Related papers: Tutorial on Scale and Conformal Symmetries in Dive…
The conformal compactification is considered in a hierarchy of hypercomplex projective spaces with relevance in physics including Minkowski and Anti-de Sitter space. The geometries are expressed in terms of bicomplex Vahlen matrices and…
Lattice simulations can play an important role in the study of dynamical electroweak symmetry breaking by providing quantitative results on the nonperturbative dynamics of candidate theories. For this programme to succeed, it is crucial to…
We give a comprehensive analysis of interrelations between the basic concepts of the modern theory of symmetry (classical and non-classical) reductions of partial differential equations. Using the introduced definition of reduction of…
We investigate a conformal-like transformation for which the spacetime interval is invariant.
The goal of these notes is to give a brief explanation of how electric-magnetic duality in four dimensions is related to the existence of an unusual conformal field theory in six dimensions.
Dimensionality reduction is a common method for analyzing and visualizing high-dimensional data across domains. Dimensionality-reduction algorithms involve complex optimizations and the reduced dimensions computed by these algorithms…
Multidimensional scaling visualizes dissimilarities among objects and reduces data dimensionality. While many methods address symmetric proximity data, asymmetric and especially three-way proximity data (capturing relationships across…
We show that there is a very simple relationship between differential and dimensional renormalization of low-order Feynman graphs in renormalizable massless quantum field theories. The beauty of the differential approach is that it achieves…
We describe a new correspondence between four-dimensional conformal field theories with extended supersymmetry and two-dimensional chiral algebras. The meromorphic correlators of the chiral algebra compute correlators in a protected sector…
We consider the statistical description of steady state fully developed incompressible fluid turbulence at the inertial range of scales in any number of spatial dimensions. We show that turbulence statistics is scale but not conformally…
We review a recent progress on fluid dynamics applied to strongly interacting nuclear matter. The efforts are made to highlight consequences of scale invariance breaking on the hydrodynamic description of a nuclear medium. Both…
Conformal and disformal transformations are now being very intensively studied in the context of various modified gravity theories. In particular, some special classes of them can be used for constructing Mimetic Dark Matter models.…
In this paper we give several conditions for a space to be minimal for conformal dimension. We show that there are sets of zero length and conformal dimension 1 thus answering a question of Bishop and Tyson. Another sufficient condition for…
We derive exact scaling relations for two-dimensional relativistic hydrodynamic turbulence in the inertial range of scales. We consider both the energy cascade towards large scales and the enstrophy cascade towards small scales. We…
Integration of nonlinear dynamical systems is usually seen as associated to a symmetry reduction, e.g. via momentum map. In Lax integrable systems, as pointed out by Kazhdan, Kostant and Sternberg in discussing the Calogero system, one…
Let $K$ be an algebraically closed field of arbitrary characteristic, $X$ an irreducible variety and $Y$ an irreducible projective variety over $K$, both are not necessarily smooth. Let $f:X\rightarrow X$ and $g:Y\rightarrow Y$ be dominant…
Integrable systems in low dimensions, constructed through the symmetry reduction method, are studied using phase portrait and variable separation techniques. In particular, invariant quantities and explicit periodic solutions are…
In this work we compile a few differential equations (ODEs) that arise from the relativistic equations in cosmological models that consider the ``constants'' as scalars functions dependent on time and they are described as perfect as well…
Disclosure of scaling relationship between observable quantities gives direct information about dynamics of natural phenomenon. This is the main reason why scaling plays a key role in the methodology of natural sciences. In this talk, Part…
We study the scalar and pseudoscalar sector in a five-dimenional model describing chiral symmetry breaking. We calculate the scalar and pseudoscalar two-point correlator, the mass spectrum and interactions. We also obtain the scalar and…