DISORDER-INDUCED INSTABILITY OF THE QUANTUM CRITICAL BEHAVIOR OF BOSE FLUIDS

2000 ◽  
Vol 14 (05) ◽  
pp. 173-179
Author(s):  
I. P. TAKOV
Keyword(s):  
Renormalization Group ◽  
Critical Behavior ◽  
Short Range ◽  
Zero Temperature ◽  
Classical Systems ◽  
Renormalization Group Equations ◽  
Quantum Critical ◽  
The One ◽  
Quantum Critical Behavior ◽  
Short Range Correlations

The one-loop renormalization-group equations for Bose fluids with randomly distributed impurities are derived and analyzed with the help of a double ∊-expansion. While the low temperature critical behavior is similar to that of classical systems with extended impurities, the proper quantum critical behavior of disordered Bose fluids at zero temperature is unstable with respect to randomly distributed impurities with short-range correlations.

The renormalization group in perturbative quantum gravity

2021 ◽  
pp. 488-493
Author(s):  
Iosif L. Buchbinder ◽  
Ilya L. Shapiro
Keyword(s):  
Renormalization Group ◽  
Quantum Gravity ◽  
Minimal Subtraction Scheme ◽  
Loop Approximation ◽  
Renormalization Group Equations ◽  
Gauge Fixing ◽  
Perturbative Renormalization ◽  
Fourth Derivative ◽  
Perturbative Quantum ◽  
The One

This is a short chapter summarizing the main results concerning the renormalization group in models of pure quantum gravity, without matter fields. The chapter starts with a critical analysis of non-perturbative renormalization group approaches, such as the asymptotic safety hypothesis. After that, it presents solid one-loop results based on the minimal subtraction scheme in the one-loop approximation. The polynomial models that are briefly reviewed include the on-shell renormalization group in quantum general relativity, and renormalization group equations in fourth-derivative quantum gravity and superrenormalizable models. Special attention is paid to the gauge-fixing dependence of the renormalization group trajectories.

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