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  • 1
    Electronic Resource
    Electronic Resource
    Chern–Simons terms in metric-affine space-time: Bianchi identities as Euler–Lagrange equations (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 2169-2180 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The metric-affine gauge theory of gravity encompasses a space-time with the following geometrical fields: coframe cursive-thetaα, metric g, and an independent linear connection Γαβ. Within this geometrical framework, all four-forms B=dC are constructed which qualify as boundary terms for a gauge Lagrangian, that is, they are GL(4,R)-scalars as well as exact forms derived from Chern–Simons type three-forms C. The result of our search is summarized in Eq. (4.20). The translational piece dCTT is new. The boundary terms effectively serve as Lagrangians for the Bianchi identities of nonmetricity, torsion, and curvature. In the canonical formalism, the normal parts of the Chern–Simons three-forms represent generating functions that are capable of generating new Ashtekar type variables. Eventually, the Bach–Lanczos identity is generalized to the metric-affine space-time.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529191
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Bianchi identities and the automatic conservation of energy-momentum and angular momentum in general-relativistic field theories (1986)
    Springer
    Foundations of physics 16 (1986), S. 267-293 
    Details
    ISSN: 1572-9516
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Automatic conservation of energy-momentum and angular momentum is guaranteed in a gravitational theory if, via the field equations, the conservation laws for the material currents are reduced to the contracted Bianchi identities. We first execute an irreducible decomposition of the Bianchi identities in a Riemann-Cartan space-time. Then, starting from a Riemannian space-time with or without torsion, we determine those gravitational theories which have automatic conservation: general relativity and the Einstein-Cartan-Sciama-Kibble theory, both with cosmological constant, and the nonviable pseudoscalar model. The Poincaré gauge theory of gravity, like gauge theories of internal groups, has no automatic conservation in the sense defined above. This does not lead to any difficulties in principle. Analogies to 3-dimensional continuum mechanics are stressed throughout the article.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01889477
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Exterior calculus on the computer: The REDUCE-package EXCALC applied to general relativity and to the Poincaré gauge theory (1987)
    Springer
    General relativity and gravitation 19 (1987), S. 197-218 
    Details
    ISSN: 1572-9532
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The computer algebra system REDUCE has recently been enriched by a package on exterior calculus. Here we apply the EXCALC package to the calculation of quantities within the Poincaré gauge theory of gravity, general relativity being included in this scheme as a spcial case. Thereby we simplify and streamline earlier results found by means of tensor-analytical REDUCE calculations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00770331
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  • 4
    Electronic Resource
    Electronic Resource
    Progress in metric-affine gauge theories of gravity with local scale invariance (1989)
    Springer
    Foundations of physics 19 (1989), S. 1075-1100 
    Details
    ISSN: 1572-9516
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Einstein's general relativity theory describes very well the gravitational phenomena in themacroscopic world. In themicroscopic domain of elementary particles, however, it does not exhibit gauge invariance or approximate Bjorken type scaling, properties which are believed to be indispensible for arenormalizable field theory. We argue that thelocal extension of space-time symmetries, such as of Lorentz and scale invariance, provides the clue for improvement. Eventually, this leads to aGL(4, R)-gauge approach to gravity in which the metric and the affine connection acquire the status ofindependent fields. The Yang-Mills type field equations, the Noether identities, and conformal models of gravity are discussed within this framework. After symmetry breaking, Einstein's GR surfaces as an effective “low-energy” theory.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01883159
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  • 5
    Electronic Resource
    Electronic Resource
    Mapping Noether identities into Bianchi identities in general relativistic theories of gravity and in the field theory of static lattice defects (1990)
    Springer
    International journal of theoretical physics 29 (1990), S. 1185-1206 
    Details
    ISSN: 1572-9575
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Noether identities resulting from external symmetries represent “conservation” laws in relativistic field theories and balance laws in 3-dimensional continuum statics, respectively. In a suitably selected 4-dimensional non-Euclidean space-time (3-dimensional stress space), the momentum currents (stresses) entering the conservation (balance) laws can be mapped such that the Noether identities become Bianchi identities, or irreducible pieces thereof. Using a metric-affine space with independent metricg αβ and connection Γ α β , we derive the following types of mapping prescriptions: momentum current → (contraction of) curvature; spin current → torsion; shear current → trace-free nonmetricity; dilation current → Weyl 1-form. The last two mappings constitute the main result. The mapping of the dilation current turns out to be exceptional, since it does not yield a nontrivial Bianchi identity.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00672931
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    Paper (German National Licenses)
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