Related papers: Periods and Feynman amplitudes
Motivated by the limited interaction between the mathematical physics community and theoretical physicists - particularly in high-energy theory - we present a computation that is typically the first example in QFT courses but, to our…
I describe a mathematical framework for the efficient processing of the very large sets of Feynman diagrams contributing to the scattering of many particles. I reexpress the established numerical methods for the recursive construction of…
In perturbative quantum field theory one encounters certain, very specific geometries over the integers. These perturbative quantum geometries determine the number contents of the amplitude considered. In the article `Modular forms in…
We review the most recent progress in our understanding of quantum mechanical observables in cosmology in the perturbative regime. It relies on an approach that considers them directly as functions of the data at the space-like boundary at…
An unambiguous definition of Feynman amplitudes in the Wess-Zumino-Witten sigma model and the Chern-Simon gauge theory with a general Lie group is determined by a certain geometric structure on the group. For the WZW amplitudes, this is a…
Physicists become acquainted with special functions early in their studies. Consider our perennial model, the harmonic oscillator, for which we need Hermite functions, or the Laguerre functions in quantum mechanics. Here we choose a…
We present a method for symbolic calculation of Feynman amplitudes for processes involving both massless and massive fermions. With this approach fermion strings in a specific amplitude can be easily evaluated and expressed as basic Lorentz…
Scattering amplitudes are both a wonderful playground to discover novel ideas in Quantum Field Theory and simultaneously of immense phenomenological importance to make precision predictions for e.g.~particle collider observables and more…
In quantum theory, physical amplitudes are usually presented in the form of Feynman perturbation series in powers of coupling constant $\al .$ However, it is known that these amplitudes are not regular functions at $\alpha=0 .$ For QCD, we…
The method of the calculation of the multi-loop superstring amplitudes is proposed. The amplitudes are calculated from the equations that are none other than Ward identities. They are derived from the requirement that the discussed…
In this paper we show how Feynman diagrams, which are used as a tool to implement perturbation theory in quantum field theory, can be very useful also in classical mechanics, provided we introduce also at the classical level concepts like…
This review paper discusses the identification of regions, a crucial first step in applying the "method-of-regions" technique. A systematic approach based on Newton polytope geometry has proven successful and efficient for many cases.…
The amplitude of a Feynman graph in Quantum Field Theory is related to the point-count over finite fields of the corresponding graph hypersurface. This article reports on an experimental study of point counts over F_q modulo q^3, for graphs…
We review the Consistent Amplitude approach to Quantum Theory and argue that quantum probabilities are explicitly Bayesian. In this approach amplitudes are tools for inference. They codify objective information about how complicated…
We review Kreimer's construction of a Hopf algebra associated to the Feynman graphs of a perturbative quantum field theory.
We consider scalar quantum fields on the sphere, both massive and massless. In the massive case we show that the correlation functions define amplitudes which are trace class operators between tensor products of a fixed Hilbert space. We…
The amplitude of subdivergence-free logarithmically divergent Feynman graphs in $\phi^4$-theory in 4 spacetime dimensions is given by a single number, the Feynman period. We numerically compute the periods of 1.3 million completed graphs,…
Results of extensive computations of moments of the Riemann zeta function on the critical line are presented. Calculated values are compared with predictions motivated by random matrix theory. The results can help in deciding between those…
We investigate the properties of the amplitude induced by the anomaly. In a relatively high energy region those amplitudes are constructed by the vector meson poles and the anomaly terms, in which the anomaly terms can be essentially…
Feynman's laws of quantum dynamics are concisely stated, discussed in comparison with other formulations of quantum mechanics and applied to selected problems in the physical optics of photons and massive particles as well as flavour…