Related papers: Classical eikonal from Magnus expansion
The classical eikonal is defined to be the generator of all scattering observables in a scattering problem in classical mechanics. It was originally introduced as the log of the quantum S-matrix in the classical limit. But its classical…
We revisit the fundamentals of two different methods for calculating classical observables: the eikonal method, which is a scattering amplitude-based method, and the worldline quantum field theory (WQFT) method. The latter has been…
We investigate the Magnus expansion of the $N$-operator in relativistic quantum field theory, which is related to the $S$-matrix via $S = e^{iN}$. We develop direct methods to compute matrix elements of the $N$-operator, which we refer to…
The Magnus expansion provides an exponential representation of one-parameter operator families, expressed as a series expansion in its generators. This is useful for example in quantum mechanics for expressing a unitary evolution determined…
Both the classical time-ordering and the Magnus expansion are well-known in the context of linear initial value problems. Motivated by the noncommutativity between time-ordering and time derivation, and related problems raised recently in…
Two fundamentally distinct types of quantities are both called "eikonal" in present amplitudes literature. The unitarity of the S-matrix ensures it can be written as the exponential of a Hermitian operator. The eikonal generator or…
Approximate resolution of linear systems of differential equations with varying coefficients is a recurrent problem shared by a number of scientific and engineering areas, ranging from Quantum Mechanics to Control Theory. When formulated in…
The logarithm of the time-evolution operator has been termed Magnusian, on account of the fact that its expansion describes the Magnus series. The diagrammatic expansion and computation of the classical Magnusian has been completely…
An exponential representation of the S-matrix provides a natural framework for understanding the semi-classical limit of scattering amplitudes. While sharing some similarities with the eikonal formalism it differs from it in details.…
We study the eikonal scattering of two gravitationally interacting bodies, in the regime of large angular momentum and large center of mass energy. We show that eikonal exponentiation of the scattering phase matrix is a direct consequence…
Using $\mathcal N=8$ supergravity as a theoretical laboratory, we extract the 3PM gravitational eikonal for two colliding massive scalars from the classical limit of the corresponding elastic two-loop amplitude. We employ the eikonal phase…
Eikonal exponentiation in QFT describes the emergence of classical physics at long distances in terms of a non-trivial resummation of infinitely many diagrams. Long ago, 't Hooft proposed a beautiful correspondence between…
Magnus expansion (ME) provides a general way to expand the real-time propagator of a time-dependent Hamiltonian within the exponential such that the unitarity is satisfied at any order. We use this property and explicit integration of…
We propose a unified approach for different exponential perturbation techniques used in the treatment of time-dependent quantum mechanical problems, namely the Magnus expansion, the Floquet--Magnus expansion for periodic systems, the…
We use a Magnus approximation at the level of the equations of motion for a harmonic system with a time-dependent frequency, to find an expansion for its in-out effective action, and a unitary expansion for the Bogoliubov transformation…
We describe an efficient approximation algorithm for evaluating the ground-state energy of the classical Ising Hamiltonian with linear terms on an arbitrary planar graph. The running time of the algorithm grows linearly with the number of…
A classical approximation to time dependent quantum mechanical scattering in the M\o{}ller formalism is presented. Numerically, our approach is similar to a standard Classical-Trajectory-Monte-Carlo calculation. Conceptually, however, our…
We present algorithms for solving high-frequency acoustic scattering problems in complex domains. The eikonal and transport partial differential equations from the WKB/geometric optic approximation of the Helmholtz equation are solved…
We study the (ambi-)twistor model for spinning particles interacting via electromagnetic field, as a toy model for studying classical dynamics of gravitating bodies including effects of both spins to all orders. We compute the momentum kick…
We propose two possible eikonal operators encoding the effects of classical radiation as coherent states of gravitons and show how to compute from them different classical observables. In the first proposal, only genuinely propagating…