Spin-statistics Theorem - Why The Bogus Argument Fails

Why The Bogus Argument Fails

To prove spin/statistics, it is necessary to use relativity (though there are a few nice methods which do not use field theoretic tools). In relativity, there are no local fields which are pure creation operators or annihilation operators. Every local field both creates particles and annihilates the corresponding antiparticle. This means that in relativity, the product of the free real spin-0 field has a nonzero vacuum expectation value, because in addition to creating particles and annihilating particles, it also includes a part which creates and then annihilates a particle:

And now the heuristic argument can be used to see that G(x) is equal to G(−x), which tells you that the fields cannot be anti-commuting.

Read more about this topic:  Spin-statistics Theorem

Famous quotes containing the words argument and/or fails:

    If we could produce one or two more Madame Curies, that would accomplish far more for the advancement of women than any amount of agitation, argument and legislation.
    Virginia Crocheron Gildersleeve (1877–1965)

    I am dead against art’s being self-expression. I see an inherent failure in any story which fails to detach itself from the author—detach itself in the sense that a well-blown soap-bubble detaches itself from the bowl of the blower’s pipe and spherically takes off into the air as a new, whole, pure, iridescent world. Whereas the ill-blown bubble, as children know, timidly adheres to the bowl’s lip, then either bursts or sinks flatly back again.
    Elizabeth Bowen (1899–1973)