The general structure of the conformal anomaly and the dilaton’s effect to the anomaly are analysed. First we give a new formal proof of the statement that the conformal anomaly, in the theory which is conformal invariant at the classical level, is conformal invariant. The heat-kernel regularization and Fujikawa’s method are taken for the analysis. We present a new explicit result of the confor...

A novel robust adaptive beamforming method for conformal array is proposed. By using interpolation technique, the cylindrical conformal array with directional antenna elements is transformed to a virtual uniform linear array with omni-directional elements. This method can compensate the amplitude and mutual coupling errors as well as desired signal point errors of the conformal array efficientl...

Conformal blocks form a system of vector bundles over the moduli space of complex curves with marked points. We discuss various aspects of these bundles. In particular, we present conjectures about the dimensions of sub-bundles. They imply a Verlinde formula for non-simply connected groups like PGL(n, C). We then explain how conformal blocks enter in the construction of conformal field theories...

The well known conformal covariance of the Dirac operator acting on spinor fields does not extend to its powers in general. For odd powers of the Dirac operator we derive an algorithmic construction in terms of associated tractor bundles computing correction terms in order to achieve conformal covariance. These operators turn out to be formally (anti-) self-adjoint. Working out this algorithm w...

We discuss non-relativistic conformal algebras generalizing the Schrödinger algebra. One instance of these algebras is a conformal, acceleration-extended, Galilei algebra, which arises also as a contraction of the relativistic conformal algebra. In two dimensions, this admits an “exotic” central extension, whereby boosts do not commute. We study general properties of non-relativistic conformal ...

We calculate conformal anomalies in noncommutative gauge theories by using path integral method (Fujikawa’s method). As well as the axial anomalies and chiral gauge anomalies, the conformal anomalies take the form of the straightforward Moyal deformation in the corresponding conformal anomalies in ordinary gauge theories. However, Moyal star product leads the difference in the coefficient of th...

BGG-operators form sequences of invariant differential operators and the first of these is overdetermined. Interesting equations in conformal geometry described by these operators are those for Einstein scales, conformal Killing forms and conformal Killing tensors. We present a deformation procedure of the tractor connection which yields an invariant prolongation of the first operator. The expl...

We present a conformal theory for intermittent scalar fields. As an example, we consider the energy flux from large to small scales in the developed turbulent flow. The conformal correlation functions are found in the inertial range of scales. In the simplest case, the theory leads to the log-normal model. Parameters of the model are expressed via integrals of the conformal correlation function...

There are two methods of set prediction that are provably valid under the assumption of randomness: transductive conformal prediction and inductive conformal prediction. The former method is informationally efficient but often lacks computational efficiency. The latter method is, vice versa, computationally efficient but less efficient informationally. This talk discusses a new method, which we...

Abstract. We consider the GUT-like model with two scalar fields which has infinitesimal deviation from the conformal invariant fixed point at high energy region. In this case the dominating quantum effect is the conformal trace anomaly and the interaction between the anomaly-generated propagating conformal factor of the metric and the usual dimensional scalar field. This interaction leads to th...