## The Evolution of Quantum Field Theory, From QED to Grand Unification

**Gerard ‘t Hooft**

In the early 1970s, after a slow start, and lots of hurdles, Quantum Field Theory emerged as the superior doctrine for understanding the interactions between relativistic sub-atomic particles.

After the conditions for a relativistic field theoretical model to be renormalizable were established, there were two other developments that quickly accelerated acceptance of this approach: first the Brout-Englert-Higgs mechanism, and then asymptotic freedom.

Together, these gave us a complete understanding of the perturbative sector of the theory, enough to give us a detailed picture of what is now usually called the Standard Model.

Crucial for this understanding were the strong indications and encouragements provided by numerous experimental findings.

Subsequently, non-perturbative features of the quantum field theories were addressed, and the first proposals for completely unified quantum field theories were launched.

Since the use of continuous symmetries of all sorts, together with other topics of advanced mathematics, were recognised to be of crucial importance, many new predictions were pointed out, such as the Higgs particle, supersymmetry and baryon number violation.

There are still many challenges ahead…

… Read more at http://arxiv.org/pdf/1503.05007v1.pdf

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