Related papers: The box integrals in momentum-twistor geometry
One of the most important mathematical tools necessary for Quantum Field Theory calculations is the field propagator. Applications are always done in terms of plane waves and although this has furnished many magnificent results, one may…
The technique of functional integration over velocities is applied to the calculation of the propagator of a spinning particle with and without anomalous magnetic moment. A representation for the spin factor is obtained in this context for…
The symmetries of a scalar field theory in multifractional spacetimes are analyzed. The free theory realizes the Poincar\'e algebra, and the associated symmetries are modifications of ordinary translations and Lorentz transformations. In…
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 employ the modification of the basic Penrose formula in twistor theory, which allows to introduce commuting composite space-time coordinates. It appears that in the course of such modification the internal symmetry SU(2) of two-twistor…
A new first integral for the equations corresponding to twisting type-N vacuum gravitational fields with two non-commuting Killing vectors is introduced. A new reduction of the problem to a complex second-order ordinary differential…
The generalized projection-tensor geometry introduced in an earlier paper is extended. A compact notation for families of projected objects is introduced and used to summarize the results of the previous paper and obtain fully projected…
We review in a pedagogical way the method of differential equations for the evaluation of D-dimensionally regulated Feynman integrals. After dealing with the general features of the technique, we discuss its application in the context of…
A method for the evaluation of the epsilon expansion of multi-loop massless Feynman integrals is introduced. This method is based on the Gegenbauer polynomial technique and the expansion of the Gamma function in terms of harmonic sums.…
We illustrate a rigorous approach to express the totally symmetric isotropic tensors of arbitrary rank in the $n$-dimensional Euclidean space as a linear combination of products of Kronecker deltas. By making full use of the symmetries, one…
Quantum geometry, i.e., the quantum theory of intrinsic and extrinsic spatial geometry, is a cornerstone of loop quantum gravity. Recently, there have been many new ideas in this field, and I will review some of them. In particular, after a…
The purpose of this paper is to introduce the notion of mixed twistor structure, a generalization of the notion of mixed Hodge structure. The utility of this notion is to make possible a theory of weights for various things surrounding…
This thesis carries out a detailed investigation of the action for pure Yang- Mills theory which L. Mason formulated in twistor space. The rich structure of twistor space results in greater gauge freedom compared to the theory in ordinary…
New analytic formulas for one-loop three-point Feynman integrals in general space-time dimension ($d$) are presented in this paper. The calculations are performed at general configurations for internal masses and external momenta. The…
The motion of a particle in the field of dispiration (due to a wedge disclination and a screw dislocation) is studied by path integration. By gauging $SO(2) \otimes T(1)$, first, we derive the metric, curvature, and torsion of the medium of…
One of the main difficulties in studying Quantum Field Theory, in the perturbative regime, is the calculation of D-dimensional Feynman integrals. In general, one introduces the so-called Feynman parameters and associated with them the…
The role of the quantum universal enveloping algebras of symmetries in constructing non-commutative geometry of the space-time including vector bundles, measure, equations of motion and their solutions is discussed. In the framework of the…
We give the full representation theory of the gravitational extended corner symmetry group in two-dimensions. This includes projective representations, which correspond to representations of the quantum corner symmetry group. We find that…
A "Bochner-type" integral for vector lattice-valued functions with respect to (possibly infinite) vector lattice-valued measures is presented with respect to abstract convergences, satisfying suitable axioms, and some fundamental properties…
In this article, we analyze the fundamental global and local symmetries involved in the action for the free relativistic point particle. Moreover, we identify a hidden local symmetry, whose explicit consideration and factorization utilizing…