Light cone

Summary

In special and general relativity, a light cone (or "null cone") is the path that a flash of light, emanating from a single event (localized to a single point in space and a single moment in time) and traveling in all directions, would take through spacetime. Details If one imagines the light confined to a two-dimensional plane, the light from the flash spreads out in a circle after the event E occurs, and if we graph the growing circle with the vertical axis of the graph representing time, the result is a cone, known as the future light cone. The past light cone behaves like the future light cone in reverse, a circle which contracts in radius at the speed of light until it converges to a point at the exact position and time of the event E. In reality, there are three space dimensions, so the light would actually form an expanding or contracting sphere in three-dimensional (3D) space rather than a circle in 2D, and the light cone would actually be a four-dimensional version

Official source

https://en.wikipedia.org/wiki/Light_cone

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We exhibit non-equivariant perturbations of the blowup solutions constructed in [18] for energy critical wave maps into

\mathbb{S}^2

. Our admissible class of perturbations is an open set in some sufficiently smooth topology and vanishes near the light cone. We show that the blowup solutions from [18] are rigid under such perturbations, including the space-time location of blowup. As blowup is approached, the dynamics agrees with the classification obtained in [7], and all six symmetry parameters converge to limiting values. Compared to the previous work [16] in which the rigidity of the blowup solutions from [18] under equivariant perturbations was proved, the class of perturbations considered in the present work does not impose any symmetry restrictions. Separation of variables and decomposing into angular Fourier modes leads to an infinite system of coupled nonlinear equations, which we solve for small admissible data. The nonlinear analysis is based on the distorted Fourier transform, associated with an infinite family of Bessel type Schrödinger operators on the half-line indexed by the angular momentum

n

. A semi-classical WKB-type spectral analysis relative the parameter

\hbar=\frac{1}{n+1}

for large

|n|

allows us to effectively determine the distorted Fourier basis for the entire infinite family. Our linear analysis is based on the global Liouville-Green transform as in the earlier work [4, 5].

2020

We study the momentum-space 4-point correlation function of identical scalar operators in conformal field theory. Working specifically with null momenta, we show that its imaginary part admits an expansion in conformal blocks. The blocks are polynomials in the cosine of the scattering angle, with degree corresponding to the spin of the intermediate operator. The coefficients of these polynomials are obtained in a closed-form expression for arbitrary spacetime dimension d > 2. If the scaling dimension of the intermediate operator is large, the conformal block reduces to a Gegenbauer polynomial f on the contrary the scaling dimension saturates the unitarity bound, the block is different Gegenbauer polynomial These results are then used as an inversion formula to compute OPE coefficients in a free theory example.

SPRINGER2018

, ,

We report on the experimental investigation of the Floquet-Bloch modes propagation inside photonic crystal (PhC) structures as well as their emission from the structures with far-field optics. We demonstrate that far-field optical experiments can be used to retrieve fundamental optical properties of PhC structures, Such as the light path, the dispersion Curves above and below the light cone, and the equi-frequency Surfaces both in one and two dimensions, in a single step and without numerical post-processing.

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2008

We exhibit non-equivariant perturbations of the blowup solutions constructed in [18] for energy critical wave maps into

\mathbb{S}^2

n

. A semi-classical WKB-type spectral analysis relative the parameter

\hbar=\frac{1}{n+1}

for large

|n|

allows us to effectively determine the distorted Fourier basis for the entire infinite family. Our linear analysis is based on the global Liouville-Green transform as in the earlier work [4, 5].

2020