Related papers: Perturbative analysis of the gradient flow in non-…
At an elementary level, we present some non-perturbative aspects of non-abelian gauge theories in four dimensional space-time. Some rigorous results have been obtained in the framework of supersymmetric theories, and a very rich physics…
Physical quantities in gauge theories have to be gauge-independent. However their evaluation can be greatly simplified by working in particular gauges. Since physical quantities have to be gauge invariant, it is important to establish an…
The gradient-flow formalism is applied to a non-Abelian gauge theory with scalar and fermionic particles, dubbed "scalar QCD". It is shown that the flowed scalar quark requires a field renormalization, albeit only beyond the one-loop level.…
Using connection with quantum field theory, the infinitesimal covariant abelian gauge transformation laws of relativistic two-particle constraint theory wave functions and potentials are established and weak invariance of the corresponding…
In perturbative consideration of the Yang--Mills gradient flow, it is useful to introduce a gauge non-covariant term ("gauge-fixing term") to the flow equation that gives rise to a Gaussian damping factor also for gauge degrees of freedom.…
The gradient flow method is a renormalization scheme in which the gauge field is flowed by the diffusion equation. The gradient flow scheme has benefits that the observables composed of flowed gauge fields do not require further…
We consider time dependent correlation functions of non-abelian gauge fields at finite temperature. An effective theory for the soft ($p\sim g^2 T$) field modes is derived by integrating out the field modes with momenta of order $T$ and of…
Recently, the connections between gradient flow and renormalization group have been explored analytically and numerically. Gradient flow (when modified by a field rescaling) can be characterized as a continuous blocking transformation. In…
We prove that the real four-dimensional Euclidean noncommutative \phi^4-model is renormalisable to all orders in perturbation theory. Compared with the commutative case, the bare action of relevant and marginal couplings contains…
The non-perturbative renormalization-group approach is extended to lattice models, considering as an example a $\phi^4$ theory defined on a $d$-dimensional hypercubic lattice. Within a simple approximation for the effective action, we solve…
We derive renormalised finite functional flow equations for quantum field theories in real and imaginary time that incorporate scale transformations of the renormalisation conditions, hence implementing a flowing renormalisation. The flows…
We study the relaxation process in normal and anomalous diffusion regimes for systems described by a generalized Langevin equation (GLE). We demonstrate the existence of a very general correlation function which describes the relaxation…
The gradient flow bears a close resemblance to the coarse graining, the guiding principle of the renormalization group (RG). In the case of scalar field theory, a precise connection has been made between the gradient flow and the RG flow of…
The gradient property of the renormalisation group (RG) flow of multiscalar theories is examined perturbatively in $d=4$ and $d=4-\varepsilon$ dimensions. Such theories undergo RG flows in the space of quartic couplings $\lambda^I$.…
The present work investigates the evolution of linear perturbations of time-dependent ideal fluid flows with advected quantities, expressed in terms of the second order variations of the action corresponding to a Lagrangian defined on a…
We propose a generalization of the gradient flow equation for quantum field theories with nonlinearly realized symmetry. Applying the equation to $\mathcal{N}=1$ $SU(N)$ super Yang-Mills theory in four dimensions, we construct a…
The flow equations of the renormalisation group permit to analyse the perturbative $n$-point functions of renormalisable quantum field theories. Rigorous bounds implying renormalisablility allow to control large momentum behaviour, infrared…
This paper derives the Feynman rules for the diagrammatic perturbation expansion of the effective action around an arbitrary solvable problem. The perturbation expansion around a Gaussian theory is well known and composed of one-line…
We study, using the example of general covariance, to what extent a would-be non-abelian extension of free field abelian gauge theory can be helped by a field redefinition; answer - not much! However, models resulting from dimensional…
The scope of constrained differential renormalization is to provide renormalized expressions for Feynman graphs, preserving at the same time the Ward identities of the theory. It has been shown recently that this can be done consistently at…