Related papers: Possible Minkowskian Language in Two-level Systems
The famous Minkowski inequality provides a sharp lower bound for the mixed volume $V(K,M[n-1])$ of two convex bodies $K,M\subset\mathbb{R}^n$ in terms of powers of the volumes of the individual bodies $K$ and $M$. The special case where $K$…
We develop the first steps towards an analysis of geometry on the quantum spacetime proposed in [1]. The homogeneous elements of the universal differential algebra are naturally identified with operators living in tensor powers of Quantum…
This note is by no means a comprehensive study of Minkowski's space-time formalism of special relativity. The mathematician, Hermann Minkowski was Einstein's former mathematics professor at the Z\"urich Polytechnic. During his studies at…
Canonical quantization of quantum field theory models is inherently related to the Lorentz invariant partition of classical fields into the positive and the negative frequency parts $u(x) = u^+(x) + u^-(x),$ performed with the help of…
We prove that every continuous map acting on the four-dimensional Minkowski space and preserving light cones in one direction only is either a Poincar\'e similarity, that is, a product of a Lorentz transformation and a dilation, or it is of…
James Clerk Maxwell unknowingly discovered a correct relativistic, quantum theory for the light quantum, forty-three years before Einstein postulated the photon's existence. In this theory, the usual Maxwell field is the quantum wave…
New Orlicz Brunn-Minkowski inequalities are established for rigid motion compatible Minkowski valuations of arbitrary degree. These extend classical log-concavity properties of intrinsic volumes and generalize seminal results of Lutwak and…
The special theory of relativity has fundamentally changed our views of space and time. The relativity of simultaneity in particular, and the theory of relativity as a whole, still presents significant difficulty for beginners in the…
An extension of the finite and infinite Lie groups properties of complex numbers and functions of complex variable is proposed. This extension is performed exploiting hypercomplex number systems that follow the elementary algebra rules. In…
In 1971, Feynman et al. published a paper on hadronic mass spectra and transition rates based on the quark model. Their starting point was a Lorentz-invariant differential equation. This equation can be separated into a Klein-Gordon…
By analyzing the Einstein-box thought experiment with the principle of relativity, it is shown that Abraham's light momentum and energy in a medium cannot constitute a Lorentz four-vector, and they consequentially break global momentum and…
We present here the linear regime of the Einstein's field equations in the characteristic formulation. Through a simple decomposition of the metric variables in spin-weighted spherical harmonics, the field equations are expressed as a…
Maximal supergravity in four dimensions admits two inequivalent dyonic gaugings of the group $\mathrm{SO}(4) \times \mathrm{SO}(2,2) \ltimes T^{16}$. Both admit a Minkowski vacuum with residual $\mathrm{SO}(4) \times \mathrm{SO}(2)^2$…
One of the most fruitful results from Minkowski's geometric viewpoint on number theory is his so called 1st Fundamental Theorem. It provides an optimal upper bound for the volume of an o-symmetric convex body whose only interior lattice…
Einstein distinguished between ``principle'' and ``constructive'' theories in physics, and although he thought the latter were more explanatory than the former, he regarded his 1905 formulation of special relativity theory as a principle…
If there is a null gradient field in 1+3 dimensional space-time, we can set up a kind of light-cone coordinate system in the space-time. In such coordinate system, the metric takes a simple form, which is much helpful for simplifying and…
The author has proposed five rules that permit conscious observers to be included in quantum mechanics. In the present paper, these rules are applied to the observation of a non-local pair of correlated particles. Rule (4) again prevents an…
The Lorentz transformation is derived without assuming the existence of Maxwell's equations, or that the speed of light is a constant, or even that light exists. This leads us logically to sonsider the existence of a primal field called…
The picture of space-time that Minkowski created in 1907 has been followed by two important developments in physics not contained in the original picture: general relativity and quantum mechanics. We will argue that the use of concepts of…
A modification of Kaluza-Klein theory is proposed in which, as a result of a symmetry breaking, five-dimensional space-time is partially parallelized implying the appearance of torsion fields. A naturally chosen action functional leads to…