By van Nieuwenhuizen P.

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**Extra info for Advanced quantum gauge field theory**

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4) One could now describe all weak interactions by this theory (¯ pn)(¯ eν) (¯ ν e)(¯ np) (¯ pn)(¯ np) (¯ ν e)(¯ eν) (¯ eν)(¯ ν µ) (¯ np)(¯ ν µ) nuclear β decay proton decay in nuclei weak nuclear forces electron-neutrino scattering µ decay µ-capture in nuclei This universal four-fermion theory was very successful, despite the fact that it was nonrenormalizable. Also an understanding of nonleptonic weak decays was developed, and applied to such decays as Λ → p + π. In 1956 a puzzle arose: charged K mesons were found to decay into two pions, but also into three pions.

In the Heisenberg picture states are time-independent while operators are in general time-dependent. Applying this to Q|ψ = 0, where also Q is time-independent, one can solve the equation Q|ψ = 0 most easily by using a basis in Hilbert space in terms of which fields take on a very simple form at asymptotic times t0 → ±∞. This basis are the in- and out-states, corresponding to free in- and out- fields. 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.

A physical state is only determined up to terms of the form Q|χ . fact that one can solve the equations Q|ψ = 0 in closed form. 42 1. A BRIEF HISTORY OF QUANTUM GAUGE FIELD THEORY Thus physical states form equivalence classes, and there is always one state in an equivalence class which only depends on transversal modes and which is without any quartet states. (iii) physical states have vanishing ghost number, so they have quartet admixtures with equal numbers of ghost and antighost oscillators.

### Advanced quantum gauge field theory by van Nieuwenhuizen P.

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