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Prog. Theor. Phys. Vol. 55 No. 4 (1976) pp. 1259-1275

[ Full Text PDF : FREE ACCESS (1056K) ]

Canonical Quantization of Massless Tensor Field in General Covariant Gauge

Toshiei Kimura

Research Institute for Theoretical Physics, Hiroshima University, Takehara, Hiroshima-ken 725

(Received September 13, 1975)

Abstract:

In order to find a massive tensor field theory which tends to massless limit smoothly, canonical quantization of massless tensor field is carried out in general covariant gauges. To specify a gauge, three auxiliary fields are introduced. Generally there appears a gauge independent parameter b which plays an important role in the quantization procedure. When b ≠1 four-dimensional commutation relations among fields can be derived through a straightforward extension of the method devised for quantum electrodynamics. There exists a massive tensor theory which connects with massless one, although Lagrangian does not coincide with the Fierz-Pauli one when the auxiliary vector fields are absent. When b = 1 it is necessary to introduce scalar fields in addition to the vector fields and to follow the method of Dirac's new Poisson bracket. In this case another gauge independent parameter β appears in propagator for graviton and affects the interaction between matters. It is shown that in the case with b = 1 and β= ∞, there exists not only a massless tensor theory consistent with experimental facts but also a massive theory which tends to the massless one smoothly.


URL : http://ptp.ipap.jp/link?PTP/55/1259/
DOI : 10.1143/PTP.55.1259

[ Full Text PDF : FREE ACCESS (1056K) ] Citation:

References:

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Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 59 No. 2 (1978) pp. 579-589 :
    Massless Spin Two Field, Covariant Quantization in a General Covariant Gauge
    L. Fernandez, A. Foussats, R. Laura, J. Lewis and O. Zandron
  2. Progress of Theoretical Physics Vol. 59 No. 3 (1978) pp. 972-985 :
    Indefinite-Metric Quantum Field Theory of General Relativity
    Noboru Nakanishi
  3. Progress of Theoretical Physics Vol. 59 No. 6 (1978) pp. 2175-2177 :
    Remarks on the Indefinite-Metric Quantum Field Theory of General Relativity
    Noboru Nakanishi
  4. Progress of Theoretical Physics Vol. 60 No. 3 (1978) pp. 857-867 :
    A Unified Lagrangian Formulation for Massive and Massless Tensor Fields
    R. Laura and O. Zandron
  5. Progress of Theoretical Physics Vol. 62 No. 5 (1979) pp. 1385-1395 :
    Indefinite-Metric Quantum Field Theory of General Relativity. VII
    Noboru Nakanishi
  6. Progress of Theoretical Physics Vol. 68 No. 5 (1982) pp. 1749-1764 :
    Canonical Quantum Theory of Gravitational Field with Higher Derivatives. II
    Shoichiro Kawasaki and Tadahiko Kimura
  7. Progress of Theoretical Physics Vol. 96 No. 3 (1996) pp. 639-651 :
    Massless Limits of Massive Tensor Fields
    Shinji Hamamoto

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