Related papers: Complex geometry and fundamental physical law
We present the basic concepts of tensor products of vector spaces, emphasizing linear algebraic and combinatorial techniques as needed for applied areas of research. The topics include (1) Introduction; (2) Basic multilinear algebra; (3)…
We start from a new theory (discussed earlier) in which the arena for physics is not spacetime, but its straightforward extension-the so called Clifford space ($C$-space), a manifold of points, lines, areas, etc..; physical quantities are…
The traditional study of plane and space algebraic curves by looking at their tangent vectors, curvatures and torsions provides geometric, but unfortunately not sufficient information about individual curves in order to be able to…
In the most general formulation of gravity, the metric and connection are independent degrees of freedom, and the connection may include torsion and non-metricity (or distortion, collectively) degrees of freedom, resulting in a huge number…
In this work, we review a plethora of modified theories of gravity with generalized curvature-matter couplings. The explicit nonminimal couplings, for instance, between an arbitrary function of the scalar curvature $R$ and the Lagrangian…
Gravity stands apart from other fundamental interactions in that it is locally equivalent to an accelerated frame and can be transformed away. Again it is indistinguishable from the geometry of space-time (which is an arena for all other…
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…
Higher order derivatives of functions are structured high dimensional objects which lend themselves to many alternative representations, with the most popular being multi-index, matrix and tensor representations. The choice between them…
Starting from a description of various generalized function algebras based on sequence spaces, we develop the general framework for considering linear problems with singular coefficients or non linear problems. Therefore, we prove…
The real physical space is derived from a mathematical space constructed as a tessellation lattice of primary balls, or superparticles. Mathematical characteristics, such as distance, surface and volume, generate in the fractal tessellation…
In this paper we study finite dimensional algebras, in particular finite semifields, through their correspondence with nonsingular threefold tensors. We introduce a alternative embedding of the tensor product space into a projective space.…
These are lecture notes for a course on the theory of Clifford algebras, with special emphasis on their wide range of applications in mathematics and physics. Clifford algebra is introduced both through a conventional tensor algebra…
In three-dimensional Euclidean geometry, the scalar product produces a number associated to two vectors, while the vector product computes a vector perpendicular to them. These are key tools of physics, chemistry and engineering and…
We discuss how the vector nature of magnetic fields, and the geometrical interpretation of gravity introduced by general relativity, lead to a special coupling between magnetism and spacetime curvature. This magneto-geometrical interaction…
Basic algebraic and combinatorial properties of finite vector spaces in which individual vectors are allowed to have multiplicities larger than $ 1 $ are derived. An application in coding theory is illustrated by showing that multispace…
We introduce the key concepts of duality mappings and metric extensor. The fundamental identities involving the duality mappings are presented, and we disclose the logical equivalence between the so-called metric tensor and the metric…
Expanding the work of arXiv:1504.08040, we show that black holes obey a second law for linear perturbations to bifurcate Killing horizons, in any covariant higher curvature gravity coupled to scalar and vector fields. The vector fields do…
Over the last two years, the canonical approach to quantum gravity based on connections and triads has been put on a firm mathematical footing through the development and application of a new functional calculus on the space of gauge…
For certain problems involving vector fields, it is possible to find an associated imaginary field that, in conjunction with the first, forms a complex field for which the equation can be solved. This result is generalized to arbitrary…
An attempt is made to construct space and obtain dynamics from Loop Algebras and their elements. We define three new products between loops namely 'Vertical Product', 'Horizontal Product' and 'Total Product'. As for the dynamics, we obtain…