Related papers: Fourier transform from momentum space to twistor s…
We develop ambitwistor string theories for 4 dimensions to obtain new formulae for tree-level gauge and gravity amplitudes with arbitrary amounts of supersymmetry. Ambitwistor space is the space of complex null geodesics in complexified…
In a Minkowski spacetime, one may transform the Dirac wave function under the spin group, as one transforms coordinates under the Poincar\'e group. This is not an option in a curved spacetime. Therefore, in the equation proposed…
Events in Minkowski space-time can be obtained from the intersection of two twistors with no helicity. These can be represented within the geometric (Clifford) algebra formalism, in a particular conformal space that is constructed from a…
In this paper we obtain new sufficient conditions for representation of a function as an absolutely convergent Fourier integral. Unlike those known earlier, these conditions are given in terms of belonging to weighted spaces. Adding weights…
We review aspects of twistor theory, its aims and achievements spanning thelast five decades. In the twistor approach, space--time is secondary with events being derived objects that correspond to compact holomorphic curves in a complex…
In applied mathematics generally and fluid dynamics in particular, the role of complex variable methods is normally confined to two-dimensional motion and the association of points with complex numbers via the assignment w = x+i y. In this…
We show that MHV diagrams are the Feynman diagrams of certain twistor actions for gauge theories in an axial gauge. The gauge symmetry of the twistor action is larger than that on space-time and this allows us to fix a gauge that makes the…
We define an infinite class of unitary transformations between position and momentum fractional spaces, thus generalizing the Fourier transform to a special class of fractal geometries. Each transform diagonalizes a unique Laplacian…
An account is given of how the 'box integrals', as used for one-loop calculations in massless field theory, appear in momentum-twistor geometry. Particular attention is paid to the role of compact contour integration in representing the…
A momentum-space approach to conformal field theory offers a new perspective on cosmological correlators and better reveals the underlying connections to scattering amplitudes. This thesis explores the interplay between integral…
The twistor construction is applied for obtaining examples of generalized complex structures (in the sense of N. Hitchin) that are not induced by a complex or a symplectic structure.
The search for a geometrical understanding of dualities in string theory, in particular T-duality, has led to the development of modern T-duality covariant frameworks such as Double Field Theory, whose mathematical structure can be…
The aim of this paper is to study three dimensional Lorentzian conformal field theories in twistor space. We formulate the conformal Ward identities and solve for two and three point Lorentzian Wightman functions. We found that the Helicity…
In this paper, we develop a momentum super space formalism for $\mathcal{N}=1,2$ superconformal field theories in three dimensions. First, we solve for super-correlators in the usual momentum superspace variables. However, we found that…
With respect to the Dirac operator and the conformally invariant Laplacian, an explicit description of the inverse Penrose transform on Riemannian twistor spaces is given. A Dolbeault representative of cohomology on the twistor space is…
Iterative Fast Fourier Transform methods are useful for calculating the fields in composite materials and their macroscopic response. By iterating back and forth until convergence, the differential constraints are satisfied in Fourier…
This paper determines how to define a discretely implemented Fourier transform when analysing an observed spatial point process. To develop this transform we answer four questions; first what is the natural definition of a Fourier…
Relying on a mathematical analogy of the pure states of the two-qubit system of quantum information theory with four-component spinors we introduce the concept of the intrinsic entanglement of spinors. To explore its physical sense we study…
The Fourier coefficient map is considered as an operator from a weighted Lorentz space on the circle to a weighted Lorentz sequence space. For a large range of Lorentz indices, necessary and sufficient conditions on the weights are given…
Using the twist deformation of $U(igl(4,R))$, the linear part of the diffeomorphism, we define a scalar function and construct a free scalar field theory in four-dimensional $\kappa$-Minkowski spacetime. The action in momentum space turns…