Related papers: The geometry of physical observables
In this paper, we classify Jordan superalgebras of dimension up to three over an algebraically closed field of characteristic different of two. Our main motivation to obtain such classification comes out from the intention to give an answer…
Jordan operator algebras are norm-closed spaces of operators on a Hilbert space which are closed under the Jordan product. The discovery of the present paper is that there exists a huge and tractable theory of possibly nonselfadjoint Jordan…
In the paper "Is there a Jordan geometry underlying quantum physics?" (Int. J. Theor. Phys., to appear; arXiv:0801.3069 [math-ph]), generalized projective geometries have been proposed as a framework for a geometric formulation of Quantum…
We propose a model for the universe based on Jordan algebras. The action consists of cubic terms with coefficients being the structure constants of a Jordan algebra. Coupling constants only enter the theory via symmetry breaking which also…
A certain generalization of the mathematical formalism of quantum mechanics beyond operator algebras is considered. The approach is based on the concept of conditional probability and the interpretation of the Lueders - von Neumann quantum…
Using geometric approach we formulate quantum theory in terms of Jordan algebras. We analyze the notion of (quasi)particle (=elementary excitation of translation-invariant stationary state) and the scattering of (quasi)particles in this…
We solve an open problem in spectral geometry: the construction of finite-dimensional, discrete geometries coordinatized by non-simple, exceptional Jordan algebras. The approach taken is readily generalisable to broad classes of…
The aim of this paper is to offer an overview of the most important applications of Jordan structures inside mathematics and also to physics, up-dated references being included. For a more detailed treatment of this topic see - especially -…
Physical systems, characterized by an ensemble of interacting elementary constituents, can be represented and studied by different algebras of observables or operators. For example, a fully polarized electronic system can be investigated by…
The purpose of this article is to introduce projective geometry over composition algebras : the equivalent of projective spaces and Grassmannians over them are defined. It will follow from this definition that the projective spaces are in…
The classification, up to isomorphism, of two-dimensional (not necessarily commutative) Jordan algebras over algebraically closed fields and $\mathbb{R}$ is presented in terms of their matrices of structure constants.
Over a field of characteristic $0$ we give a concrete, computation--ready description of Jordan algebra structures and their low--order deformation theory. The Jordan identity is quartic in the elements and cubic in the multiplication, and…
In this survey paper we give an overview over constructions of geometries associated to Jordan structures (algebras, triple systems and pairs), featuring analogs of these constructions with the Lie functor on the one hand and with the…
We define symmetric spaces in arbitrary dimension and over arbitrary non-discrete topological fields $\K$, and we construct manifolds and symmetric spaces associated to topological continuous quasi-inverse Jordan pairs and -triple systems.…
We study linear spaces of symmetric matrices whose reciprocal is also a linear space. These are Jordan algebras. We classify such algebras in low dimensions, and we study the associated Jordan loci in the Grassmannian.
Based on a more careful canonical analysis, we motivate a reduced quantization - in the sense of superspace quantization - of slightly inhomogeneous cosmology in place of the Dirac quantization in the existing literature, and provide it in…
A geometric realization of the projective completion of the Jordan pair corresponding to a three-graded Lie algebra is given which permits to develop a geometric structure theory of the projective completion. This will be used in Part II of…
We establish that many fundamental concepts and techniques in quantum field theory and collider physics can be naturally understood and unified through a simple new geometric language. The idea is to equip the space of collider events with…
We give the algebraic and geometric classification of complex four-dimensional Jordan superalgebras. In particular, we describe all irreducible components in the corresponding varieties.
The purpose of this paper is to introduce Hom-alternative algebras and Hom-Jordan algebras. We discuss some of their properties and provide construction procedures using ordinary alternative algebras or Jordan algebras. Also, we show that a…