symmetries in nuclei, tokyo, 2008 symmetries in nuclei p. van isacker grand accélérateur national...
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Symmetries in Nuclei, Tokyo, 2008
Symmetries in Nuclei
P. Van IsackerGrand Accélérateur National d’Ions
Lourds,Caen, France
Symmetries in Nuclei, Tokyo, 2008
Symmetries in Nuclei
Symmetry and its mathematical description
The role of symmetry in physicsSymmetries of the nuclear shell modelSymmetries of the interacting boson model
Symmetries in Nuclei, Tokyo, 2008
What is symmetry?
Oxford Dictionary of English: “(beauty resulting from the) right correspondence of parts; quality of harmony or balance (in size, design) between parts”Examples: disposition of a French garden; harmony of themes in a symphony.
Symmetries in Nuclei, Tokyo, 2008
Etymology
Ancient Greek roots:“sun” means “with, together”“metron” means “measure”
For the ancient Greeks symmetry was closely related to harmony, beauty and unity.
Plato (Timaeus): Regular polyhedra are afforded a central place in the doctrine of natural elements.
Aristotle: “The chief forms of beauty are orderly arrangement [taxis], proportion [symmetria] and definiteness [horismenon].”
Symmetries in Nuclei, Tokyo, 2008
Origin
For the ancient Greeks symmetry implied the notion of commensurability and proportion.
17th century: Symmetry starts to imply also an relation of equality of elements that are opposed (eg. between left and right).
19th century: Definition of symmetry via the notion of invariance under transformations such as translations, rotations, reflections. Introduction of the notion of a group of transformations.
Symmetries in Nuclei, Tokyo, 2008
Symmetries around us
Bilateral symmetry.Translational symmetry.Rotational symmetries.Reflection-rotation symmetry.Glide-reflection symmetry.Scale invariance.Conformal invariance.Temporal symmetries.
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ˆ H , ˆ T [ ] = 0
Symmetries in Nuclei, Tokyo, 2008
Bilateral symmetry
Object with two halves that are each others mirror image.
Most widespread symmetry in Nature: (wo)man, animals, insects, flowers…
Symmetries in Nuclei, Tokyo, 2008
Palindromes
Word equivalent of objects with bilateral symmetry, invented by Sotades the Obscene of Maronea.
Examples:Napoleon: “Able was I ere I saw Elba.”In Dutch (kreeftzin or ‘lobster sentence’): “Nelli
plaatst op ‘n parterretrap ‘n pot staalpillen.”
About 10% of DNA letters form palindromic sequences, essential in the fight against mutations.
Symmetries in Nuclei, Tokyo, 2008
Bilateral symmetry
Man is conditioned by bilateral symmetry (cfr. Rorschach test).
Symmetry plays a crucial role in mate selection.
Symmetries in Nuclei, Tokyo, 2008
Rotational symmetry
Object that transforms into itself after rotation over a given angle.
Two types occur frequently in Nature:Discrete rotations over 2/n where n is the order of the
rotationContinuous rotations: axial or spherical
Symmetries in Nuclei, Tokyo, 2008
Discrete rotations
Order 3: clover Order 5: starfish
Order 7: algae Order 9: centriole
Symmetries in Nuclei, Tokyo, 2008
Continuous rotations
Axial symmetry
Spherical symmetry
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