We start with a simple introduction into the renormalization group (RG) in quantum field theory and give an overview of the renormalization group method. The third section is devoted to essential topics of the renorm-group use in the QFT. Here, some fresh results are included. Then we turn to the remarkable proliferation of the RG ideas into various fields of physics. The last section summarizes an impressive recent progress of the "QFT renormalization group" application in mathematical physics.We start with a simple introduction into the renormalization group (RG) in quantum field theory and give an overview of the renormalization group method. The third section is devoted to essential topics of the renorm-group use in the QFT. Here, some fresh results are included. Then we turn to the remarkable proliferation of the RG ideas into various fields of physics. The last section summarizes an impressive recent progress of the "QFT renormalization group" application in mathematical physics.

arXiv:hep-th/9909024Sep 4, 19994 citations

Renormalization group approach to quantum bosonized systems

Gaetano Busiello, L. De Cesare

Il Nuovo cimento della Società italiana di fisica. B/Il Nuovo cimento BOct 1, 198041 citations

Critical Scattering and Dynamical Scaling in an Heisenberg Ferromagnet Neutron Spin Echo versus Renormalization Group Theory

Michel Alba, Stéphanie Pouget, Peter Fouquet +2 more

High resolution Neutron Spin Echo (NSE) spectroscopy was used to investigate the dynamics of an 3D Heisenberg ferromagnet in the exchange-controlled regime over a broad range of temperatures and momentum transfer. These results allow for the first time an extensive comparison between the experimental dynamical critical behavior and the predictions of the Renormalization Group (RG) theory. The agreement is exhaustive and surprising as the RG theory accounts not only for the critical relaxation but also for the shape crossover towards an exponential diffusive relaxation when moving from the critical to the hydrodynamic regime above $T_C$ .High resolution Neutron Spin Echo (NSE) spectroscopy was used to investigate the dynamics of an 3D Heisenberg ferromagnet in the exchange-controlled regime over a broad range of temperatures and momentum transfer. These results allow for the first time an extensive comparison between the experimental dynamical critical behavior and the predictions of the Renormalization Group (RG) theory. The agreement is exhaustive and surprising as the RG theory accounts not only for the critical relaxation but also for the shape crossover towards an exponential diffusive relaxation when moving from the critical to the hydrodynamic regime above $T_C$.

arXiv:cond-mat/0703702Mar 27, 20072 citations

Application of the renormalization group in many-body quantum mechanics

B. I. S. van der Ventel

Jan 1, 19950 citations

Critical scaling of the ac conductivity for a superconductor above Tc

Robert A. Wickham, Alan T. Dorsey

We consider the effects of critical superconducting fluctuations on the scaling of the linear ac conductivity, $\ensuremath{\sigma}(\ensuremath{\omega}),$ of a bulk superconductor slightly above ${T}_{c}$ in zero applied magnetic field. The dynamic renormalization-group method is applied to the relaxational time-dependent Ginzburg-Landau model of superconductivity, with $\ensuremath{\sigma}(\ensuremath{\omega})$ calculated via the Kubo formula to $O({\ensuremath{\epsilon}}^{2})$ in the $\ensuremath{\epsilon}=4\ensuremath{-}d$ expansion. The critical dynamics are governed by the relaxational $\mathrm{XY}$ -model renormalization-group fixed point. The scaling hypothesis $\ensuremath{\sigma}(\ensuremath{\omega})\ensuremath{\sim}{\ensuremath{\xi}}^{2\ensuremath{-}d+z}S(\ensuremath{\omega}{\ensuremath{\xi}}^{z})$ proposed by Fisher, Fisher, and Huse is explicitly verified, with the dynamic exponent $z\ensuremath{\approx}2.015,$ the value expected for the $d=3$ relaxational $\mathrm{XY}$ model. The universal scaling function $S(y)$ is computed and shown to deviate only slightly from its Gaussian form, calculated earlier. The present theory is compared with experimental measurements of the ac conductivity of ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ near ${T}_{c},$ and the implications of this theory for such experiments is discussed.We consider the effects of critical superconducting fluctuations on the scaling of the linear ac conductivity, $\ensuremath{\sigma}(\ensuremath{\omega}),$ of a bulk superconductor slightly above ${T}_{c}$ in zero applied magnetic field. The dynamic renormalization-group method is applied to the relaxational time-dependent Ginzburg-Landau model of superconductivity, with $\ensuremath{\sigma}(\ensuremath{\omega})$ calculated via the Kubo formula to $O({\ensuremath{\epsilon}}^{2})$ in the $\ensuremath{\epsilon}=4\ensuremath{-}d$ expansion. The critical dynamics are governed by the relaxational $\mathrm{XY}$-model renormalization-group fixed point. The scaling hypothesis $\ensuremath{\sigma}(\ensuremath{\omega})\ensuremath{\sim}{\ensuremath{\xi}}^{2\ensuremath{-}d+z}S(\ensuremath{\omega}{\ensuremath{\xi}}^{z})$ proposed by Fisher, Fisher, and Huse is explicitly verified, with the dynamic exponent $z\ensuremath{\approx}2.015,$ the value expected for the $d=3$ relaxational $\mathrm{XY}$ model. The universal scaling function $S(y)$ is computed and shown to deviate only slightly from its Gaussian form, calculated earlier. The present theory is compared with experimental measurements of the ac conductivity of ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ near ${T}_{c},$ and the implications of this theory for such experiments is discussed.

arXiv:cond-mat/9906124Physical review. B, Condensed matterMar 1, 200018 citations

Renormalized Perturbation Theory and Field-Theoretic Renormalization Group

Lothar Schäfer

Springer eBooksJan 1, 19991 citation

T_C

We consider the effects of critical superconducting fluctuations on the scaling of the linear ac conductivity, $\ensuremath{\sigma}(\ensuremath{\omega}),$ of a bulk superconductor slightly above

{T}_{c}

in zero applied magnetic field. The dynamic renormalization-group method is applied to the relaxational time-dependent Ginzburg-Landau model of superconductivity, with $\ensuremath{\sigma}(\ensuremath{\omega})$ calculated via the Kubo formula to $O({\ensuremath{\epsilon}}^{2})$ in the $\ensuremath{\epsilon}=4\ensuremath{-}d$ expansion. The critical dynamics are governed by the relaxational

\mathrm{XY}

-model renormalization-group fixed point. The scaling hypothesis $\ensuremath{\sigma}(\ensuremath{\omega})\ensuremath{\sim}{\ensuremath{\xi}}^{2\ensuremath{-}d+z}S(\ensuremath{\omega}{\ensuremath{\xi}}^{z})$ proposed by Fisher, Fisher, and Huse is explicitly verified, with the dynamic exponent $z\ensuremath{\approx}2.015,$ the value expected for the

d=3

relaxational

\mathrm{XY}

model. The universal scaling function

S(y)

is computed and shown to deviate only slightly from its Gaussian form, calculated earlier. The present theory is compared with experimental measurements of the ac conductivity of ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ near

{T}_{c},

and the implications of this theory for such experiments is discussed.