File r37/lisp/csl/html/r37_0410.html artifact a1d382f025 part of check-in 3af273af29

<A NAME=EPS>

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



<B>EPS</B> _ _ _  _ _ _  _ _ _  _ _ _ <B>operator</B><P>
<P>
 
The <em>eps</em> operator denotes the completely antisymmetric tensor of 
order 4 and its contraction with Lorentz four-vectors, as used in 
high-energy physics calculations. 
 <P> <H3> 
syntax: </H3>
<P>
<P>
<em>eps</em>(&lt;vector-expr&gt;,&lt;vector-expr&gt;,&lt;vector-expr&gt;, 
&lt;vector-expr&gt;) 
<P>
<P>
<P>
&lt;vector-expr&gt; must be a valid vector expression, and may be an index. 
<P>
<P>
 <P> <H3> 
examples: </H3>
<P><PRE><TT>
vector g0,g1,g2,g3; 

eps(g1,g0,g2,g3); 

  - EPS(G0,G1,G2,G3); 


eps(g1,g2,g0,g3); 

  EPS(G0,G1,G2,G3); 


eps(g1,g2,g3,g1); 

  0

</TT></PRE><P>Vector identifiers are ordered alphabetically by REDUCE. When an o
dd number 
of transpositions is required to restore the canonical order to the four 
arguments of <em>eps</em>, the term is ordered and carries a minus sign. When an
 
even number of transpositions is required, the term is returned ordered and 
positive. When one of the arguments is repeated, the value 0 is returned. 
A contraction of the form 
eps(_i j mu nu p_mu q_nu) 
is represented by <em>eps(i,j,p,q)</em> when <em>i</em> and <em>j</em> have been
 
declared to be of type 
<A HREF=r37_0412.html>index</A>. 
<P>
<P>
<P>