TY - JOUR

T1 - Comment on 'Controversy concerning the definition of quark and gluon angular momentum' by Elliot Leader

AU - Lin, Huey Wen

AU - Liu, Keh Fei

PY - 2012/3/15

Y1 - 2012/3/15

N2 - It is argued by the author that the canonical form of the quark energy-momentum tensor with a partial derivative instead of the covariant derivative is the correct definition for the quark momentum and angular momentum fraction of the nucleon in covariant quantization. Although it is not manifestly gauge-invariant, its matrix elements in the nucleon will be nonvanishing and are gauge-invariant. We test this idea in the path-integral quantization by calculating correlation functions on the lattice with a gauge-invariant nucleon interpolation field and replacing the gauge link in the quark lattice momentum operator with unity, which corresponds to the partial derivative in the continuum. We find that the ratios of three-point to two-point functions are zero within errors for both the u and d quarks, contrary to the case without setting the gauge links to unity.

AB - It is argued by the author that the canonical form of the quark energy-momentum tensor with a partial derivative instead of the covariant derivative is the correct definition for the quark momentum and angular momentum fraction of the nucleon in covariant quantization. Although it is not manifestly gauge-invariant, its matrix elements in the nucleon will be nonvanishing and are gauge-invariant. We test this idea in the path-integral quantization by calculating correlation functions on the lattice with a gauge-invariant nucleon interpolation field and replacing the gauge link in the quark lattice momentum operator with unity, which corresponds to the partial derivative in the continuum. We find that the ratios of three-point to two-point functions are zero within errors for both the u and d quarks, contrary to the case without setting the gauge links to unity.

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U2 - 10.1103/PhysRevD.85.058901

DO - 10.1103/PhysRevD.85.058901

M3 - Review article

AN - SCOPUS:84863337772

SN - 1550-7998

VL - 85

JO - Physical Review D - Particles, Fields, Gravitation and Cosmology

JF - Physical Review D - Particles, Fields, Gravitation and Cosmology

IS - 5

M1 - 058901

ER -