The generalized Erlangen program and setting a geometry for four- dimensional conformal fields
- Tel Aviv Univ. (Israel). Sackler Faculty of Exact Sciences
- Koeln Univ. (Germany). Inst. fuer Theoretische Physik
This is the text of a talk at the International Symposium on ``Mathematical Physics towards the XXI Century`` held in March 1993 at Beersheva, Israel. In the first part we attempt to summarize XXth Century Physics, in the light of Kelvin`s 1900 speech ``Dark Clouds over XIXth Century Physics.`` Contrary to what is usually said, Kelvin predicted that the ``clouds`` (relativity and quantum mechanics) would revolutionize physics and that one hundred years might be needed to harmonize them with classical physics. Quantum Gravity can be considered as a leftover from Kelvin`s program -- so are the problems with the interpretation of quantum mechanics. At the end of the XXth Century, the Standard Model is the new panoramic synthesis, drawn in gauge-geometric lines -- realizing the Erlangen program beyond F. Klein`s expectations. The hierarchy problem and the smallness of the cosmological constant are our ``clouds``, generations and the Higgs sector are to us what radioactivity was in 1900. In the second part we describe Metric-Affine spacetimes. We construct the Noether machinery and provide expressions for the conserved energy and hypermomentum. Superimposing conformal invariance over the affine structure induces the Virasoro-like infinite constraining algebra of diffeomorphisms, applied with constant parameters and opening the possibility of a 4DCFT, similar to 2DCFT.
- Research Organization:
- Univ. of Texas, Austin, TX (United States)
- Sponsoring Organization:
- USDOE, Washington, DC (United States)
- DOE Contract Number:
- FG05-85ER40200
- OSTI ID:
- 10159491
- Report Number(s):
- DOE/ER/40200-323; ON: DE94013524; BR: 35KA02000/KA0101000
- Resource Relation:
- Other Information: PBD: 22 Oct 1993
- Country of Publication:
- United States
- Language:
- English
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