File r37/lisp/csl/html/r37_0409.html artifact dfc6d9b859 part of check-in a57e59ec0d

<A NAME=HE_dot>

<TITLE>HE_dot</TITLE></A>
<b><a href=r37_idx.html>INDEX</a></b><p><p>



<B>.</B> _ _ _ <B>HE-DOT</B> _ _ _  _ _ _  _ _ _  _ _ _ <B>operator</B><P>
<P>
 
The . operator is used to denote the scalar product of two Lorentz 
four-vectors. 
 <P> <H3> 
syntax: </H3>
<P>
<P>
&lt;vector&gt; <em>.</em> &lt;vector&gt; 
<P>
<P>
<P>
&lt;vector&gt; must be an identifier declared to be of type <em>vector</em> to h
ave 
the scalar product definition. When applied to arguments that are not 
vectors, the 
<A HREF=r37_0043.html>cons</A> operator is used, 
whose symbol is also ``dot.'' 
<P>
<P>
 <P> <H3> 
examples: </H3>
<P><PRE><TT>
vector aa,bb,cc; 

let aa.bb = 0; 

aa.bb; 

  0 


aa.cc; 

  AA.CC 


q := aa.cc; 

  Q := AA.CC 


q; 

  AA.CC

</TT></PRE><P>Since vectors are special high-energy physics entities that do not
 contain 
values, the . product will not return a true scalar product. You can 
assign a scalar identifier to the result of a . operation, or assign a . 
operation to have the value of the scalar you supply, as shown above. Note 
that the result of a . operation is a scalar, not a vector. 
<P>
<P>
The metric tensor g(u,v) can be represented by <em>u.v</em>. If contraction 
over the indices is required, <em>u</em> and <em>v</em> should be declared to 
be of type 
<A HREF=r37_0412.html>index</A>. 
<P>
<P>
The dot operator has the highest precedence of the infix operators, so 
expressions involving . and other operators have the scalar product 
evaluated first before other operations are done. 
<P>
<P>
<P>