Related papers: A Rigorous Derivation of the Functional Renormalis…
Motivated by the study of quantum fields in a Friedman-Robertson-Walker (FRW) spacetime, the one-loop effective action for a scalar field defined in the ultrastatic manifold $R\times H^3/\Gamma$, $H^3/\Gamma$ being the finite volume,…
The renormalization of higher-dimensional operators in quantum field theory is essential for phenomenological analyses in particle physics, and plays a significant role in the study of critical phenomena. We present a framework for…
The problem of renormalization in perturbative quantum field theory (pQFT) can be described in a rigorous way through the theory of extension of distributions. In the framework of pQFT a certain type of distribution appears, given by…
The canonical approach to quantum gravity has been put on a firm mathematical foundation in the recent decades. Even the quantum dynamics can be rigorously defined, however, due to the tremendously non-polynomial character of the…
The exact renormalization group is applied to a nonlinear diffusion equation with a discontinuous diffusion coefficient. The generating functional of the solution for the initial-value problem of nonlinear diffusion equations is first…
The process of renormalization to eliminate divergences arising in quantum field theory is not uniquely defined; one can always perform a finite renormalization, rendering finite perturbative results ambiguous. The consequences of making…
We revisit optimization of functional renormalization group flows by analyzing regularized loop integrals. This leads us to a principle, the Principle of Strongest Singularity, and a corresponding order relation which allows to order…
Working with scalar field theories, we discuss choices of regulator that, inserted in the functional renormalization group equation, reproduce the results of dimensional regularization at one and two loops. The resulting flow equations can…
Renormalization Group Equations in integro-differential form describing the evolution of cascades or resumming logarithmic scaling violations have been known in quantum field theory for a long time. These equations have been traditionally…
We review current progress in the functional renormalization group treatment of disordered systems. After an elementary introduction into the phenomenology, we show why in the context of disordered systems a functional renormalization group…
Renormalization group method is one of the most powerful tool to obtain approximate solutions to differential equations. We apply the renormalization group method to Hamiltonian systems whose integrable parts linearly depend on action…
It is shown that the renormalization group (RG) method for global analysis can be formulated in the context of the classical theory of envelopes: Several examples from partial differential equations are analyzed. The amplitude equations…
In physics we attempt to infer the rules governing a system given only the results of imprecise measurements. This is an ill-posed problem because certain features of the system's state cannot be resolved by the measurements. However, by…
Symanzik showed that quantum field theory can be formulated on a space with boundaries by including suitable surface interactions in the action to implement boundary conditions. We show that to all orders in perturbation theory all the…
The path integral formulation of Quantum Field Theory implies an infinite set of local, Schwinger-Dyson-like relations. Exact renormalization group equations can be cast as a particular instance of these relations. Furthermore, exact scheme…
We apply Renormalization Group techniques to the Real Time formulation of thermal field theory. Due to the separation between the $T=0$ and the $T\neq 0$ parts of the propagator in this formalism, one can derive exact evolution equations…
This review paper uses renormalization group techniques for signal detection in nearly-continuous positive spectra. We highlight universal aspects of the analogue field-theory approach. The first aim is to present an extended…
We will examine a particular mathematical derivation in a paper by P. Falkensteiner and H. Grosse (F&G) [1]. In [1] a quantity "delta(A)" is defined. This quantity is generated when the normal ordered generalized charge operator undergoes a…
It is shown that the renormalisation group (RG) equation can be viewed as an equation for Lie transport of physical amplitudes along the integral curves generated by the $\beta$-functions of a quantum field theory. The anomalous dimensions…
The result from developing and applying the notions of functional self-similarity and the Bogoliubov renormalization group to boundary-value problems in mathematical physics during the last decade are reviewed. The main achievement is the…