Anomalies and renormalization of mixed states in quantum theories
Abstract
In a Hamiltonian approach to anomalies, parity and time-reversal symmetries can be restored by introducing suitable impure (or mixed) states. However, the expectation values of observables such as the Hamiltonian diverges in such impure states. Here, we show that such divergent expectation values can be treated within a renormalization group (RG) framework, leading to a set of β-functions in the moduli space of the operators representing the observables. This leads to well-defined expectation values of the Hamiltonian in a phase where the impure state restores the P and T symmetry. We also show that this RG procedure leads to a mass gap in the spectrum. Such a framework may be relevant for long wavelength descriptions of condensed matter systems such as the quantum spin Hall (QSH) effect.
References
- J. A. Harvey, Tasi 2003 lectures on anomalies , arXiv:hep-th/0509097 . Google Scholar
- Nuovo Cimento A 60 , 47 ( 1969 ) . Crossref, ISI, ADS, Google Scholar
- Phys. Rev. 177 , 2426 ( 1969 ) . Crossref, ISI, ADS, Google Scholar
- Phys. Rev. D 29 , 285 ( 1984 ) . Crossref, ISI, ADS, Google Scholar
- Phys. Rev. 182 , 1517 ( 1969 ) . Crossref, ISI, ADS, Google Scholar
- Nucl. Phys. B 243 , 449 ( 1984 ) . Crossref, ISI, ADS, Google Scholar
- Nucl. Phys. B 234 , 269 ( 1984 ) . Crossref, ISI, ADS, Google Scholar
- Phys. Lett. B 117 , 324 ( 1982 ) . Crossref, ISI, ADS, Google Scholar
- Int. J. Mod. Phys. A 8 , 653 ( 1993 ) . Link, ISI, ADS, Google Scholar
- Nucl. Phys. B 461 , 581 ( 1996 ) . Crossref, ISI, ADS, Google Scholar
- Int. J. Mod. Phys. A 7 , 4655 ( 1992 ) . Link, ISI, ADS, Google Scholar
- Int. J. Mod. Phys. A 10 , 1969 ( 1995 ) . Link, ISI, ADS, Google Scholar
- Int. J. Mod. Phys. A 9 , 3417 ( 1994 ) . Link, ISI, ADS, Google Scholar
- Phys. Rev. D 34 , 674 ( 1986 ) . Crossref, ISI, ADS, Google Scholar
- Ann. Phys. 159 , 220 ( 1985 ) . Crossref, ISI, ADS, Google Scholar
- , M.A.B. Beg Memorial Volume , eds.
A. Ali and P. Hoodbhoy ( World Scientific , 1991 ) . Google Scholar - Commun. Math. Phys. 99 , 103 ( 1985 ) . Crossref, ISI, ADS, Google Scholar
- Phys. Rev. D 85 , 025017 ( 2012 ) . Crossref, ISI, ADS, Google Scholar
-
M. Reed and B. Simon , Methods of Modern Mathematical Physics: Fourier Analysis, Self-Adjointness 2 ( Academic Press , 1975 ) . Google Scholar - Phys. Rev. D 66 , 125013 ( 2002 ) . Crossref, ISI, ADS, Google Scholar
- Phys. Rev. Lett. 87 , 220402 ( 2001 ) . Crossref, ISI, ADS, Google Scholar
- Phys. Lett. A 372 , 2967 ( 2008 ) . Crossref, ISI, ADS, Google Scholar
-
Z. F. Ezawa , Quantum Hall Effects: Field Theoretical Approch and Related Topics , 2nd edn. ( World Scientific , 2008 ) . Link, Google Scholar - Nucl. Phys. B 659 , 437 ( 2003 ) . Crossref, ISI, ADS, Google Scholar
- Phys. Lett. A 311 , 87 ( 2003 ) . Crossref, ISI, ADS, Google Scholar
- Eur. Phys. J. C 58 , 159 ( 2008 ) . Crossref, ISI, ADS, Google Scholar
- Phys. Lett. B 505 , 191 ( 2001 ) . Crossref, ISI, ADS, Google Scholar
- Phys. Lett. B B526 , 121 ( 2002 ) . Crossref, ISI, ADS, Google Scholar
- JHEP 11 , 126 ( 2011 ) . Crossref, ISI, ADS, Google Scholar
- Phys. Rev. D 48 , 5940 ( 1993 ) . Crossref, ISI, ADS, Google Scholar
- Phys. Rev. Lett. 110 , 080503 ( 2013 ) . Crossref, ISI, ADS, Google Scholar
- Phys. Rev. Lett. 95 , 146802 ( 2005 ) . Crossref, ISI, ADS, Google Scholar
- Eur. Phys. J. Plus 127 , 118 ( 2012 ) . Crossref, ISI, Google Scholar
