Sudarshan: Seven Science Quests
Spin Statistics
There was the unmistakable connection between the spin of a particle and the symmetry of the many particle wave functions. Bose had proposed Bose statistics for photons; Fermi and Dirac had shown that the Pauli exclusion principle could be translated into the statistics obeyed by spin 1/2 particles. When quantum mechanics and subsequently quantum field theory were developed, the connection received more attention. The history of ideas up to and including W. Pauliís work is systematically presented in the monograph "Wolfgang Pauli and the Spin-Statistics Relation" by Duck and Sudarshan.

That the symmetry of the many particle wave functions could be Bose, Fermi, or more general statistics was shown to depend on the connectivity of the configuration space. Imbo and Sudarshan studied this question in a series of papers but these considerations did not yield the connection between spin and statistics. Duck and Sudarshan showed that attempts to do this by various authors "beg the question".

For quantum field theory, Pauliís proof depended on invoking relativistic invariance; but the major impact of particle statistics is in the non-relativistic domain such as atomic structure, nuclear structure, theory of metals, theory of superconductivity, and the theory of phonons, etc. Sudarshan showed that this connection can be obtained from the symmetry of scalars bilinear in a field. He also showed that this product is symmetric for integer spin and antisymmetric for half integer spins. These results were presented in his paper in the Proceedings of the Indian Academy of Science (1965) and subsequent publications including the monograph by Duck and Sudarshan, and in a paper (in the American Journal of Physics) which deals with fields with internal symmetries.

When the theory is applied to two space dimensions we get the anyon statistics (discovered by Wilczek). The spin-statistics relation in higher dimensions have been investigated by Boya and Sudarshan. They found that in all dimensions integer spin particles obey Bose statistics. But there are some dimensions in which the spinor field may obey either Fermi or Bose statistics.

See more detailed REVIEW and REFERENCES below.
Schedule of symposium talks for Spin Statistics.
Next topic overview: IV. Quantum Optical Coherence
REFERENCES

The Fundamental Theorem on the Connection between Spin and Statistics, in Proc. Nobel Symposium 8; Elementary Particle Theory, Relativistic Groups and Analyticity, Nils Svartholm (ed.), Almqvist and Wiksell, Stockholm (1968), pp.379-386.

The Fundamental Theorem on the Relation between Spin and Statistics, Proc. Indian Acad. Sci. LXVII, 284 (1968).

A World of Bose Particles, in Science Today, Bombay, India (January 1974); Am. J. Phys. 43(1), 69 (1975).

Topological and Algebraic Aspects of Quantization: Symmetries and Statistics; with Tom Imbo and Chandni Imbo, Ann. Inst. Henri Poincare 49, 387-396 (1988).

Inequivalent Quantization in Multiply-Connected Spaces. Il; with P. A. Horvathy and G. Morandi, Nuovo Cim. 20, 201 (1989).

The Dynamical Basis of the Spin-Statistics Relation. Invited lecture at the Lochlainn O' Raifearthaigh and the Sixth Irish Conference on Quantum Field Theory, Dublin (1998).

Toward an Understanding of the Spin-Statistics Theorem; with Ian Duck, Am. J. Phys. 66(4), 284 (1998).

Pauli and the Spin-Statistics Theorem; with Ian Duck, World Scientific, Singapore (1998). [BOOK].

What Price the Spin-Statistics Theorem; with Ian Duck. Submitted to Proc. Roy. Soc. London.

Non Relativistic Proof Of Spin-Statistics Theorem; with A. Shaji, http://arxiv.org/pdf/quant-ph/0306033 (2003).

Spin Statistics Relation In Arbitrary Number Of Space Dimensions; with L. J. Boya (in preparation).
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Next topic overview: IV. Quantum Optical Coherence

 

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Sudarshan Symposium, Nov. 5-7, 2006
Curriculum Vitae
Seven Science Quests
V-A: Universal Theory
of Weak Interaction
Symmetry
Spin Statistics
Quantum Optical Coherence:
Sudarshan Representation
Quantum Zeno Effect
Theory of Tachyons
Quantum Mechanics
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