On Peculiarities and Pit Falls in Path Integrals

Path integrals can be rigorously defined only in low dimensional systems where the small distance limit can be taken. Particularly non-trivial models in more than four dimensions can only be handled with considerable amount of speculation. In this lecture we try to put these various aspects in perspective.Comment: Opening Lecture given at the 7th International Conference on Path Integrals, "From Quarks to Galaxies", Antwerp, 27 to 31 May 2002. Uses gthstyle.sty Reprt-no: ITF-2002/41; SPIN-2002/2

The Glorious Days of Physics - Renormalization of Gauge theories

This is an account of the author's recollections of the turbulent days preceding the establishment of the Standard Model as an accurate description of all known elementary particles and forces.Comment: 21 pages plain TeX, 4 figures PostScript. Small cosmetic - yet important - changes were made in the original manuscrip

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

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.Comment: 25 pages in total. A contribution to: The Standard Theory up to the Higgs discovery - 60 years of CERN - L. Maiani and G. Rolandi, ed

The Grand View of Physics

Abdus Salam was known for his `grand views', grand views of science as well as grand views of society. In this talk the grand view of theoretical physics is put in perspective.Comment: 5 pages, 1 figure. Presented at Salam +50, Imperial College, London, July 7, 200

Black hole unitarity and antipodal entanglement

Hawking particles emitted by a black hole are usually found to have thermal spectra, if not exactly, then by a very good approximation. Here, we argue differently. It was discovered that spherical partial waves of in-going and out-going matter can be described by unitary evolution operators independently, which allows for studies of space-time properties that were not possible before. Unitarity dictates space-time, as seen by a distant observer, to be topologically non-trivial. Consequently, Hawking particles are only locally thermal, but globally not: we explain why Hawking particles emerging from one hemisphere of a black hole must be 100 % entangled with the Hawking particles emerging from the other hemisphere. This produces exclusively pure quantum states evolving in a unitary manner, and removes the interior region for the outside observer, while it still completely agrees locally with the laws of general relativity. Unitarity is a starting point; no other assumptions are made. Region I and the diametrically opposite region II of the Penrose diagram represent antipodal points in a PT or CPT relation, as was suggested before. On the horizon itself, antipodal points are identified. A candidate instanton is proposed to describe the formation and evaporation of virtual black holes of the type described here. Some important explanations and discussion points are added. In the latest of the paper, again some minor inaccuracies are corrected.Comment: 15 pages, 1 figur