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We investigate generic properties of one-loop amplitudes in unordered gauge theories in four dimensions. For such theories the organisation of amplitudes in manifestly crossing symmetric expressions poses restrictions on their structure and…
We consider the three-loop mixed strong-electroweak (${\mathcal{O}}(\alpha \alpha_s^2)$) corrections to the quark form factor. We compute the master integrals which are appearing in the Feynman diagrams containing a single massive boson in…
We evaluate the master integrals for the two-loop, planar box-diagrams contributing to the elastic scattering of muons and electrons at next-to-next-to leading-order in QED. We adopt the method of differential equations and the Magnus…
We extend the generalized D-dimensional unitarity method for numerical evaluation of one-loop amplitudes by incorporating massive particles. The issues related to extending the spinor algebra to higher dimensions, treatment of external…
Quantum field theory provides the framework for the most fundamental physical theories to be confirmed experimentally and has enabled predictions of unprecedented precision. However, calculations of physical observables often require great…
Using the spectral properties of orthogonal polynomials, we introduce a finite version of quantum field theory for elementary particles. Closed-loop integrals in the Feynman diagrams for computing transition amplitudes are finite.…
The QED vacuum polarization in external monochromatic plane-wave electromagnetic fields is calculated with spatial and temporal variations of the external fields being taken into account. We develop a perturbation theory to calculate the…
In a recent paper \cite{ft} a new powerful method to calculate Feynman diagrams was proposed. It consists in setting up a Taylor series expansion in the external momenta squared. The Taylor coefficients are obtained from the original…
This thesis contains two parts. The first part deals with pion-nucleon/meson-baryon scattering in the Kadyshevsky formalism. This formalism is introduced and discussed. Problems may arise when derivative couplings and/or higher spin fields…
The goal of this paper is to make a connection between tropical geometry, representations of quantum affine algebras, and scattering amplitudes in physics. The connection allows us to study important and difficult questions in these areas:…
Tree amplitudes of the production of two kinds of scalar particles at threshold from one virtual particle are calculated in a model of two scalar fields with $O(2)$ symmetric quartic interaction and unequal masses. These amplitudes exhibit…
The analytic integration and simplification of multi-loop Feynman integrals to special functions and constants plays an important role to perform higher order perturbative calculations in the Standard Model of elementary particles. In this…
We derive a minimal set of Feynman rules for the loop amplitudes in unitary models of closed strings, whose target space is a simply laced (extended) Dynkin diagram. The string field Feynman graphs are composed of propagators, vertices…
The effective action includes all quantum corrections arising in a given quantum field theory. Thus it serves as a powerful generating functional from which quantum-corrected scattering amplitudes can be constructed via tree-level…
The perturbative approach to quantum field theories has made it possible to obtain incredibly accurate theoretical predictions in high-energy physics. Although various techniques have been developed to boost the efficiency of these…
We provide a new set of on-shell recursion relations for tree-level scattering amplitudes, which are valid for any non-trivial theory of massless particles. In particular, we reconstruct the scattering amplitudes from (a subset of) their…
Threshold amplitudes are considered for $n$-particle production in arbitrary scalar theory. It is found that, like in $\phi ^4$, leading-$n$ corrections to the tree level amplitudes, being summed over all loops, exponentiate. This result…
The scattering equation formalism is a general framework for calculation of amplitudes in theories of massless particles. We provide a detailed introduction to the 4D scattering equation framework accessible to non-experts, outline current…
In any consistent massive quantum field theory there are well known bounds on scattering amplitudes at high energies. In conformal field theory there is no scattering amplitude, but the Mellin amplitude is a well defined object analogous to…
We derive an alternative representation of the leading-order contribution to the polarization operator in strong-field quantum electrodynamics with a plane-wave electromagnetic background field, which is manifestly symmetric with respect to…