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Prog. Theor. Phys. Vol. 76 No. 5 (1986) pp. 1166-1176

[ Full Text PDF : FREE ACCESS (431K) ]

(3+1)-Structure of Space-Time in \overlinePoincaré Gauge Theory of Gravity

Toshiharu Kawai

Department of Physics, Osaka City University, Osaka 558

(Received June 23, 1986)

Abstract:

The (3+1)-structure of space-time in a \overlinePoincaré gauge theory of gravity proposed in a previous work is studied. It is shown that there is a unit, time-like vector field N on the space-time manifold M. This, together with an R4-valued Higgs type field ψ, corresponds to a global cross section of an associated bundle of the principal fiber bundle over M having the covering group of the Poincaré group as the structure group. The field N is inherent in the formulation and coincides with the 0-th of the vierbein fields in particular gauges. Frobenius's condition for N, which ensures the existence of a slicing of M into a family of space-like surfaces, is considered. This condition leads to a new constraint for vierbein fields. Lagrangian densities leading to Frobenius's condition are given.


URL : http://ptp.ipap.jp/link?PTP/76/1166/
DOI : 10.1143/PTP.76.1166

[ Full Text PDF : FREE ACCESS (431K) ] Citation:

References:

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Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 78 No. 1 (1987) pp. 16-21 :
    Mass and Spin of Exact Solutions of the Poincaré Gauge Theory
    Peter Baeckler, Ralf Hecht, Friedrich W. Hehl and Takeshi Shirafuji
  2. Progress of Theoretical Physics Vol. 79 No. 4 (1988) pp. 920-935 :
    Energy-Momentum and Angular Momentum in \overlinePoincaré Gauge Theory of Gravity
    Toshiharu Kawai
  3. Progress of Theoretical Physics Vol. 79 No. 6 (1988) pp. 1420-1430 :
    Special Relativistic Limits of \overlinePoincaré Gauge Theory of Gravity
    Tetsuo Fukui, Toshiharu Kawai and Hirofumi Saitoh
  4. Progress of Theoretical Physics Vol. 80 No. 4 (1988) pp. 711-730 :
    Gauge Theory of Gravitation
    Takeshi Shirafuji and Masahumi Suzuki
  5. Progress of Theoretical Physics Vol. 81 No. 2 (1989) pp. 280-285 :
    A Note on \overlinePoincaré Gauge Theory of Gravity
    Toshiharu Kawai and Hirofumi Saitoh
  6. Progress of Theoretical Physics Vol. 81 No. 6 (1989) pp. 1119-1123 :
    A Note on \overlinePoincaré Gauge Theory of Gravity
    Toshiharu Kawai and Hirofumi Saitoh
  7. Progress of Theoretical Physics Vol. 82 No. 1 (1989) pp. 183-206 :
    Energy-Momentum and Angular Momentum in \overlinePoincaré Gauge Theory of Gravity and Physical Multiplets of Torsion Fields
    Tetsuo Fukui
  8. Progress of Theoretical Physics Vol. 82 No. 4 (1989) pp. 850-862 :
    Extended Spinor Structure and Exotic Spinor Field in \overlinePoincaré Gauge Theory of Gravity
    Toshiharu Kawai
  9. Progress of Theoretical Physics Vol. 83 No. 5 (1990) pp. 1003-1024 :
    Gravity as a Gauge Theory with Spontaneously Broken Internal Super-Poincaré Symmetry
    Hirofumi Saitoh
  10. Progress of Theoretical Physics Vol. 84 No. 5 (1990) pp. 993-1007 :
    Group of Paths, Holonomy Groups and Nonintegrable Phase Factors in \overlinePoincar é Gauge Theory of Gravity
    Toshiharu Kawai
  11. Progress of Theoretical Physics Vol. 85 No. 4 (1991) pp. 901-926 :
    An Extended New General Relativity as a Reduction of \overlinePoincaré Gauge Theory of Gravity
    Toshiharu Kawai and Naoki Toma

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