We quantize the bosonized chiral Schwinger model by using the systematic Batalin-FradkinVilkovisky formalism. We derive a Becchi-Rouet-Stora-Tyutin gauge-fixed covariant action showing that the auxiliary fields introduced in the formalism turn into the Wess-Zumino scalar.

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We quantize the self-dual massive theory by using the Batalin-Tyutin Hamiltonian method, which systematically embeds a second class constraint system into a first class one in extended phase space by introducing new fields. Through this analysis we obtain simultaneously the Stiickelberg scalar term related to the explicit gauge-breaking effect and a new type of Wess-Zumino action related to the Chern-Simons term. PACS number(s): ll.lO.Ef, 11.15.Tk

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From three-dimensional massive QED, we obtain the temperature-dependent Chern-Simons action by calculating the vacuum current at finite temperature.

We study the Lorentz transformation of the minimal chiral Schwinger model in terms of the alternative action. We automatically obtain a chiral constraint, which is equivalent to the frame constraint introduced by McCabe, in order to solve the frame problem in phase space. As a result we obtain the Lorentz invariant spectrum in any moving frame by choosing a frame parameter.

The compactifications of the eight-dimensional Einstein-Maxwell theory and the Einstein-Maxwell-scalar system into four-dimensional Minkowski space ( M 4 ) x S 2 x S 2 are found to be unstable.