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Prog. Theor. Phys. Vol. 42 No. 5 (1969) pp. 1191-1205

[ Full Text PDF : FREE ACCESS (851K) ]

Divergence of Axial-Vector Current in the Gravitational Field

Toshiei Kimura

Research Institute for Theoretical Physics, Hiroshima University, Takehara, Hiroshima-ken

(Received June 14, 1969)

Abstract:

To clarify the similarity and dissimilarity between the electromagnetic and gravitational fields, the vacuum expectation value of the divergence of the axial-vector current is evaluated in the external gravitational field. Within the framework of the perturbation approach in the Minkowski space, the requirement of gauge invariance yields the finite extra term in addition to the expected term. The additional term comes from the diagrams of the triangle closed loop and the two-sided closed loop which is linked to the former to maintain gauge invariance. Within the covariance formalism in the Riemannian space-time, it is also examined whether the additional term can be inferred directly from the field equations by giving a proper definition of the operator of the axial-vector current. To maintain gauge invariance explicitly, the spinor fields in the current are separated infinitesimally and are parallel-transported back. A difficulty lies in defining the correct current which gives the same additional term as given by the perturbation treatment in the Minkowski space. The origin of the difficulty is discussed in connection with the non-local nature of the gravity.


URL : http://ptp.ipap.jp/link?PTP/42/1191/
DOI : 10.1143/PTP.42.1191

[ Full Text PDF : FREE ACCESS (851K) ] Citation:

References:

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Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 44 No. 5 (1970) pp. 1353-1370 :
    Divergence of Axial-Vector Current in the Gravitational Field. II
    Toshiei Kimura
  2. Progress of Theoretical Physics Vol. 63 No. 2 (1980) pp. 683-695 :
    Axial Anomaly for Gravitino and Unconventional FP Ghosts
    Ryusuke Endo and Toshiei Kimura
  3. Progress of Theoretical Physics Vol. 66 No. 6 (1981) pp. 2011-2024 :
    Conformal and Axial Anomalies in Riemann-Cartan Space
    Toshiei Kimura
  4. Progress of Theoretical Physics Vol. 71 No. 6 (1984) pp. 1366-1384 :
    Gauge Dependence of the Grabvitational Conformal Anomaly for the Electromagnetic Field
    Ryusuke Endo
  5. Progress of Theoretical Physics Vol. 73 No. 3 (1985) pp. 803-821 :
    Path Integral Derivation of the Chiral Anomalies in Higher Dimensional Curved Space-Time
    Ryusuke Endo and Masaru Takao
  6. Progress of Theoretical Physics Vol. 74 No. 4 (1985) pp. 866-880 :
    Anomalies in Four-Dimensional Curved Space with Torsion
    Satoshi Yajima and Toshiei Kimura
  7. Progress of Theoretical Physics Vol. 78 No. 2 (1987) pp. 440-452 :
    Chiral Anomalies of Anti-Symmetric Tensor Gauge Fields in Higher Dimensions
    Ryusuke Endo and Masaru Takao
  8. Progress of Theoretical Physics Vol. 78 No. 4 (1987) pp. 886-907 :
    A Space-Time Approach to Chiral Anomalies
    Hidenaga Yamagishi
  9. Progress of Theoretical Physics Vol. 116 No. 1 (2006) pp. 197-215 :
    Overlap Lattice Fermion in a Gravitational Field
    Masashi Hayakawa, Hiroto So and Hiroshi Suzuki
  10. Progress of Theoretical Physics Supplement No.85 (1985) pp. 250-255 :
    Anomalies
    William A. Bardeen
  11. Progress of Theoretical Physics Supplement No.167 (2007) pp. 44-52 :
    Mesotron Decays and the Role of Anomalies
    William A. Bardeen

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