Related papers: Analytic integration methods in quantum field theo…
The numerical unitarity approach has been important for obtaining reliable QCD predictions for the LHC. Here I discuss the extension of the approach beyond the leading quantum corrections for computing multi-loop amplitudes. The numerical…
The constructive method of determining amplitudes from on-shell pole structure has been shown to be promising for calculating amplitudes in a more efficient way. However, challenges have been encountered when a massless internal photon is…
The Hopf algebra structure underlying Feynman diagrams which governs the process of renormalization in perturbative quantum field theory is reviewed. Recent progress is briefly summarized with an emphasis on further directions of research.
We elaborate on the proposed general boundary formulation as an extension of standard quantum mechanics to arbitrary (or no) backgrounds. Temporal transition amplitudes are generalized to amplitudes for arbitrary spacetime regions. State…
We give a pedagogical review to alternative, first quantised approaches to calculating graviton scattering amplitudes, giving an introduction to string inspired approaches and presenting more recent work based on the worldline formalism of…
The field of scattering amplitudes plays a central role in elementary-particle physics. This includes various problems of broader interest for collider physics, gravitational physics, and fundamental principles underlying quantum field…
We calculate field theory loop amplitudes by string methods, applied to half-maximal 4-point one-loop graviton amplitudes. Infrared divergences are regulated similarly to soft-collinear effective field theory (SCET): new mass scales are…
The standard model of the quantum theory of measurement is based on an interaction Hamiltonian in which the observable-to-be-measured is multiplied with some observable of a probe system. This simple Ansatz has proved extremely fruitful in…
In this talk we present techniques for calculating one-loop amplitudes for multi-leg processes using Feynman diagrammatic methods in a semi-algebraic context. Our approach combines the advantages of the different methods allowing for a fast…
It is discussed an opportunity to introduce new class of quantum algorithms based on possibility to express amplitude of transition between two states of quantum system as sum of some function along all possible classical paths. Continuous…
We present methods for the numerical evaluation of the master integrals that appear in the calculation of scattering amplitudes at higher order in perturbative quantum field theory. We follow the general strategy of solving first-order…
The presence of strong electromagnetic fields adds huge complexity to QED Feynman diagrams, such that new methods are required to calculate higher-loop and higher-multiplicity scattering amplitudes. Here we use the worldline formalism to…
We present a rigorous and functorial quantization scheme for affine field theories, i.e., field theories where local spaces of solutions are affine spaces. The target framework for the quantization is the general boundary formulation,…
One of the main challenges in obtaining predictions for collider experiments from perturbative quantum field theory, is the direct evaluation of the Feynman integrals it gives rise to. In this chapter, we review an alternative bootstrap…
A framework to represent and compute two-loop $N$-point Feynman diagrams as double-integrals is discussed. The integrands are 'generalised one-loop type" multi-point functions multiplied by simple weighting factors. The final integrations…
Feynman path integrals are now a standard tool in quantum physics and their use in differential geometry leads to new mathematical insights. A logical treatment of quantum phenomena seems to require a sustained mathematical analysis of path…
Amplitudes $A_n$ in $d$-dimensional scalar field theory are generated, to all orders in the coupling constant and at $n$-point. The amplitudes are expressed as a series in the mass $m$ and coupling $\lambda$. The inputs are the classical…
A generalized Feynman-Kac formula based on the Wiener measure is presented. Within the setting of a quantum particle in an electromagnetic field it yields the standard Feynman-Kac formula for the corresponding Schr\"odinger semigroup. In…
We discuss a new simple field theory approach of Coulomb systems. Using a description in terms of fields, we introduce in a new way the statistical degrees of freedom in relation with the quantum mechanics. We show on a series of examples…
Some well-known examples of constrained quantum systems commonly quantized via Feynman path integrals are re-examined using the notion of conditional integrators introduced in [1]. The examples yield some new perspectives on old results. As…