Related papers: Symplectic vs pseudo-Euclidean space-time with ext…
It is conjectured that in the origin of space-time there lies a symplectic rather than metric structure. The complex symplectic symmetry Sp(2l,C), l\ge1 instead of the pseudo-orthogonal one SO(1,d-1), d\ge4 is proposed as the space-time…
The advantages to consider the ordinary space-time as the symplectic rather than pseudo-orthogonal one are indicated, and the consequences of extending this view to extra space/time dimensions are discussed.
We classify simply-connected homogeneous ($D+1$)-dimensional spacetimes for kinematical and aristotelian Lie groups with $D$-dimensional space isotropy for all $D\geq 0$. Besides well-known spacetimes like Minkowski and (anti) de Sitter we…
We consider nontrivial critical models in $d=6+\epsilon$ spacetime dimensions with anticommuting scalars transforming under the symplectic group $\text{Sp}(N)$. These models are nonunitary, but the couplings are real and all operator…
The symplectization of an overtwisted contact structure in Euclidean 3--space is shown to be an exotic symplectic structure on Euclidean 4--space. The technique can be extended to produce exotic symplectic structures in higher dimensional…
The formal structure of the early Einstein's Special Relativity follows the axiomatic deductive method of Euclidean geometry. In this paper we show the deep-rooted relation between Euclidean and space-time geometries that are both linked to…
By analogy with complex numbers, a system of hyperbolic numbers can be introduced in the same way: z=x+h*y with h*h=1 and x,y real numbers. As complex numbers are linked to the Euclidean geometry, so this system of numbers is linked to the…
We describe the relation between vectors and spinors in complex spacetime in an unconventional chirally asymmetric manner, using purely right-handed spinors, with Minkowski spacetime getting Wick rotated to a four-dimensional Euclidean…
The relations between the hidden symmetries of the six-dimensional pseudo-Euclidean space with signature (+++ -- ) and the conserved quantum characteristics of elementary particles is established. The hidden symmetries are brought out by…
A consistent description of the fundamental interactions of particle physics based upon the assumption of 6 real extra dimensions is presented. The usual 4-dimension space-time, a curved hypersurface with the Lorentz group as local…
We realize the hamiltonian action of the one spatial Poincare group G, analogous to the projective unitary representation, on a coadjoint orbit of G whic we interpret as a symplectic space-time where the time is associated to a physical…
In this paper we consider the ``symplectic'' version of the Euler equations studied by Ebin \cite{ebin}. We show that these equations are globally well-posed on the Sobolev space $H^s(\mathbb{R}^{2n})$ for $n \geq 1$ and $s > 2n/2+1$. The…
The aim of this note is to present a construction of symplectic structures on orientable globally hyperbolic 4-dimensional lorentzian manifolds. Said structures are defined on the manifold itself, not on its cotangent bundle. It also…
We introduce the symplectic group $\mathrm{Sp}_2(G, \sigma)$ associated to a Lie subgroup $G$ of a (possibly noncommutative) associative algebra $A$ equipped with an anti-involution $\sigma$. Our construction recovers several classical Lie…
Two families of symplectic methods specially designed for second-order time-dependent linear systems are presented. Both are obtained from the Magnus expansion of the corresponding first-order equation, but otherwise they differ in…
The concept of space group has long served as the fundamental framework to describe the physical properties of crystalline materials, from electronic bands to photonic dispersions. The recent progress of spatiotemporal control, such as…
Of those gauge theories of gravity known to be equivalent to general relativity, only the biconformal gauging introduces new structures - the quotient of the conformal group of any pseudo-Euclidean space by its Weyl subgroup always has…
A conventional space-time diagram is $r-ct$ one, which satisfies the Minkowski geometry. This geometry conflict the intuition from the Euclid geometry. In this work an Euclid space-time diagram is proposed to describe relativistic world…
Normed division and Clifford algebras have been extensively used in the past as a mathematical framework to accommodate the structures of the standard model and grand unified theories. Less discussed has been the question of why such…
In this paper we deal with symplectic Lie algebras. All symplectic structures are determined for dimension four and the corresponding Lie algebras are classified up to equivalence. Symplectic four dimensional Lie algebras are described…