The non-relativistic dynamics of a spin-1/2 particle in a monopole field possesses a rich supersymmetry structure. One supersymmetry, uncovered by d'Hoker and Vinet, is of the standard type: it squares to the Hamiltonian. In this paper we show the presence of another supersymmetry which squares to the Casimir invariant of the full rotation group. The geometrical origin of this supersymmetry is traced, and its relationship with the constrained dynamics of a spinning particle on a sphere centered at the monopole is described. * On leave of absence from DAMTP,
The presence of Killing-Yano tensors implies the existence of non-standard supersymmetries in point particle theories on curved backgrounds. In a string theoretical context these are symmetries of the modes describing the particle-like behavior of the string. In the presence of isometries we show that, in addition to these, one can also define a new type of non-standard supersymmetry among a mixture of particle and winding modes. The interplay with T-duality is also examined and illustrated by explicit examples. *
Anomalies can be anticipated at the classical level without changing the classical cohomology, by introducing extra degrees of freedom. In the process, the anomaly does not quite disappear. We show that, in fact, it is shifted to new symmetries that come with the extra fields.
Anomalies and BRST invariance are governed, in the context of Lagrangian Batalin-Vilkovisky quantization, by the master equation, whose classical limit is (S, S) = 0. Using Zimmerman's normal products and the BPHZ renormalisation method, we obtain a corresponding local quantum operator equation, which is valid to all orders in perturbation theory. The formulation implies a calculational method for anomalies that is useful also outside this context and that remains completely within regularised perturbation theory. It makes no difference in principle whether the anomaly appears at one loop or at higher loops. The method is illustrated by computing the one-and two-loop anomalies in chiral W 3 gravity.
Starting from the requirement that a Lagrangian field theory be invariant under both Schwinger-Dyson BRST and Schwinger-Dyson anti-BRST symmetry, we derive the BRST-anti-BRST analogue of the Batalin-Vilkovisky formalism. This is done through standard Lagrangian gauge fixing respecting the extended BRST symmetry. The solutions of the resulting Master Equation and the gauge-fixing procedure for the quantum action can be brought into forms that coincide with those obtained earlier on algebraic grounds by Batalin, Lavrov and Tyutin.hepth@xxx/9302050
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