Related papers: General Relativity from Intersection Theory
We use Picard-Lefschetz theory to prove a new formula for intersection numbers of twisted cocycles associated to a given arrangement of hyperplanes. In a special case when this arrangement produces the moduli space of punctured Riemann…
Feynman integral reduction based on intersection theory provides an alternative to the traditional integration-by-parts method, yet its practical application has been constrained by the large number of variables required in the computation.…
Recent proposals suggested quantum clock interferometry for tests of the Einstein equivalence principle. However, atom interferometric models often include relativistic effects only in an ad hoc fashion. Here, instead, we start from the…
A generalization of Wilson line operators at subleading power in the soft expansion has been recently introduced as an efficient building block of gravitational scattering amplitudes for non-spinning objects. The classical limit in this…
Feynman integrals obey linear relations governed by intersection numbers, which act as scalar products between vector spaces. We present a general algorithm for constructing multivariate intersection numbers relevant to Feynman integrals,…
A century after its formulation by Einstein, it is time to incorporate special relativity early in the physics curriculum. The approach advocated here employs a simple algebraic extension of vector formalism that generates Minkowski…
The aim of this note is to describe the computation of post-Minkwoskian Hamiltonians in modified theories of gravity. Exploiting a recent relation between amplitudes of massive scalars and Hamiltonians for relativistic point-particles, we…
Using the implicit function theorem we demonstrate that solutions to the classical part of the relativistic Lippmann-Schwinger equation are in one-to-one correspondence with those of the energy equation of a relativistic two-body system. A…
A survey is given on mathematical structures which emerge in multi-loop Feynman diagrams. These are multiply nested sums, and, associated to them by an inverse Mellin transform, specific iterated integrals. Both classes lead to sets of…
Extended Theories of Gravity can be considered a new paradigm to cure shortcomings of General Relativity at infrared and ultraviolet scales. They are an approach that, by preserving the undoubtedly positive results of Einstein's Theory, is…
General Relativity is the modern theory of gravitation. It has replaced the newtonian theory in the description of the gravitational phenomena. In spite of the remarkable success of the General Relativity Theory, the newtonian gravitational…
We consider a Gaussian random matrix theory in the presence of an external matrix source. This matrix model, after duality (a simple version of the closed/open string duality), yields a generalized Kontsevich model through an appropriate…
Taking a hint from Dirac's large number hypothesis, we note the existence of cosmologically combined conservation laws that work to cosmologically long time. We thus modify Einstein's theory of general relativity with fixed gravitation…
We submit a classical unification of the special and general relativities via the new isominkowskian geometry in which the two relativities are differentiated by the basic unit. We then show that the unification admits an operator image in…
In this work the worldline quantum field theory (WQFT) approach to computing observables of the classical general relativistic two-body system is presented. Compact bodies such as black holes or neutron stars are described in an effective…
An extension of the theory of General Relativity is proposed, based on pseudo-complex space-time coordinates. The new theory corresponds to the introduction of two, in general different, metrics which are connected through specific…
In this paper it is introduced and studied an alternative theory of gravitation in flat Minkowski space. Using an antisymmetric tensor, which is analogous to the tensor of electromagnetic field, a non-linear connection is introduced. It is…
Canonical Feynman integrals are of great interest in the study of scattering amplitudes at the multi-loop level. We propose to construct $d\log$-form integrals of the hypergeometric type, treat them as a representation of Feynman integrals,…
The post-Minkowskian expansion of Einstein's general theory of relativity has received much attention in recent years due to the possibility of harnessing the computational power of modern amplitude calculations in such a classical context.…
Twisted period integrals are ubiquitous in theoretical physics and mathematics, where they inhabit a finite-dimensional vector space governed by an inner product known as the intersection number. In this work, we uncover the associated…