Related papers: Feynman Amplitudes and Cosmic Galois group

We decompose renormalized Feynman rules according to the scale and angle dependence of amplitudes. We use parametric representations such that the resulting amplitudes can be studied in algebraic geometry.

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…

We present the current status of the application of our approach of exact amplitude-based resummation in quantum field theory to two areas of investigation: precision QCD calculations of all three of us as needed for LHC physics and the…

There is currently a high demand for theoretical predictions for processes at next-to-next-to-leading order (NNLO) and beyond, mainly due to the large amount of data which has already been collected at LHC. This requires practical methods…

R. P. Feynman was quite fond of inventing new physics. It is shown that some of his physical ideas can be supported by the mathematical instruments available from the Lorentz group. As a consequence, it is possible to construct a…

A systematic study of recursive renormalization of Feynman amplitudes is carried out both in Euclidean and in Minkowski configuration space. For a massless quantum field theory (QFT) we use the technique of extending associate homogeneous…

We propose to call a class of deformed Feynman integrals as twisted Feynman integrals, where the integrand has an additional exponential factor linear in loop momenta. Such integrals appear in various contexts: tensor reduction of Feynman…

This reply addresses concerns expressed in a comment (arXiv:2508.16689v1) on arXiv:submit/6841332 [physics.gen-ph] 29 Sep 2025 the paper given in the title (arXiv:2501.02022v2), hereafter referred to as the paper.

We describe the origins of recurrence relations between field theory amplitudes in terms of the construction of Feynman diagrams. In application we derive recurrence relations for the amplitudes of QED which hold to all loop orders and for…

These notes briefly discuss Fourier transforms of finite measures and extensions of Fourier integrals to points in complex domains.

Using different Lubin-Tate groups, we compare $(\phi, \Gamma)$ modules associated to a Galois representation via Fontaine's theory.

These are lecture notes of a mini-course given by the first author in Moscow in July 2019, taken by the second author and then edited and expanded by the first author. They were also a basis of the lectures given by the first author at the…

Categorification of scattering amplitudes for planar Feynman diagrams in scalar field theories with a polynomial potential is reported. Amplitudes for cubic theories are directly written down in terms of projectives of hearts of…

A unified treatment of Schwinger parametrised Feynman amplitudes is suggested which addresses vertices of arbitrary order on the same footing as propagators. Contributions from distinct diagrams are organised collectively. The scheme is…

This set of lectures provides an overview of the basic theory and phenomenology of the cosmic microwave background. Topics include a brief historical review; the physics of temperature and polarization fluctuations; acoustic oscillations of…

We investigate some Galois groups of linearized polynomials over fields such as $\mathbb{F}_q(t)$. The space of roots of such a polynomial is a module for its Galois group. We present a realization of the symmetric powers of this module, as…

Floquet time crystals, characterized by momentum gaps (k-gaps), have sparked intense interest across various branches of physics due to their intriguing dynamics and promising applications. Despite growing theoretical efforts, the…

We present a complementary study to a new model for generating magnetic fields of cosmological interest. The driving mechanism is the photoionisation process by photons provided by the first luminous sources. Investigating the transient…

This is an essay to accompany the author's lecture at the introductory workshop on `Nonabelian fundamental groups in arithmetic geometry' at the Newton Institute, Cambridge in July, 2009.

This paper aims at giving a novel approach to investigate the behavior of the renormalization group flow for tensorial group field theories to all orders of the perturbation theory. From an appropriate choice of the kinetic kernel, we build…