相关论文: Remarks on the conformal transformations
Since 100 years or so, it has been usually accepted that the " conformal group " could be defined in an arbitrary dimension n as the group of transformations preserving a non degenerate flat metric up to a nonzero invertible point depending…
Conformal group of transformations in the momentum space, consisting of translations $p'_{\mu}=p_{\mu}+h_{\mu}$, rotations $p'_{\mu}=\Lambda^{\nu}_{\mu}p_{\nu}$, dilatation $p'_{\mu}=\lambda p_{\mu}$ and inversion $p'_{\mu}=…
By using fundamental units c, h, G as conversion factors one can easily transform the dimensions of all observables. In particular one can make them all ``geometrical'', or dimensionless. However this has no impact on the fact that there…
We investigate the behaviour of elliptic Feynman integrals under modular transformations. This has a practical motivation: Through a suitable modular transformation we can achieve that the nome squared is a small quantity, leading to fast…
Conformal invariance plays a significant role in many areas of Physics, such as conformal field theory, renormalization theory, turbulence, general relativity. Naturally, it also plays an important role in geometry: theory of Riemannian…
We present the explicit form of the diffeomorphisms of the time variable that transform the measure for quantum free massless particle into the measure for quantum free massive particle.
One of the most challenging problems in the domain of 2-D image or 3-D shape is to handle the non-rigid deformation. From the perspective of transformation groups, the conformal transformation is a key part of the diffeomorphism. According…
We provide a simple geometric meaning for deformations of so-called $T{\overline T}$ type in relativistic and non-relativistic systems. Deformations by the cross products of energy and momentum currents in integrable quantum field theories…
Certain notions of convergence of sequences functions such as pointwise convergence and (uniform) convergence on compact or bounded sets come from suitable topological function spaces; see [1]. Under certain conditions these topologies…
Unparticles are realized by deconstruction in higher extra dimensions. It is shown that in this framework when the scale invariance is broken, the corresponding spectral function of the unparticle is shifted by an amount of the breaking…
We present a brief review of some recent results on conformal anomalies in four and more dimensions. The discussion is intended for relativists, so some background on the quantum origin of anomalies and of their simple properties in D=2 is…
As a consequence of the wave nature of light, invisibility devices based on isotropic media cannot be perfect. The principal distortions of invisibility are due to reflections and time delays. Reflections can be made exponentially small for…
We formulate explicitly the necessary and sufficient conditions for the local invertibility of a field transformation involving derivative terms. Our approach is to apply the method of characteristics of differential equations, by treating…
Topics concerning metric dimension related invariants in graphs are nowadays intensively studied. This compendium of combinatorial and computational results on this topic is an attempt of surveying those contributions that are of the…
The rigidity transition occurs when, as the density of microscopic components is increased, a disordered medium becomes able to transmit and ensure macroscopic mechanical stability, owing to the appearance of a space-spanning rigid…
All possible transformations from the Robertson-Walker metric to those conformal to the Lorentz-Minkowski form are derived. It is demonstrated that the commonly known family of transformations and associated conformal factors are not…
We classify all functions which, when applied term by term, leave invariant the sequences of moments of positive measures on the real line. Rather unexpectedly, these functions are built of absolutely monotonic components, or reflections of…
The role of the conformal group in electrodynamics in four space-time dimensions is re-examined. As a pedagogic example we use the application of conformal transformations to find the electromagnetic field for a charged particle moving with…
A geometric generalization of first-order Lagrangian formalism is used to analyse a conformal field theory for an arbitrary primary field. We require that global conformal transformations are Noetherian symmetries and we prove that the…
Jamming is a fundamental transition that governs the mechanical behavior of particulate media, including sand, foam and dense suspensions but also biological tissues: Upon compression, particulate media can change from freely flowing to a…