Group Invariant Solutions without Transversality and the Principle of Symmetric Criticality
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We extend Lie's classical method for finding group invariant solutions to the case of non-transverse group actions. For this extension of Lie's method we identify a local obstruction to the principle of symmetric criticality. Two examples of non-transverse symmetry reductions for the potential form of Maxwell's equations are then examined.
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Cited by 2 Pith papers
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Canonical quantization of all minisuperspaces with consistent symmetry reductions
Canonical quantization of all consistent symmetry reductions of the Einstein-Hilbert Lagrangian, with solutions to the Wheeler-DeWitt equation both with and without imposed conformal symmetries.
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Canonical quantization of all minisuperspaces with consistent symmetry reductions
All minisuperspaces from symmetry reductions of the Einstein-Hilbert Lagrangian that obey the principle of symmetric criticality are canonically quantized and their Wheeler-DeWitt equations are solved.
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