)$, while linearly realizing them on $SU(2)$.…
Quantum field theory is mostly known as the most advanced and well-developed theory in physics, which combines quantum mechanics and special relativity consistently. In this work, we study the spinless quantum field theory, namely the…
A sketch is given of a circle of ideas relating quantum field theories with representation theory. The main mathematical ingredients are spinor geometry and the gauge group equivariant K-theory of the space of connections.
We take quantum theory and replace $\mathbb{C}$ by $\mathbb{C}[\varepsilon]$ where $\varepsilon^2=0$, i.e. we extend quantum theory to the ring of dual complex numbers. The aim is to develop a common language in which to treat continuous…
As shown in our publications, quantum theory based on a finite ring of characteristic $p$ (FQT) is more general than standard quantum theory (SQT) because the latter is a degenerate case of the former in the formal limit $p\to\infty$. One…
It is believed that gravity will be explained in the framework of the existing quantum theory when one succeeds in eliminating divergencies at large momenta or small distances (although the phenomenon of gravity has been observed only at…
The paper presents the representation of quantum field theory without introduction of infinity bare masses and coupling constants of fermions. Counter-terms, compensating for divergent quantities in self-energy diagrams of fermions and…
The only evidence we have for a discrete reality comes from quantum measurements; without invoking these measurements, quantum theory describes continuous entities. This seeming contradiction can be resolved via analysis that treats…
We present the elements of a new approach to the foundations of quantum theory and probability theory which is based on the algebraic approach to integration, information geometry, and maximum relative entropy methods. It enables us to deal…
After more than a century since its birth, Quantum Theory still eludes our understanding. If asked to describe it, we have to resort to abstract and ad hoc principles about complex Hilbert spaces. How is it possible that a fundamental…
The geometric form of standard quantum mechanics is compatible with the two postulates: 1) The laws of physics are invariant under the choice of experimental setup and 2) Every quantum observation or event is intrinsically statistical.…
We introduce the notion of background independent quantum field theory. The distinguishing feature of this theory is that the dynamics can be formulated without recourse to a background metric structure. We show in a simple model how the…
Quantum General Relativity (QGR), sometimes called Loop Quantum Gravity, has matured over the past fifteen years to a mathematically rigorous candidate quantum field theory of the gravitational field. The features that distinguish it from…
We first give simple arguments in favor of the "Zero Constants Party", i.e. that quantum theory should not contain fundamental dimensionful constants at all. Then we argue that quantum theory should proceed not from a space-time background…