- 期刊
- OpenAccess
Implications of Trγ5=0 in Lattice Gauge Theory
並列摘要
We analyze the implications of the relation Trγ5 = 0, which is customarily assumed in practical lattice calculations. On the basis of the finite dimensional representations of the Ginsparg-Wilson algebra, it is shown that this relation reflects the species doubling in lattice theory; topological excitations associated with species doublers, which have eigenvalue 2/a, contribute to Trγ5 without any suppression. In this sense, the relation Trγ5 = 0 is valid only when we allow the presence of unphysical states in the Hilbert space; this statement is also valid in the Pauli-Villars regularization. If one eliminates the contributions of the unphysical states, the trace Trγ5 is replaced by TrГ5 ≡ Trγ5(1 - 1/2aD) which gives rise to the Pontryagin index, to be consistent with the continuum analysis.
並列關鍵字
無資料被引用紀錄
延伸閱讀
- Li, Y. J. (2012). Construction of Some Topological Quantum Field Theories [master's thesis, National Tsing Hua University]. Airiti Library. https://www.airitilibrary.com/Article/Detail?DocID=U0016-0908201218175681
- BOI, L. (2004). GEOMETRICAL AND TOPOLOGICAL FOUNDATIONS OF THEORETICAL PHYSICS: FROM GAUGE THEORIES TO STRING PROGRAM. International Journal of Mathematics and Mathematical Sciences, 2004(), 1777-1836-133. https://doi.org/10.1155/S0161171204304400
- Tarasov, V. E. (2014). Fractional Quantum Field Theory: From Lattice to Continuum. Advances in High Energy Physics, 2014(), 983-996-193. https://doi.org/10.1155/2014/957863
- Chen, Y. Y. (1994). A Note on the Gauge Invariance of Perturbation Theory. Chinese Journal of Physics, 32(3), 225-229. https://www.airitilibrary.com/Article/Detail?DocID=05779073-199406-201212220002-201212220002-225-229
- Pavičić, M. (2016). Classical Logic and Quantum Logic with Multiple and Common Lattice Models. Advances in Mathematical Physics, 2016(), 733-744. https://doi.org/10.1155/2016/6830685