Related papers: Tunnelling amplitudes through localised external p…
Most renormalizable quantum field theories can be rephrased in terms of Feynman diagrams that only contain dressed irreducible 2-, 3-, and 4-point vertices. These irreducible vertices in turn can be solved from equations that also only…
The quantum mechanical tunneling through multiple quantum barriers is a long-standing and well-known problem. Three methods proposed earlier to calculate the tunneling probabilities and energy splitting: (1). Instanton Method (2) WKb…
We describe a computational investigation of tunneling at finite energy in a weakly coupled quantum mechanical system with two degrees of freedom. We compare a full quantum mechanical analysis to the results obtained by making use of a…
A simple construction is presented which allows computing the transition amplitude of a quantum circuit to be encoded as computing the permanent of a matrix which is of size proportional to the number of quantum gates in the circuit. This…
Process of quantum tunneling of particles in various physical systems can be effectively controlled even by a weak and slow varying in time electromagnetic signal if to adapt specially its shape to a particular system. During an…
We propose a framework for calculating two-loop Feynman diagrams which appear within a renormalizable theory in the general mass case and at finite external momenta. Our approach is a combination of analytical results and of high accuracy…
In this talk we discuss mathematical structures associated to Feynman graphs. Feynman graphs are the backbone of calculations in perturbative quantum field theory. The mathematical structures -- apart from being of interest in their own…
The purpose of this review is to bridge the gap between a standard course in quantum field theory and recent fascinating developments in the studies of on-shell scattering amplitudes. We build up the subject from basic quantum field theory,…
The world-line representation of quantum field theory is a powerful framework for the computation of perturbative multi-leg Feynman amplitudes. In particular, in gauge theories, it provides an efficient way, via point particle Grassmann…
There remains the old question of how long a quantum particle takes to tunnel through a potential barrier higher than its incident kinetic energy. In this article a solution of the question is proposed on the basis of a realistic…
Using the recently introduced ACV reduced-action approach to transplanckian scattering of light particles, we show that the $S$-matrix in the region of classical gravitational collapse is related to a tunneling amplitude in an effective…
A way to efficiently compute helicity amplitudes for arbitrary tree-level scattering processes in QCD is presented. The scattering amplitude is evaluated recursively through a set of Dyson-Schwinger equations. The computational cost of this…
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…
In this thesis, we study the structure of Group Field Theories (GFTs) from the point of view of renormalization theory. Such quantum field theories are found in approaches to quantum gravity related to Loop Quantum Gravity (LQG) on the one…
The Feynman path integral in p-adic quantum mechanics is considered. The probability amplitude ${\cal K}_p (x^{\prime\prime},t^{\prime\prime}; x^\prime,t^\prime)$ for one-dimensional systems with quadratic actions is calculated in an exact…
We show that space-time modulation of electromagnetic potentials enables Klein tunneling far below the static threshold. The derived kinematics reveal oblique transitions that can connect opposite-energy continua without requiring their…
Using analyticity of the vacuum wave-functional under complex scalings, the vacuum of a quantum field theory may be reconstructed from a derivative expansion valid for slowly varying fields. This enables the eigenvalue problem for the…
Schwinger's formalism in quantum field theory can be easily implemented in the case of scalar theories in $D$ dimension with exponential interactions, such as $\mu^D\exp(\alpha\phi)$. In particular, we use the relation $$…
The classic paper by Fleming, Mehen and Stewart cast doubts on the convergence of spin-triplet nucleon-nucleon partial wave scattering amplitudes when following the proposal of Kaplan, Savage and Wise to construct nuclear effective field…
Recently, we proposed a new approach for calculating Feynman graphs amplitude using the Gaussian representation for propagators which was proven to be exact in the limit of graphs having an infinite number of loops. Regge behavior was also…