-
1
-
-
84927317562
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-
Lectures on Gravitation, compiled by F.B. Morinigo and W.G. Wagner (California Institute of Technology, Pasadena, California, 1962/63).
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-
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Feynman, R.P.1
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3
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84927317561
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see also F.W. Hehl, in, edited by, P.G. Bergmann, V. de Sabbata, NATO Advanced Study Institute Series B: Physics, Vol. 58, Plenum, New York, p. 5.
-
(1980)
Cosmology and Gravitation: Spin, Torsion, Rotation, and Supergravity, Proceedings of the International School, Erice, Italy, 1979
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-
-
5
-
-
84927317560
-
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edited by, H. Mitter, H. Gausterer, Lecture Notes in Physics, Vol. 396, Springer, Berlin, p. 123.
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(1991)
Recent Aspects of Quantum Fields, Proceedings of the XXXth International Univer sitäts wo chen für Kernphysik, Schladming, Austria, 1991
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Isham, C.J.1
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8
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0001391418
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This is analogous to the connection representation in which the ``triad density" is represented by the functional derivative underline underline{*}{ vartheta}B:= δ / δ { buildrel pm over { underline{A}B}} with respect to the canonically conjugate Ashtekar variable buildrel pm over{ underline{A}B}. This provides a mapping from the Hamiltonian constraint of gravity with a cosmological term to the Chern Simons three form [7] of the Ashtekar Sen connection, see
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(1992)
Nucl. Phys.
, vol.385 B
, pp. 587
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Brügmann, B.1
Gambini, R.2
Pullin, J.3
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11
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84927317559
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E.W. Mielke, Geometrodynamics of Gauge Fields On the Geometry of Yang Mills and Gravitational Gauge Theories (Akademie Verlag, Berlin, 1987).
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12
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0007169325
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In a fiber bundle approach, one introduces first the bundle of affine frames A(M):= P( Mn, A, n,R), π, δ where π denotes the projection to the base manifold and δ the (left) action of the structure group A(n,R) on the bundle. Active affine gauge transformations are the vertical automorphisms of A(M). Similarly as the diffeomorphisms of the base manifold Mn, they form the infinite dimensional group { cal A}(n, R):=C∞( AM) timesAd A(n, R). The group { cal G}{ cal L}(n, R):=C∞(AM) timesAdGL (n, R) of linear gauge transformations and the group { cal T}(n, R):=C∞ (AM) timesAd Rn of local translations are subgroups of { cal A}(n, R). Taking the cross section in the associated bundle is abbreviated by C∞ and Ad denotes the adjoint representation with respect to GL(n,R). Because of its construction, the group of local translations { cal T}(n, R) is locally isomorphic to the group of active diffeomorphisms Diff(n,R) of the manifold, cf.
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(1973)
Lett. Nuovo Cimento
, vol.8
, pp. 988
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Ogievetsky, V.I.1
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14
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36549102742
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The infinite dimensional group Diff(n,R) contains the (n+n2) dimensional group A(n,R)H of holonomic affine transformations as a subgroup, cf.
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(1985)
J. Math. Phys.
, vol.26
, pp. 2030
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Bergmann, P.G.1
Komar, A.B.2
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15
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84927317557
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which is generated by the fields Pi=- partiali and Li{}j =-xi partialj. Note that differentiable coordinate transformations, which leave exterior forms invariant, are regarded as passive diffeomorphisms.
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18
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84927317555
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V.N. Ponomariev, A.O. Bravinsky, and Yu.N. Obukhov, Geometrodynamical Methods and Gauge Approach to the Theory of Gravitational Interactions, in Russian (Energoatomisdat, Moscow, 1985).
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22
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Otherwise there also exists, for example, the nontrivial solution Tα=aηαβξβ and Rαβ=aηαβ, with the dimensionful constant a.
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33
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84927317545
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L. O'Raifeartaigh, in Differential Geometry, Group Representations, and Quantization, edited by J.D. Hennig, W. Lücke, and J. Tolar, Lecture Notes in Physics, Vol. 379 (Springer, Berlin, 1991), p. 99.
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35
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84927317544
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Phys. Rep. (to be published);
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39
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84927317543
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J.D. Hennig, in Conformal Geometry and Spacetime Gauge Theories, Proceedings of the 2nd International Wigner Conference, Goslar, 1991, edited by H.D. Doebner et al. (World Scientific, Singapore, 1992).
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40
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The plus sign is in accordance with our earlier conventions for active trans for mations.
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42
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84927317541
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Y. Ne'eman, in Differential Geometrical Methods in Mathematical Physics, edited by K. Bleuler, H.R. Petry, and A. Reetz, Lecture Notes in Mathematics, Vol. 676 (Springer Verlag, Berlin, 1978), p. 189.
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44
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84927317539
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T.W.B. Kibble and K.S. Stelle, in Progress in Quantum Field Theory: Festschrift for Umezawa, edited by H. Ezawa and S. Kamefuchi (Elsevier, New York, 1986), p. 57.
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