TY - JOUR

T1 - Topological obstruction in block-spin transformations

AU - Fujiwara, Takanori

AU - Hayashi, Takuya

AU - Suzuki, Hiroshi

AU - Wu, Ke

N1 - Funding Information:
We would like to thank Peter Weisz for valuable comments and careful reading of the manuscript. This work was completed during the time when two of us (T.F. and H.S.) attended the Ringberg workshop. They would like to thank Martin Lüscher, Erhard Seiler and Peter Weisz for the kind hospitality. T.F. thanks Ryuji Uchino for discussions at the early stage of this work. He would also like to express his thank to Dieter Maison for the kind hospitality during his stay at Max Planck Institute. K.W. is very grateful to Fumihiko Sakata for the warm hospitality and to Faculty of Science of Ibaraki University for the financial support during his visit at Ibaraki University.
Copyright:
Copyright 2006 Elsevier B.V., All rights reserved.

PY - 2000/9/7

Y1 - 2000/9/7

N2 - Block-spin transformations from a fine lattice to a coarse one are shown to give rise to a one-to-one correspondence between the zero-modes of the Ginsparg-Wilson Dirac operator on the fine lattice and those on the coarse lattice. The index is then preserved under the blocking process. Such a one-to-one correspondence is violated and the block-spin transformation becomes necessarily ill-defined when the absolute value of the index is larger than 2rN, where N is the number of the sites on the coarse lattice and r is the dimension of the gauge group representation of the fermion variables. (C) 2000 Elsevier Science B.V.

AB - Block-spin transformations from a fine lattice to a coarse one are shown to give rise to a one-to-one correspondence between the zero-modes of the Ginsparg-Wilson Dirac operator on the fine lattice and those on the coarse lattice. The index is then preserved under the blocking process. Such a one-to-one correspondence is violated and the block-spin transformation becomes necessarily ill-defined when the absolute value of the index is larger than 2rN, where N is the number of the sites on the coarse lattice and r is the dimension of the gauge group representation of the fermion variables. (C) 2000 Elsevier Science B.V.

UR - http://www.scopus.com/inward/record.url?scp=0034618389&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034618389&partnerID=8YFLogxK

U2 - 10.1016/S0370-2693(00)00920-5

DO - 10.1016/S0370-2693(00)00920-5

M3 - Article

AN - SCOPUS:0034618389

VL - 488

SP - 428

EP - 434

JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

SN - 0370-2693

IS - 3-4

ER -