Related papers: A magic connection between massive and massless di…
In vacuum space-times the exterior derivative of a Killing vector field is a two-form that satisfies Maxwell equations without electromagnetic sources. Using the algebraic structure of this two-form we have set up a new formalism for the…
We calculate convergent 3-loop Feynman diagrams containing a single massive loop equipped with twist $\tau =2$ local operator insertions corresponding to spin $N$. They contribute to the massive operator matrix elements in QCD describing…
While modern optics is largely a physics of harmonic oscillators and two-by-two matrices, it is possible to learn about some hidden properties of the two-by-two matrix from optical systems. Since two-by-two matrices can be divided into…
In this work we compute the most general massive one-loop off-shell three-point vertex in D-dimensions, where the masses, external momenta, and exponents of propagators are arbitrary. This follows our previous paper in which we have…
A systematic study of the scalar one-loop two-, three-, and four-point Feynman integrals is performed. We consider all cases of mass assignment and external invariants and derive closed expressions in arbitrary space-time dimension in terms…
N=4 supersymmetric Yang-Mills theory exhibits a rather surprising duality of Wilson-loop vacuum expectation values and scattering amplitudes. In this paper, we investigate this correspondence at the diagram level. We find that one-loop…
The linking integral is an invariant of the link-type of two manifolds immersed in a Euclidean space. It is shown that the ordinary Gauss integral in three dimensions may be simplified to a winding number integral in two dimensions. This…
For any two disjoint oriented circles embedded into the 3-dimensional real projective space, we construct a 3-dimensional configuration space and its map to the projective space such that the linking number of the circles is the half of the…
The off-shell version of the c-map is presented, based on a systematic off-shell reduction from four to three space-time dimensions for supergravity theories with eight supercharges. In the reduction, the R-symmetry group is enhanced to…
We present analytical results for all master integrals for massless three-point functions, with one off-shell leg, at four loops. Our solutions were obtained using differential equations and direct integration techniques. We review the…
For two-loop two-point diagrams with arbitrary masses, an algorithm to derive the asymptotic expansion at large external momentum squared is constructed. By using a general theorem on asymptotic expansions of Feynman diagrams, the…
The new generalization of the gauge interaction for the bosonic strings is found. We consider some quasiequivariant maps from the space of metrics on the worldsheet to the space of $n$-tuples of one- and two-dimensional loops. The…
We show the value of mass-momentum diagrams for analyzing collision problems in classical mechanics in one dimension. Collisions are characterized by the coefficient of restitution and the momentum of the interacting particles both before…
We study quantum aspects of field theories defined on N=1/2 superspace, where both bosonic and fermionic coordinates are made non(anti)commutative. We compute the one-loop effective superpotential, and we find that planar and nonplanar…
We review several multi-loop techniques for analytical massless Feynman diagram calculations in relativistic quantum field theories: integration by parts, the method of uniqueness, functional equations and the Gegenbauer polynomial…
I will review some of the recent intense activity concerning infrared and collinear divergences in gauge theory amplitudes. The central quantity in these studies is the multi-particle soft anomalous dimension matrix, which is completely…
We propose nonlinear Dirac equations where the conformal degree of the self-interaction terms are equal to that of the Dirac operator and the coupling parameters are dimensionless. As such, the massless equation is conformally invariant and…
We show that for a class of two-loop diagrams, the on-shell part of the integration-by-parts (IBP) relations correspond to exact meromorphic one-forms on algebraic curves. Since it is easy to find such exact meromorphic one-forms from…
We describe a model of massive matter fields interacting through higher-spin gauge fields in 2+1 dimensional space-time. The two main conclusions are that the parameter of mass $M$ appears as a module characterizing an appropriate vacuum…
We study gauge theories with N=1 supersymmetry in 2+1 dimensions. We start by calculating the 1-loop effective superpotential for matter in an arbitrary representation. We then restrict ourselves to gauge theories with fundamental matter.…