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Quantization of Even-Dimensional Actions of Chern-Simons Form with Infinite Reducibility
We investigate the quantization of even-dimensional topological actions of
Chern-Simons form which were proposed previously. We quantize the actions by
Lagrangian and Hamiltonian formulations {\`a} la Batalin, Fradkin and
Vilkovisky. The models turn out to be infinitely reducible and thus we need
infinite number of ghosts and antighosts. The minimal actions of Lagrangian
formulation which satisfy the master equation of Batalin and Vilkovisky have
the same Chern-Simons form as the starting classical actions. In the
Hamiltonian formulation we have used the formulation of cohomological
perturbation and explicitly shown that the gauge-fixed actions of both
formulations coincide even though the classical action breaks Dirac's
regularity condition. We find an interesting relation that the BRST charge of
Hamiltonian formulation is the odd-dimensional fermionic counterpart of the
topological action of Chern-Simons form. Although the quantization of two
dimensional models which include both bosonic and fermionic gauge fields are
investigated in detail, it is straightforward to extend the quantization into
arbitrary even dimensions. This completes the quantization of previously
proposed topological gravities in two and four dimensions.Comment: 50 pages, latex, no figure
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