Related papers: Possible Minkowskian Language in Two-level Systems
Newman and Rovelli have used singular Hamilton-Jacobi transformations to reduce the phase space of general relativity in terms of the Ashtekar variables. Their solution of the gauge constraint cannot be inverted and indeed has no Minkowski…
For vacuum Maxwell theory in four dimensions, a supplementary condition exists (due to Eastwood and Singer) which is invariant under conformal rescalings of the metric, in agreement with the conformal symmetry of the Maxwell equations.…
We consider Minkowski spacetime, the set of all point-events of spacetime under the relation of causal accessibility. That is, ${\sf x}$ can access ${\sf y}$ if an electromagnetic or (slower than light) mechanical signal could be sent from…
Given a real number $q$ and a star body in the $n$-dimensional Euclidean space, the generalized dual curvature measure of a convex body was introduced by Lutwak-Yang-Zhang [43]. The corresponding generalized dual Minkowski problem is…
The unique Nature of the Lorentz group in four dimensions is the root cause of the many remarkable properties of the Einstein spacetimes, in particular their operational structure on the 2-forms. We show how this operational structure can…
In 1867, during the time when Maxwell was publishing his electromagnetic theory, L. Lorenz published his theory equating light vibrations with electric currents. Starting from Kirchhoff's Ohm's law expression, Lorenz introduces scalar…
It was shown by Gribov, Ioffe, Pomeranchuk in 1966 and by Ioffe in 1969 that a space-time picture is needed for the Lorentz deformation of hadronic interaction region. It is shown that this deformation is a squeeze transformation. It is…
The class of Zeeman topologies on spacetimes in the frame of relativity theory is considered to be of powerful intuitive justification, satisfying a sequence of properties with physical meaning, such as the group of homeomorphisms under…
We show that D=4 Minkowski space is an emergent concept related to a class of operators in extended Hilbert space with no positive-definite scalar product. We start with the idea of position-like and momentum-like operators (Plewa 2019 J.…
While the Lorentz group serves as the basic language for Einstein's special theory of relativity, it is turning out to be the basic mathematical instrument in optical sciences, particularly in ray optics and polarization optics. The beam…
The nonlinear stability of Minkowski spacetime has been one of the central achievements in the mathematical theory of general relativity and, more broadly, in the analysis of nonlinear geometric wave equations. Since the seminal work of…
In this paper, we endow the space of continuous translation invariant valuation on convex sets generated by mixed volumes coupled with a suitable Radon measure on tuples of convex bodies with two appropriate norms. This enables us to…
This paper combines the post-Minkowskian expansion of general relativity with the language of intersection theory. Because of the nature of the soft limit inherent to the post-Minkowskian expansion, the intersection-based approach is of…
We discuss the discrete light-cone quantization (DLCQ) of a scalar field theory on the maximally supersymmetric pp-wave background in ten dimensions. It has been shown that the DLCQ can be carried out in the same way as in the…
We define a new type of wavelet frame adapted to the study of wave equations, that we call Minkowski curvelets, by reference to the curvelets introduced by Cand\`es, Demanet and Donoho. These space-time, strongly anisotropic, directional…
In this paper, we aim to resolve two fundamental issues in the dynamics of relativity: (i) Under what condition, the time-column space integrals of a Lorentz four-tensor constitute a Lorentz four-vector, and (ii) under what condition, the…
In curved spacetime, Maxwell's equations can be expressed in forms valid in Minkowski background, with the effect of the metric (gravity) appearing as effective polarizations and magnetizations. The electric and magnetic (EM) fields depend…
For research in the field of transformation optics and for the calculation of optically inhomogeneous lenses the method of geometrization of the Maxwell equations seems to be perspective. The basic idea is to transform the coefficients of…
The question how to Lorentz transform an N-particle wave function naturally leads to the concept of a so-called multi-time wave function, i.e. a map from (space-time)^N to a spin space. This concept was originally proposed by Dirac as the…
The Bethe-Salpeter Equation for a two-scalar, S-wave bound system, interacting through a massive scalar, is investigated within the ladder approximation. By assuming a Nakanishi integral representation of the Bethe-Salpeter amplitude, one…