Higher-rank conformal fields in the \(\mathrm{Sp}(2M)\)-symmetric generalized space-time. (English) Zbl 1178.81207
Theor. Math. Phys. 145, No. 1, 1400-1424 (2005); translation from Teor. Mat. Fiz. 145, No. 1, 35-65 (2005).
Summary: We study various \(\mathrm{Sp}(2M)\)-invariant field equations corresponding to rank-\(r\) tensor products of the Fock (singleton) representation of \(\mathrm{Sp}(2M)\). These equations describe localization on “branes” of different dimensions embedded in the generalized space-time \(\mathcal{M}\_M\) with matrix (i.e., “central charge”) coordinates. We consider the case of a bilinear tensor product in detail and show that the conserved currents built from bilinears of rank-1 fields in \(\mathcal{M}\_M\) satisfy the field equations for rank-2 fields in \(\mathcal{M}\_M\). We also show that rank-2 fields in \(\mathcal{M}\_M\) are equivalent to rank-1 fields in \(\mathcal{M}\_{2M}\).
MSC:
| 81T20 | Quantum field theory on curved space or space-time backgrounds |
| 81R20 | Covariant wave equations in quantum theory, relativistic quantum mechanics |
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