Re: Law of Conservation of Baryon Number
- From: Hendrik van Hees <hees@xxxxxxxxxxxxx>
- Date: Sun, 20 Aug 2006 14:43:40 +0000 (UTC)
Uncle Al wrote:
For every symmetry in physics continuous in time or approximated by a
Taylor series there is a conserved propertry in physics, and
vice-versa.
What do you mean by "continuous in time"? That's not Noether's theorem.
Noether's theorem applies to all one-parameter Lie groups, i.e., each
one-parameter Lie group which leaves the equations of motion invariant
leads to a conserved quantity, and each conserved quantity leads to a
one-parameter Lie group which is symmetry of the equations of motion.
This is enforced by Noether's theorems.
http://www.mazepath.com/uncleal/lajos.htm#b5
A symmetry can be broken explicitly - a term in the action or
equations of motion may not be invariant. A symmetry can be broken
anomalously - not all classical theory symmetries exist in the
corresponding quantum theory. Quantum field theory anomaly spoils
renormalizability. Anomaly absence in the Standard Model is crucial.
Also this is a little bit too much simplified. Only the local gauge
symmetries must not be broken in any way to lead to a renormalizable
interaction of non-abelian gauge fields. In the standard model is at
least one important anomaly, namely the U_A(1) anomaly, which is
empirically very important, leading to the correct rate of pion decay
to photons (see, e.g., Weinberg, Quantum Theory of Fields, Vol. II).
There ya go, Pilgrim.
I fear, you'd come not far that way ;-).
--
Hendrik van Hees Texas A&M University
Phone: +1 979/845-1411 Cyclotron Institute, MS-3366
Fax: +1 979/845-1899 College Station, TX 77843-3366
http://theory.gsi.de/~vanhees/faq mailto:hees@xxxxxxxxxxxxx
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