Related papers: Spacetime is Right-handed
The concept of Euclidean time is proposed which is dual to the usual Minkowski time. The De Sitter solution is shown to be dual to the anti-De Sitter solution under the dual transformation in which Euclidean time and Minkowski time are…
Some properties of the Clifford algebras Cl(3,0), Cl(1,3), Cl(1,3)(C), Cl(4,1) and Cl(2,4) are presented, and three isomorphisms between the Dirac-Clifford algebra C x Cl(1,3) and Cl(4,1) are exhibited, in order to construct conformal maps…
Penrose's Spin Geometry Theorem is extended further, from $SU(2)$ and $E(3)$ (Euclidean) to $E(1,3)$ (Poincar\'e) invariant elementary quantum mechanical systems. The Lorentzian spatial distance between any two non-parallel timelike…
In the 2-spinor formalism, the gravity can be dealt with curvature spinors with four spinor indices. Here we show a new effective method to express the components of curvature spinors in the rank-2 $4 \times 4$ tensor representation for the…
We explore how the topology of spacetime fabric is encoded into the local structure of Riemannian metrics using the gauge theory formulation of Euclidean gravity. In part I, we provide a rigorous mathematical foundation to prove that a…
We show that the space of Euclid's parameters for Pythagorean triples is endowed with a natural symplectic structure and that it emerges as a spinor space of the Clifford algebra $\mathbb{R}_{2,1}$, whose minimal version may be…
We introduce spinors, at a level appropriate for an undergraduate or first year graduate course on relativity, astrophysics or particle physics. The treatment assumes very little mathematical knowledge (mainly just vector analysis and some…
We obtain a continuous Wick rotation for Dirac, Majorana and Weyl spinors $\psi \to \exp ({1\over 2} \theta \gamma^4 \gamma^5)\psi$ which interpolates between Minkowski and Euclidean field theories.
The flow of time moves in one direction in any spatial position and orientation in this universe. Chiral objects, which lack mirror symmetry, retain their chirality regardless of their position or orientation. Despite being seemingly…
We studied the behavior of nonlinear spinor field within the scope of a static cylindrically symmetric space-time. It is found that the energy-momentum tensor (EMT) of the spinor field in this case possesses nontrivial non-diagonal…
Rosenfeld's geometric approach to spinors is considered, according to which the coordinates of spinors are represented by the coordinates of the plane generators of the maximal dimension of the absolutes of non-Euclidean spaces. As an…
We explicitly construct the SO(d,d) transformations of Ramond-Ramond field strengths and potentials, along with those of the space-time supersymmetry parameters, the gravitinos and the dilatinos in type-II theories. The results include the…
Spacetime inversion symmetries such as parity and time reversal play a central role in physics, but they are usually treated as global symmetries. In quantum gravity there are no global symmetries, so any spacetime inversion symmetries must…
The spinor representation of spin-1/2 states can equally well be mapped to a single unit quaternion, yielding a new perspective despite the equivalent mathematics. This paper first demonstrates a useable map that allows Bloch-sphere…
This paper develops a geometric model for coupled two-state quantum systems (qubits), which is formulated using geometric (aka Clifford) algebra. It begins by showing how Euclidean spinors can be interpreted as entities in the geometric…
We investigate complex quaternion-valued exterior differential forms over 4-dimensional Lorentzian spacetimes and explore Weyl spinor fields as minimal left ideals within the complex quaternion algebra. The variational derivation of the…
A classical continuum theory corresponding to Barrett and Crane's model of Euclidean quantum gravity is presented. The fields in this classical theory are those of SO(4) BF theory, a simple topological theory of an so(4) valued 2-form…
Dynamics is considered as a corollary of the space-time geometry. Evolution of a particle in the space-time is described as a chain of connected equivalent geometrical objects. Space-time geometry is determined uniquely by the world…
Benefiting from the index spinorial formalism, the Killing spinor equation is integrated in six-dimensional spacetimes. The integrability conditions for the existence of a Killing spinor are worked out and the Killing spinors are classified…
The space-time length R between a moving source and the observation point is calculated in order to substitute with it the spatial distance D, normally used in the Newton's law of gravitation, as well as in any inverse-square-law.…