Lattice QCD Study for the Relation Between Confinement and Chiral Symmetry Breaking by Takahiro Doi

Author:Takahiro Doi
Language: eng
Format: epub
Publisher: Springer Singapore, Singapore

(2.46)

where is even number on the temporally odd-number lattice. Thus, the relation (2.17) is rewritten as

(2.47)

using the modified KS formalism. Note that the (modified) KS formalism is an exact mathematical method for spin-diagonalizing the Dirac operator, not an approximation. Thus Eqs. (2.44) and (2.47) are exactly equivalent. Therefore, each Dirac-mode contribution to the Polyakov loop can be obtained by solving the eigenvalue equation of the KS Dirac operator whose dimension is instead of the original Dirac operator whose dimension is on the temporally odd-number lattice.

Note again that a specific fermion like the KS fermion is not used. We just use the KS formalism for diagonalizing the naive Dirac operator defined by Eq. (2.3), and obtain all the eigenvalues and the eigenfunctions. Actually, all the eigenvalues and eigenfunctions can be obtained without the KS formalism by the direct diagonalization of the Dirac operator , and they gives the same results. however, the numerical cost is larger.

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