Related papers: Some combinatorial interpretations in perturbative…
The mathematical formalism necessary for the diagramatic evaluation of quantum corrections to a conformally invariant field theory for a self-interacting scalar field on a curved manifold with boundary is considered. The evaluation of…
This paper describes perturbative framework, on the basis of closed-time-path formalism, for studying quasiuniform relativistic quantum field systems near equilibrium and nonequilibrium quasistationary systems. At the first part, starting…
Starting from a recently-introduced algebraic structure on spin foam models, we define a Hopf algebra by dividing with an appropriate quotient. The structure, thus defined, naturally allows for a mirror analysis of spin foam models with…
The general normal ordering problem for boson strings is a combinatorial problem. In this note we restrict ourselves to single-mode boson monomials. This problem leads to elegant generalisations of well-known combinatorial numbers, such as…
We review the homotopy algebraic perspective on perturbative quantum field theory: classical field theories correspond to homotopy algebras such as $A_\infty$- and $L_\infty$-algebras. Furthermore, their scattering amplitudes are encoded in…
This paper describes perturbative framework, on the basis of the closed-time-path formalism, in terms of quasiparticle picture for studying quasiuniform relativistic quantum field systems near equilibrium and nonequilibrium quasistationary…
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…
Dyson-Schwinger equations are integral equations in quantum field theory that describe the Green functions of a theory and mirror the recursive decomposition of Feynman diagrams into subdiagrams. Taken as recursive equations, the…
We analyze a class of coupled quantum systems whose dynamics can be understood via two uncoupled, lower-dimensional quantum settings with auxiliary interactions. The general reduction scheme, based on algebraic properties of the potential…
One-dimensional atomic mixtures of fermions can effectively realize spin chains and thus constitute a clean and controllable platform to study quantum magnetism. Such strongly correlated quantum systems are also of sustained interest to…
A diagram approach to classical nonlinear stochastic field theory is introduced. This approach is intended to serve as a link between quantum and classical field theories, resulting in an independent constructive characterisation of the…
We show that sums over graphs such as appear in the theory of Feynman diagrams can be seen as integrals over discrete groupoids. From this point of view, basic combinatorial formulas of the theory of Feynman diagrams can be interpreted as…
We review some recent developments in nonperturbative studies of quantum field theory (QFT) using the Schwinger-Dyson equations formulated directly in Minkowski space. We begin with the introduction of essential ideas of the integral…
We review the construction of models of algebraic quantum field theory by renormalized perturbation theory.
Our understanding of quantum field theory rests largely on explicit and controlled calculations in perturbation theory. Because of this, much recent effort has been devoted to improve our grasp of perturbative techniques on cosmological…
We define in this paper several Hopf algebras describing the combinatorics of the so-called multi-scale renormalization in quantum field theory. After a brief recall of the main mathematical features of multi-scale renormalization, we…
In this article we present a refined summation theory based on Karr's difference field approach. The resulting algorithms find sum representations with optimal nested depth. For instance, the algorithms have been applied successively to…
A derivation is given of the Feynman rules to be used in the perturbative computation of the Green's functions of a generic quantum many-body theory when the action which is being perturbed is not necessarily quadratic. Some applications…
We discuss factorization of the Dyson--Schwinger equations using the Lie- and Hopf algebra of graphs. The structure of those equations allows to introduce a commutative associative product on 1PI graphs. In scalar field theories, this…
In this paper, we proved the correspondence between Feynman diagrams in space-time and light-cone diagrams in world-sheet by using only path integral representation on free Green function in the first quantization theory. We also obtained…