Related papers: On the wave function renormalization for Wilson ac…
We use the Wilson renormalization group (RG) formulation to solve the fine-tuning procedure needed in renormalization schemes breaking the gauge symmetry. To illustrate this method we systematically compute the non-invariant couplings of…
We employ projection operator techniques in Hilbert space to derive a continuous sequence of effective Hamiltonians which describe the dynamics on successively larger length scales. We show for the case of \phi^4 theory that the masses and…
We apply the functional renormalization group theory to the dynamics of first-order phase transitions and show that a potential with all odd-order terms can describe spinodal decomposition phenomena. We derive a momentum-dependent dynamic…
We consider symplectic quaternions instead of unitary spinors sitting on a lattice, and calculate the fixed point Wilson action on a finite $2D$ plane expanded by $u_1 a e_1+ u_2 a e_2$ and on two $2D$ planes separated by $a e_1\wedge e_2$.…
Approximations based on two-particle irreducible (2PI) effective actions (also known as $\Phi$-derivable, Cornwall-Jackiw-Tomboulis or Luttinger-Ward functionals depending on context) have been widely used in condensed matter and…
We present the results of an extensive lattice calculation of the renormalization constants of bilinear and four-quark operators for the non-perturbatively O(a)-improved Wilson action. The results are obtained in the quenched approximation…
The gauge dependence problem of the effective action for general gauge theories in the framework of a modified functional renormalization group approach proposed recently is studied. It is shown that the effective action remains…
We use standard distorted wave theory techniques and dimensional regularization to find out solutions of the nucleon-nucleon Lippman--Schwinger equation with a kernel determined by the Weinberg's next-to-leading potential, which consists of…
This is an expanded version of lecture notes, delivered at the XCIII Les Houches Summer School (August 2009). Our aim is to present three very specific topics: (i) The consequences of the loss of chiral symmetry in the Wilson lattice…
General prescriptions of differential renormalization are presented. It is shown that renormalization group functions are straightforwardly expressed through some constants that naturally arise within this approach. The status of the action…
We present a renormalization group (RG) procedure which works naturally on a wide class of interacting one-dimension models based on perturbed (possibly strongly) continuum conformal and integrable models. This procedure integrates Kenneth…
The consistent description of unstable particles, renormalons, or other Schwinger--Dyson-type of solutions within the framework of perturbative gauge field theories necessitates the definition and resummation of off-shell Green's functions,…
We consider a symmetric scalar theory with quartic coupling in 4-dimensions. We show that the 4 loop 2PI calculation can be done using a renormalization group method. The calculation involves one bare coupling constant which is introduced…
Starting from the continuum Dirac operator, I construct a renormalisation group blocking which transforms the continuum action into a lattice action, and I specifically consider the Wilson and overlap formalisms. For Wilson fermions the…
In these lectures we describe the construction of a gauge invariant renormalization group equation for pure non-Abelian gauge theory. In the process, a non-perturbative gauge invariant continuum Wilsonian effective action is precisely…
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…
We discuss gauge symmetry and Ward-Takahashi identities for Wilsonian flows in pure Yang-Mills theories. The background field formalism is used for the construction of a gauge invariant effective action. The symmetries of the effective…
A geometric formulation of Wilson's exact renormalisation group is presented based on a gauge invariant ultraviolet regularisation scheme without the introduction of a background field. This allows for a manifestly background independent…
We give a functional derivation of the Ward-Takahashi identity for Yang-Mills theory in the framework of the exact renormalization group. The identity realizes non-abelian gauge symmetry nontrivially despite the presence of a momentum…
Nonperturbative renormalization and explicit construction of the effective potential of the Hartree approximation of the two-particle-irreducible formalism are carried out in an inhomogeneous field configuration describing a uniform…