Related papers: Structure functions at small x from world-lines. I…
The worldline approach to Quantum Field Theory (QFT) allows to efficiently compute several quantities, such as one-loop effective actions, scattering amplitudes and anomalies, which are linked to particle path integrals on the circle. A…
We employ analytic QCD (anQCD) approach to analyze the unpolarized nucleon structure function (NSF) in deep inelastic scattering ( DIS ) processes at the next-to-leading order (NLO) accuracy. Considering the unreliable results of underlying…
The Feynman-Schwinger representation provides a convenient framework for the cal culation of nonperturbative propagators. In this paper we first investigate an analytically solvable case, namely the scalar QED in 0+1 dimension. With this…
The worldline formalism is a useful scheme in quantum field theory which has also become a powerful tool for numerical computations. The key ingredient in this formalism is the first quantization of an auxiliary point-particle whose…
We review the theory of polarized structure functions measured in deep-inelastic lepton-nucleon scattering, focusing on the most recent developments. We concentrate on the structure function $g_1$, emphasizing the phenomenological problems…
A Feynman-Kac-type formula for a L\'evy and an infinite dimensional Gaussian random process associated with a quantized radiation field is derived. In particular, a functional integral representation of $e^{-t\PF}$ generated by the…
The worldline formalism allows one to obtain compact integral representations combining the information of large numbers of Feynman diagrams. However, their analytic calculation leads to a non-standard integration problem for which existing…
I will review some of the recent intense activity concerning infrared and collinear divergences in gauge theory amplitudes. The central quantity in these studies is the multi-particle soft anomalous dimension matrix, which is completely…
The worldline formalism provides an alternative to Feynman diagrams in the construction of amplitudes and effective actions that shares some of the superior properties of the organization of amplitudes in string theory. In particular, it…
A momentum-space approach to conformal field theory offers a new perspective on cosmological correlators and better reveals the underlying connections to scattering amplitudes. This thesis explores the interplay between integral…
I develop a mixed-space formulation of high-energy deep-inelastic scattering in the shock-wave formalism at sub-eikonal order. Starting from the quark propagator in the background field, I derive the corresponding mixed-space Feynman rules…
We describe a family of twisted partition functions for the relativistic spinning particle models. For suitable choices of fugacities this computes a refined Euler characteristics that counts the dimension of the physical states for…
We construct a family of measures for random fields based on the iterated subdivision of simple geometric shapes (triangles, squares, tetrahedrons) into a finite number of similar shapes. The intent is to construct continuum limits of scale…
A brief overview is presented of recent developments concerning resummed small-x evolution, based upon the renormalization group equation. The non-singlet and singlet structure functions are discussed for both polarized and unpolarized…
We report on the status of the calculation of deep-inelastic structure functions at three loops in perturbative QCD. The method employed allows to calculate the Mellin moments of structure functions analytically as a general function of N.…
This thesis is devoted to the first-quantized approach to quantum field theory, commonly known as the 'Worldline Formalism'. It collects most of the works completed by the author during the PhD, illustrating the versatility and efficiency…
We present a new method for evaluating tensor integrals in the large-scale structure. Decomposing a $\Lambda$CDM-like universe into a finite sum of scaling universes using the FFTLog, we can recast loop integrals for biased tracers in the…
One-loop effective action of noncommutative scalar field theory with cubic self-interaction is studied. Utilizing worldline formulation, both planar and nonplanar part of the effective action are computed explicitly. We find complete…
This report attempts to capture the essential workings of gauge links (Wilson lines) inside gauge-invariant formulations of parton distribution functions in QCD and gain some deeper insight into their key (renormalization) properties. We…
Quantum spin models with a large number of interaction partners per spin are frequently used to describe modern many-body quantum optical systems like arrays of Rydberg atoms, atom-cavity systems or trapped ion crystals. For theoretical…