By van Nieuwenhuizen P.

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16) The author met Dirac in Florida in 1978 after a seminar on supergravity. ” Since the theory contained a local 4-component spinor α (x), the author answered “Infinity to the fourth power”. Dirac only replied “That is a large number”. Afterwards he told the author that doing loop calculations (in supergravity) was the wrong approach, as it would lead to the same problems that he had encountered in the 1930’s. Rather, in his words, one had to first invent a whole new approach. For further information on this very logical, original but shy man, see [69].

As we now know, jµ is the charge density current, and then ρ need not be positive definite). He identified the problem as being due to the derivative ∂ ∂t in ρ, and set out to write down a field theory with one time derivative less. Special relativity then required also one space derivative less, and in this way Dirac factorized the Klein–Gordon equation,14 and deduced anticommutation relations for the 4 × 4 matrices which bear his name and which are a suitable generalization of the Pauli matrices.

The BRST operator (or, in fact, any other conserved charge [62] unless spontaneously broken) becomes bilinear in asymptotic fields, and the BRST transformations reduce to linear transformations on the in- and out fields. The S matrix connects in- and out-states: S|ψ, out = |ψ, in , and since the set of in-fields is the same as the set of out-fields, one may identify the in- and out states (and fields) and speak of asymptotic states and fields. The condition Q|ψ = 0 (BRST closed states) selects then asymptotic states with the following properties: (i) states |ψ have either strictly positive norm or vanishing norm.

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Advanced quantum gauge field theory by van Nieuwenhuizen P.


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