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 Free-Will Postulate in Quantum Mechanics

The so-called "free will axiom" is an essential ingredient in many discussions concerning hidden variables in quantum mechanics. In this paper we argue that "free will" can be defined in different ways. The definition usually employed is clearly invalid in strictly deterministic theories. A different, more precise formulation is proposed here, defining a condition that may well be a more suitable one to impose on theoretical constructions and models. Our axiom, to be referred to as the `unconstrained initial state' condition, has consequences similar to "free will", but does not clash with determinism, and appears to lead to different conclusions concerning causality and locality in quantum mechanics. Models proposed earlier by this author fall in this category. Imposing our `unconstrained initial state' condition on a deterministic theory underlying Quantum Mechanics, appears to lead to a restricted free-will condition in the quantum system: an observer has the free will to modify the setting of a measuring device, but has no control over the phase of its wave function. The dismissal of the usual "free will" concept does not have any consequences for our views and interpretations of human activities in daily life, and the way our minds function, but it requires a more careful discussion on what, in practice, free will actually amounts to.Comment: 8 pages, 1 figur

The Conformal Constraint in Canonical Quantum Gravity

Perturbative canonical quantum gravity is considered, when coupled to a renormalizable model for matter fields. It is proposed that the functional integral over the dilaton field should be disentangled from the other integrations over the metric fields. This should generate a conformally invariant theory as an intermediate result, where the conformal anomalies must be constrained to cancel out. When the residual metric is treated as a background, and if this background is taken to be flat, this leads to a novel constraint: in combination with the dilaton contributions, the matter lagrangian should have a vanishing beta function. The zeros of this beta function are isolated points in the landscape of quantum field theories, and so we arrive at a denumerable, or perhaps even finite, set of quantum theories for matter, where not only the coupling constants, but also the masses and the cosmological constant are all fixed, and computable, in terms of the Planck units

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