@article{b8df1b2123cc4f5f950aaaca4ec1025b,
title = "The parity anomaly in condensed matter physics",
abstract = "I discuss in detail the recently proposed physical realization of the Parity Anomaly in a PbTe-type crystal with a stacking fault. A close analogy with charged soliton states in one-dimensional systems is presented. A possible way to introduce chiral fermions in a Lattice Gauge Theory is discussed.",
author = "Eduardo Fradkin",
note = "Funding Information: 5. CONCLUSIONS AND SPECULATIONS In this work I have shown that it is possible to realize field theoretic anomalies in Condensed Matter Physics. What is also interesting is that this work points into a possible way to put chiral fermions on the lattice. The scheme is the following 7. Consider a single Dirac fermion in an odd dimensional space time (this can be achieved with Wilson fermions). If a static soliton is introduced the bound states behave like chiral fermions. This was in fact pointed out by Callan and Harvey 11 . The point here is that it can be achieved on the lattice. If the fermion mass is very large the chiral fermions become the only surviving piece of the Hilbert space. The problem is though that the gauge fields are not localized to the wall. In order to dimensionally reduce the gauge fields it may be necessary to use non-local constraints. Work in this direction is currently in progress 17 ACKNOWLEDGEMENT I wish to thank H. Hamber for having organized this conference. Much of the contents of this paper is a review of ideas and results published in ref.4. I thank my collaborators D. Boyanovsky and E. Dagotto for sharing their insights with me. This work was supported in part by a National Science Foundation grant No DMR-84-15063 at the University of Illinois and by CONICET, Argentina where I am on Sabbatical leave.",
year = "1987",
month = sep,
doi = "10.1016/0920-5632(87)90108-3",
language = "English (US)",
volume = "1",
pages = "175--183",
journal = "Nuclear Physics B (Proceedings Supplements)",
issn = "0920-5632",
publisher = "Elsevier B.V.",
number = "1",
}