From Euclidean to Minkowski space with the Cauchy–Riemann equations

From Euclidean to Minkowski space with the Cauchy-Riemann equations

We present an elementary method to obtain Green’s functions in non-perturbative quantum field theory in Minkowski space from calculated Green’s functions in Euclidean space. Since in non-perturbative field theory the analytical structure of amplitudes is many times unknown, especially in the presence of confined fields, dispersive representations suffer from systematic uncertainties. Therefore ...

Wave equations on q-Minkowski space

We give a systematic account of the exterior algebra of forms on q-Minkowski space, introducing the q-exterior derivative, q-Hodge star operator, q-coderivative, q-LaplaceBeltrami operator and the q-Lie-derivative. With these tools at hand, we then give a detailed exposition of the q-d’Alembert and q-Maxwell equation. For both equations we present a q-momentum-indexed family of plane wave solut...

A Euclidean Alternative to Minkowski Spacetime Diagram

Abstract By re-interpreting the special relativity (SR) postulates based on Euclidean 4-space-time , a geometrical model is formulated called the Euclidean Space-Time (EST) diagram. The EST diagram is a velocity vector model with a real time parameter along the 4th dimension and consequently has a (++++) metric. The model is governed by a circular function geometry and the relativistic variatio...

On images of continuous functions from a compact manifold to Euclidean space

On the Quaternionic Curves in the Semi-Euclidean Space E_4_2

In this study, we investigate the semi-real quaternionic curves in the semi-Euclidean space E_4_2. Firstly, we introduce algebraic properties of semi-real quaternions. Then, we give some characterizations of semi-real quaternionic involute-evolute curves in the semi-Euclidean space E42 . Finally, we give an example illustrated with Mathematica Programme.