Related papers: Three-loop Correction to the Instanton Density. I.…
In this second paper on quantum fluctuations near the classical instanton configurations, see {\em Phys. Rev. D \bf 92}, 025046 (2015) and arXiv:1501.03993, we focus on another well studied quantum-mechanical problem, the one-dimensional…
Feynman diagrams in the instanton background are used for the calculation of the tunneling amplitude, up to the two-loops order. Some mistakes made in the previous works are corrected. The same method is applied to the next-order…
We prove formulas for the multi-instanton corrections to the overlap and energies of a 1D same-level asymmetric double well using the Euclidean path integral. Both the odd and even instanton sectors are summed to all orders. The double well…
We present the analytic expressions of the three-loop virtual corrections to the helicity amplitudes of 2 -> 2 four-fermion scattering processes in massless QED. The contributing Feynman diagrams are grouped into integrand families…
We present a new way to compute and interpret quantum tunneling in a 1-D double-well potential. For large transition time we show that the quantum action functional gives an analytical expression for tunneling amplitudes. This has been…
This is the second paper on semiclassical approach based on the density matrix given by the Euclidean time path integral with fixed coinciding endpoints. The classical path, interpolating between this point and the classical vacuum, called…
We compute the three-loop corrections to the potential of two heavy quarks. In particular we consider in this Letter the purely gluonic contribution which provides in combination with the fermion corrections of Ref. \cite{Smirnov:2008pn}…
In Euclidean path integrals, quantum mechanical tunneling amplitudes are associated with instanton configurations. We explain how tunneling amplitudes are encoded in real-time Feynman path integrals. The essential steps are borrowed from…
The two point integrals contributing to the self energy of a particle in a three dimensional quantum field theory are calculated to two loop order in perturbation theory as well as the vacuum ones contributing to the effective potential to…
Motivated by the precision results in the electroweak theory studies of two-loopFeynman diagrams are performed. Specifically this paper gives a contribution to the knowledge of massive two-loop self-energy diagrams in arbitrary and…
We find an unexpected iterative structure within the two-loop five-gluon amplitude in N = 4 supersymmetric Yang-Mills theory. Specifically, we show that a subset of diagrams contributing to the full amplitude, including a two-loop…
We consider the quantum tunneling phenomenon in a well-behaved triple-well potential. As required by the semiclassical approximation we take into account the quadratic fluctuations over the instanton which represents as usual the localised…
We describe the calculation of the three-loop QCD corrections to quark and gluon form factors. The relevant three-loop Feynman diagrams are evaluated and the resulting three-loop Feynman integrals are reduced to a small set of known master…
Coupled instantons are introduced by generalizing the double well potential to multiple mutually coupled wells. Physically this corresponds to the simultaneous tunneling of multiple degrees of freedom. A system with four equal minima is…
Instanton theory has arisen as a practical tool for calculating tunneling splittings in molecular systems. Unfortunately, the original formulation of instanton theory fundamentally breaks down when trying to calculate the level splitting in…
We develop a new semiclassical approach, which starts with the density matrix given by the Euclidean time path integral with fixed coinciding endpoints, and proceed by identifying classical (minimal Euclidean action) path, to be referred to…
The nonperturbative effects in the quark form factor are considered in the Wilson loop formalism. The properties of the Wilson loops with cusp singularities are studied taking into account the perturbative and nonperturbative contributions,…
As part of the study of the two-body problem in Einstein's gravity, the fourth post-Newtonian order (4PN) of the two-body effective action is being computed presently by both effective field theory (EFT) methods and others. Diagrams with 3…
A comprehensive study is performed of general massive, scalar, two-loop Feynman diagrams with three external legs. Algorithms for their numerical evaluation are introduced and discussed, numerical results are shown for all different…
By using a usual instanton method we obtain the energy splitting due to quantum tunneling through the triple well barrier. It is shown that the term related to the midpoint of the energy splitting in propagator is quite different from that…