7 research outputs found
Algorithmic derivation of Dyson-Schwinger Equations
We present an algorithm for the derivation of Dyson-Schwinger equations of
general theories that is suitable for an implementation within a symbolic
programming language. Moreover, we introduce the Mathematica package DoDSE
which provides such an implementation. It derives the Dyson-Schwinger equations
graphically once the interactions of the theory are specified. A few examples
for the application of both the algorithm and the DoDSE package are provided.
The package can be obtained from physik.uni-graz.at/~mah/DoDSE.html.Comment: 17 pages, 11 figures, downloadable Mathematica package v2: adapted to
version 1.2 of DoDSE package with simplified handling and improved plotting
of graphs; references adde
The full Schwinger-Dyson tower for random tensor models
We treat random rank- tensor models as -dimensional quantum field
theories---tensor field theories (TFT)---and review some of their
non-perturbative methods. We classify the correlation functions of complex
tensor field theories by boundary graphs, sketch the derivation of the
Ward-Takahashi identity and stress its relevance in the derivation of the tower
of exact, analytic Schwinger-Dyson equations for all the correlation functions
(with connected boundary) of TFTs with quartic pillow-like interactions.Comment: Proceedings: Corfu 2017 Training School "Quantum Spacetime and
Physics Models
On non-primitively divergent vertices of Yang–Mills theory
Two correlation functions of Yang-Mills beyond the primitively divergent
ones, the two-ghost-two-gluon and the four-ghost vertices, are calculated and
their influence on lower vertices is examined. Their full (transverse) tensor
structure is taken into account. As input, a solution of the full two-point
equations - including two-loop terms - is used that respects the resummed
perturbative ultraviolet behavior. A clear hierarchy is found with regard to
the color structure that reduces the number of relevant dressing functions. The
impact of the two-ghost-two-gluon vertex on the three-gluon vertex is
negligible, which is explained by the fact that all non-small dressing
functions drop out due to their color factors. Only in the ghost-gluon vertex a
small net effect below is seen. The four-ghost vertex is found to be
extremely small in general. Since these two four-point functions do not enter
into the propagator equations, these findings establish their small overall
effect on lower correlation functions.Comment: 11 pages, 10 figure