Related papers: Exact Scheme Independence
After a short elementary introduction to the exact renormalization group for the effective action, I discuss a particular truncation of the hierarchy of flow equations that allows for the determination of the full momentum of the $n$-point…
Using continuous wavelet transform it is possible to construct a regularization procedure for scale-dependent quantum field theory models, which is complementary to functional renormalization group method in the sense that it sums up the…
The Renormalisation Group is a versatile tool for the study of many systems where scale-dependent behaviour is important. Its functional formulation can be cast into the form of an exact flow equation for the scale-dependent effective…
We propose a simple derivation of renormalization group equations and Callan-Symanzik equations as decoupling theorems of the structures underlying effective field theories.
The gauge dependence problem of alternative flow equation for the functional renormalization group is studied. It is shown that the effective two-particle irreducible effective action depends on gauges at any value of IR parameter $k$. The…
We analyze renormalization group (RG) flows in two-dimensional quantum field theories in the presence of redundant directions. We use the operator picture in which redundant operators are total derivatives. Our analysis has three levels of…
The exact renormalization group equation for pure quantum gravity is used to derive the non-perturbative $\Fbeta$-functions for the dimensionless Newton constant and cosmological constant on the theory space spanned by the Einstein-Hilbert…
We derive functional renormalization group schemes for Fermi systems which are based on the two-particle irreducible approach to the quantum many-body problem. In a first step, the cutoff is introduced in the non-interacting propagator as…
The validity of the renormalization group approach for large $N$ is clarified by using the vector model as an example. An exact difference equation is obtained which relates free energies for neighboring values of $N$. The reparametrization…
Renormalization group procedure for effective particles in the front form of Hamiltonian dynamics is applied to an elementary quantum field theory for two species of particles mixed through a mass-like interaction term. The model…
After a brief presentation of the exact renormalization group equation, we illustrate how the field theoretical (perturbative) approach to critical phenomena takes place in the more general Wilson (nonperturbative) approach. Notions such as…
In this paper we review the definition and properties of redundant operators in the exact renormalisation group. We explain why it is important to require them to be eigenoperators and why generically they appear only as a consequence of…
A hidden generalized gauge symmetry of a cutoff QED is used to show the renormalizability of QED. In particular, it is shown that corresponding Ward identities are valid all along the renormalization group flow. The exact Renormalization…
Nuclear effective field theory organizes the calculation of observables as a power series in terms of the ratio of soft and hard momentum scales. The rigorous implementation of this idea requires a mixture of perturbative and…
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…
Renormalization group (RG) invariance implies that the predictions of effective field theory are independent of the momentum cutoffs introduced during regularization. Here we report the first systematic verification of RG invariance for…
With the present trend in experimental particle physics of probing yet shorter distances and with the requirement on the theoretical side of renormalizability, conformal invariance becomes an attractive symmetry for particle interactions.…
We propose fundamental scale invariance as a new theoretical principle beyond renormalizability. Quantum field theories with fundamental scale invariance admit a scale-free formulation of the functional integral and effective action in…
The singular behavior of conformal interactions is examined within a comparative analysis of renormalization frameworks. The effective approach--inspired by the effective-field theory program--and its connection with the core framework are…
We show that the diagrammatic approach to quantum spin systems developed in a seminal work by Vaks, Larkin, and Pikin [Sov. Phys. JETP 26, 188 (1968)] can be embedded in the framework of the functional renormalization group. The crucial…