Re: left/right symmetry, manifest or not

[Jack Uretsky <jlu@HEP.ANL.GOV>]

        The truth is that the RH Rule is built into the Clifford algebra.
An easy example is with the Pauli matrices, usually defined as:
        (read s_{x} as "sigma sub-x")

s_{x}s_{y}=is_{z}   s_{i} squared =1, s_{i}s_{j}=-s_{j}s_{i},i not equal j

        This corresponds to a RH- coordinate system.  One could just as
well have written:
s_{y}s_{x}=is_{z}
which would correspond to a LH-coordinate system.

On Wed, 28 Aug 2002, Bob Sciamanda wrote:

> If I may add another novice's appreciation,
> Draw two (non-parallel) vectors (A and B) from a common vertex on a sheet
> of paper.
> Now look at this in a mirror.  If you define and represent the cross
> product AxB as a (pseudo) vector following the right hand rule in the
> "real world", the reflected objects will follow the left hand rule in the
> "mirror world".
> OTOH, if you define and represent the wedge product by a directed
> (circulation) arc going form the tip of A to the tip of B, this definition
> carries over into the "mirror world".
> Bob Sciamanda (W3NLV)
> Physics, Edinboro Univ of PA (em)
> trebor@velocity.net
> http://www.velocity.net/~trebor
>
>
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