A discrete symmetry between quarks and (generalized) leptons can exist in nature, and its spontaneous symmetry breaking scale can be as low as a few TeV. Such a discrete symmetry also has interesting implications for how electroweak symmetry is spontaneously broken, because the simplest version of the theory requires two electroweak Higgs doublets rather than one in order to provide acceptable ...

A Josephson junction laser is realised when a microwave cavity driven by voltage-biased junction. Through the ac effect, dc voltage generates periodic drive that acts on and interactions between its modes. sufficiently strong enables processes down-convert resonant with high harmonic into photons at fundamental frequency, breaking discrete time translation symmetry set frequency. Using classica...

assertion, discrete, equation, fractal, language, mind, phoneme, sentence, symmetry, syntax, truth

It is well known that a local, unitary Poincaré-invariant 2D quantum field theory with a global scaling symmetry and a discrete non-negative spectrum of scaling dimensions necessarily has both a left and a right local conformal symmetry. In this Letter, we consider a chiral situation beginning with only a left global scaling symmetry and do not assume Lorentz invariance. We find that a left con...

Abstract: Two-dimensional (2D) functions with wallpaper group symmetry can be written as Fourier series displaying both translational and point-group symmetry. We elaborate the symmetry-adapted Fourier series for each of the 17 wallpaper groups. The symmetry manifests itself through constraints on and relations between the Fourier coefficients. Visualising the equivalencies of Fourier coefficie...

We study a one parameter family of discrete Löwner evolutions driven by a random walk on the real line. We show that it converges to the stochastic Löwner evolution (SLE) under rescaling. We show that the discrete Löwner evolution satisfies Markovian-type and symmetry properties analogous to SLE, and establish a phase transition property for the discrete Löwner evolution when the parameter equa...