Hi, I have just signed up on this site. I'm 61 and live in France. British and French nationalities. My main interests are in mathematical physics. I studied physics to a graduate level at the university when I was a student, but then turned to software development for a living. I have taken up mathematics again some five years ago, with an eye on physics, and am trying to brush up on everything, and perhaps manage to understand some of the stuff that I never got to understand as a student. Like: - What is really this Hilbert space we have in quantum mechanics? In most cases (for just one simple particle), we told to use a basis formed out of vectors that are not even real vectors, because they are based on Dirac "functions" and other similar beasts. - How can the "vector" observables in this Hilbert space, such as the ##\vec R = (X, Y, Z)## position operator, be represented without reference to a particular basis? How can the Hilbert space of a ##\frac 1 2## spin particle be represented without reference to a particular basis? - Quantum field theory. I never could wrap my head around that. Relativistic quantum mechanics: does it have a referential-independent representation? What becomes of the measure principle if it is to be interpreted referential-independently? I'd also like to eventually gain a good understanding of general relativity (as a youngster I got lost in all those tensors; I hope that a more rigorous mathematical approach can bring some clarity). Apart from mathematics and physics, I am heavily into antispeciesist activism (aka animal rights); I see a deep connection between these issues - the "hard problem of consciousness", let's say - but this may not be the place to discuss that. Currently studying: Robert Geroch, Mathematical Physics (half-way through).