Related papers: Why is CPT fundamental?
The observed accelerated cosmic expansion is problematic in that it seems to require an otherwise unobserved dark energy for its origin. A possible alternative explanation has been recently given, which attempts to account for this…
Quantum theory and Lorentz structure are the twin pillars of fundamental physics today. With quantum theory kept and Lorentz structure replaced by Euclidean Jordan algebra --- a more fundamental structure, one naturally arrives at the…
A crucial step in the history of General Relativity was Einstein's adoption of the principle of general covariance which demands a coordinate independent formulation for our spacetime theories. General covariance helps us to disentangle a…
A simple mathematical procedure is introduced which allows redefining in an exact way divergent integrals and limits that appear in the basic equations of classical electrodynamics with point charges. In this way all divergences are at once…
We develop Algebraic Phase Theory (APT), an axiomatic framework for extracting intrinsic algebraic structure from phase based analytic data. From minimal admissible phase input we prove a general phase extraction theorem that yields…
General relativity required the abandonment of Euclidean geometry. Here we show that quantum theory requires the abandonment of classical logic. We show that the Hilbert space representation of quantum theory is logically inevitable. There…
The goal of this expository article is to present a proof that is as direct and elementary as possible of the fundamental theorem of complex multiplication (Shimura, Taniyama, Langlands, Tate, Deligne et al.). The article is a revision of…
The gauged Lorentz theory with torsion has been argued to have an effective theory whose non-trivial background is responsible for background gravitational curvature if torsion is treated as a quantum-mechanical variable against 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…
A group theoretical description of basic discrete symmetries (space inversion P, time reversal T and charge conjugation C) is given. Discrete subgroups of orthogonal groups of multidimensional spaces over the fields of real and complex…
A general theoretical framework that incorporates possible CPT and Lorentz violation in an extension of the standard model and in quantum electrodynamics has been developed over the last decade. The framework originates in the idea that CPT…
The \begin{it} Invariance Theorem \end{it} of M. Gerstenhaber and S. D. Schack states that if $\mathbb{A}$ is a diagram of algebras then the subdivision functor induces a natural isomorphism between the Yoneda cohomologies of the category…
The concept of {\it equivalent systems} from the thermodynamic point of view, originally introduced by Th. De Donder and I. Prigogine, is deeply investigated and revised. From our point of view, two systems are thermodynamically equivalent…
We present an elementary proof of the fundamental theorem of algebra, following Cauchy's version but avoiding his use of circular functions. It is written in the same spirit as Littlewood's proof of 1941, but reduces it to more elementary…
We propose an alternative axiomatic description for non-commutative field theories (NCFT) based on some ideas by Soloviev to nonlocal quantum fields. The local commutativity axiom is replaced by the weaker condition that the fields commute…
Quantum mechanics is an extremely successful theory of nature and yet it lacks an intuitive axiomatization. In contrast, the special theory of relativity is well understood and is rooted into natural or experimentally justified postulates.…
The formulation and some experimental implications of a general Lorentz-violating extension of the standard model are reviewed. The theory incorporates both CPT-preserving and CPT-breaking terms. It is otherwise a conventional quantum field…
This topical review gives a comprehensive overview and assessment of recent results in Causal Dynamical Triangulations (CDT), a modern formulation of lattice gravity, whose aim is to obtain a theory of quantum gravity nonperturbatively from…
We introduce here a new axiomatisation of the rational fragment of the ZX-calculus, a diagrammatic language for quantum mechanics. Compared to the previous axiomatisation introduced in [8], our axiomatisation does not use any metarule , but…
Algebraic quantum field theory is considered from the perspective of the Hochschild cohomology bicomplex. This is a framework for studying deformations and symmetries. Deformation is a possible approach to the fundamental challenge of…