Related papers: Renormalized Schwinger-Dyson functional
We introduce a general class of generating functionals for the calculation of quantum-mechanical expectation values of arbitrary functionals of fluctuating paths with fixed end points in configuration or momentum space. The generating…
A representation of the perturbation series of a general functional measure is given in terms of generalized Feynman graphs and -rules. The graphical calculus is applied to certain functional measures of L\'evy type. A graphical notion of…
The paper puts together some loosely connected observations, old and new, on the concept of a quantum field and on the properties of Feynman amplitudes. We recall, in particular, the role of (exceptional) elementary induced representations…
This paper will describe how combinatorial interpretations can help us understand the algebraic structure of two aspects of perturbative quantum field theory, namely analytic Dyson-Schwinger equations and periods of scalar Feynman graphs.…
A definition is given, in the framework of stochastic quantization, for the dynamics of a system composed of classical and quantum degrees of freedom mutually interacting. It is found that the theory breaks reflection positivity, and hence…
We give a general expression for the normally ordered form of a function F(w(a,a*)) where w is a function of boson annihilation and creation operators satisfying [a,a*]=1. The expectation value of this expression in a coherent state becomes…
The generating functional for hard thermal loops in QCD is important in setting up a resummed perturbation theory, so that all terms of a given order in the coupling constant can be consistently taken into account. It is also the functional…
A new proof of perturbative renormalizability and infrared finiteness for a scalar massless theory is obtained from a formulation of renormalized field theory based on the Wilson renormalization group. The loop expansion of the renormalized…
The Schr\"odinger functional (SF) is a powerful and widely used tool for the treatment of a variety of problems in renormalization and related areas. Albeit offering many conceptual advantages, one major downside of the SF scheme is the…
We present a method to accelerate the numerical evaluation of spatial integrals of Feynman diagrams when expressed on the real frequency axis. This can be realized through use of a renormalized perturbation expansion with a constant but…
This paper aims to show constructions of scale dependence and interaction on some probabilistic models which may be revelant for renormalization theory in Quantum Field Theory. We begin with a review of the convolution product's use in the…
The renormalization of the Chern-Simons parameter is investigated by using an exact and manifestly gauge invariant evolution equation for the scale-dependent effective average action.
The notion of non-perturbative renormalization is discussed and extended. Within the extended picture, a new non-perturbative representation for the generating functional of Green functions of quantum field theories is suggested. It is…
Feynman diagrams are the foremost tool in the perturbative study of quantum field theory. In gauge theories, the full potential of this tool is revealed when it is combined with the Slavanov-Taylor identities associated with the local gauge…
Fracton order is an intriguing new type of order which shares many common features with topological order, such as topology-dependent ground state degeneracies, and excitations with mutual statistics. However, it also has several…
We construct a stationary density functional for the partition function from a chosen set of one (boson) line irreducible Feynman diagrams. The construction does not proceed by the inversion of a Legendre transform. It is formulated for…
The Frobenius-Schwinger-Dyson equations are a rather high-brow abstract nonsense type of equations describing n-point functions of arbitrarily high composite insertions. It is not clear how to solve or even find approximate solutions of…
We explore a geometric perspective on quantum field theory by considering the configuration space, where all field configurations reside. Employing $n$-particle irreducible effective actions constructed via Legendre transforms of the…
An analog of Kreimer's coproduct from renormalization of Feynman integrals in quantum field theory, endows an analog of Kontsevich's graph complex with a dg-coalgebra structure. The graph complex is generated by orientation classes of…
The standard approach to renormalization relies, technically, on the asymptotic perturbation of Gaussian measures embodied in Feynman diagram theory. From a mathematical standpoint this is not good enough, because thereby solving the…