Related papers: On the nonlinearity of Four-Dimensional Conformal …
When developing a quantum theory for a physical system, one determines the system's symmetry group and its irreducible unitary representations. For Minkowski space, the symmetry group is the Poincar\'e group, $\mathbb{R}^4 \rtimes…
In this article, we clarify the link between the conformal (i.e. Weyl) correspondence from the Minkowski space to the de Sitter space and the conformal (i.e. SO(2,$d$)) invariance of the conformal scalar field on both spaces. We exhibit the…
The most general lagrangian describing spin 2 particles in flat spacetime and containing operators up to (mass) dimension 6 is carefully analyzed, determining the precise conditions for it to be invariant under linearized (transverse)…
Classification of quantum spinor fields according to quantum bilinear covariants is introduced in a context of quantum Clifford algebras on Minkowski spacetime. Once the bilinear covariants are expressed in terms of algebraic spinor fields,…
We present the first nonlinear term of the higher spin curvature which is covariant with respect to deformed gauge transformations that are linear in the field. We consider in detail the case of spin 3 after presenting spin 2 as an example,…
The effect of quantum corrections to a conformally invariant field theory for a self-interacting scalar field on a curved manifold with boundary is considered. The analysis is most easily performed in a space of constant curvature the…
Within the scope of a FRW cosmological model we have studied the role of spinor field in the evolution of the Universe when it is non-minimally coupled to the gravitational one. We have considered a few types of nonlinearity. It was found…
The well known conformal covariance of the Dirac operator acting on spinor fields over a semi Riemannian spin manifold does not extend to powers thereof in general. For odd powers one has to add lower order curvature correction terms in…
We study integrability of fishnet-type Feynman graphs arising in planar four-dimensional bi-scalar chiral theory recently proposed in arXiv:1512.06704 as a special double scaling limit of gamma-deformed $\mathcal{N}=4$ SYM theory. We show…
Chirality refers to the asymmetry of objects that cannot be superimposed on their mirror image. It is a concept that exists in various scientific fields and has profound consequences. Although these are perhaps most widely recognized within…
The four point function of Conformal Field Theories (CFT's) with global symmetry gives rise to multiple crossing symmetry constraints. We explicitly study the correlator of four scalar operators transforming in the fundamental…
Over the last decade it has been found that nonlinear laws of composition of momenta are predicted by some alternative approaches to "real" 4D quantum gravity, and by all formulations of dimensionally-reduced (3D) quantum gravity coupled to…
Scalar-fermion models, such as the Gross-Neveu-Yukawa model, admit natural $1d$ defects given by the exponential of a scalar field integrated along a straight line. In $4-\varepsilon$ dimensions the defect coupling is weakly relevant and…
A representation of the Lorentz group is given in terms of 4 X 4 matrices defined over the hyperbolic number system. The transformation properties of the corresponding four component spinor are studied, and shown to be equivalent to the…
This is the second of three papers on Conformal General Relativity (CGR). The conformal group is introduced here as the invariance group of the partial order of causal events in $n$D spacetime. Its general structure, discrete symmetries and…
Hypercubic groups in any dimension are defined and their conjugate classifications and representation theories are derived. Double group and spinor representation are introduced. A detailed calculation is carried out on the structures of…
The spin-orbit interaction of light is a crucial concept for understanding the electromagnetic properties of a material and realizing the spin-controlled manipulation of optical fields. Achieving these goals requires a complete description…
Relativistic spin-1/2 particles in curved spacetime are naturally described by Dirac theory, which is a dynamical and Lorentz-invariant field theory. In this work, we propose a non-dynamical fermion theory in 3+1 dimensions dubbed spinor…
We show that dual conformal symmetry, mainly studied in planar $\mathcal N = 4$ super-Yang-Mills theory, has interesting consequences for Feynman integrals in nonsupersymmetric theories such as QCD, including the nonplanar sector. A simple…
The quantum dynamics of the gravitational field non-minimally coupled to an (also dynamical) scalar field is studied in the {\em broken phase}. For a particular value of the coupling the system is classically conformal, and can actually be…