arXiv subjects
Publications and source records attributed to Géza Fülöp.
We consider BRST-invariant inner product states for quantum electrodynamics constructed from trivial BRST-invariant states and a gauge regulator. The trivial states are products of matter and ghost states and are annihilated by hermitian operators. The co-BRST operator and some further gauge-fixing regulators are found. The relation between gauge fixing and time evolution of both the trivial and the inner product states is discussed.
It has previously been shown that a BRST quantization on an inner product space leads to physical states of the form |ph>=e^[Q, ψ] |ϕ> where |ϕ> is either a trivially BRST invariant state which only depends on the matter variables, |ϕ>_1, or a solution of a Dirac quantization, |ϕ>_2. ψis a corresponding fermionic gauge fixing operator, ψ_1 or ψ_2. We show here for abelian and nonabelian models that one may also choose a linear combination of ψ_1 and ψ_2 for both choices of |ϕ> except for a discrete set of relations between the coefficients. A general form of the coBRST charge operator is also determined and shown to be equal to such a ψfor an allowed linear combination of ψ_1 and ψ_2. This means that the coBRST charge is always a good gauge fixing fermion.
The Ashtekar-Renteln Ansatz gives the self-dual solutions to the Einstein equation. A direct generalization of the Ashtekar-Renteln An\-satz to N=1 supergravity is given both in the canonical and in the covariant formulation and a geometrical property of the solutions is pointed out. (Changes: the covariant formulation and some comments about a wave function has been added)
Canonical transformations relating the variables of the ADM-, Ashtekar's and Witten's formulations of gravity are computed in 2+1~dimensions. Three different forms of the BRST-charge are given in the 2+1 dimensional Ashtekar formalism, two of them using Ashtekar's form of the constraints and one of them using the forms suggested by Witten. The BRST-charges are of different rank.