UNPUBLISHED WORK by Gerard 't Hooft


Occasionally, I hit upon old notes that never made it to any official publication medium. Just for the record, I will make them available on this site. These notes have not gone through any peer review system, and may not contain new material. They will be used in case someone asks me questions about certain topics, or just for my own personal needs. I do not know whether anyone else will be interested. The ordering might be subject to further changes, in case I hit again on some early manuscript.

  1. Gauge-invariant regularization of Yang-Mills fields. November 1971.
    An early version of a paper on dimensional regularization. Apart from some spelling errors, Eq. (2.6) should have higher order poles in the higher order terms, which was not yet known to me. The lemma mentioned at the end probably requires some extra assumptions, which will in general be fulfilled for Yang-Mills fields.
  2. A short compilation of the most common Special Functions and Polynomials and their properties, emphasizing the most important features that they all have in common.
  3. Cylindrically symmetric solutions of Einstein's equations for pure gravity, August 2006.
    A brief reaction to assertions by C.Y. Lo claiming that there would be no "dynamical" solutions to Einstein's equations. Of course there are. Cylindrical symmetry leads to simple non linear partial differential equations (Eq. (1.1)), which can be solved in terms of pure integrals. In particular one can obtain wave packets that have finite energy per unit of length in the z direction, so that they are physically meaningful. Eqs. (1.2) and (1.3) hold for the sourceless case, but for their derivation we introduced sources J(x), in Eqs. (1.4) and onwards, a point that Lo missed in his rebuttal (he probably never attempted to solve differential equations).
  4. Meccano Mathematics I", a little treatise on some nice features of meccano strips. For those who like Meccano and Euclidean geometry at high school level. December 2006.
  5. Some notes on the graded rotation group. April 2007.
    In this paper, a form of supersymmetry is discussed where the numbers of fermions and bosons are not equal. Possibly this is old stuff, but I could not find it in the literature.
  6. Meccano Math II describes the solutions to the exercises given in Meccano Math I, and more. October 2008. A remark: it was pointed out to me that dividing an angle into 3 equal parts can be done with fewer pieces, a point I had missed.
  7. Meccano Math III
  8. The molecular memory: how to construct it chemically, at least in principle (Dec. 2011).
  9. Artificial Anthropomorphic Intelligence (November 2014, chapter added January 2017)
  10. The importance of recognising fringe science.
  11. How to turn your microscope into a phase contrast microscope.
  12. Mr. Jones goes across the Horizon , in a simple language for children between 10 and 90 years old: a fairytale illustrating some of the symmetry features of a black hole, February 2021.


Gerard 't Hooft
Last revised date:
February 2021