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<H1><B>Tensors and Relativity: Chapter 3</B></H1>
<H2>Tensors in Special Relativity</H2>
<P>
<HR><FONT SIZE=+1>We need to express the equations of physics in a frame
independent way. This can be done for some equations by using four- vectors
[ e.g. Newton's Laws<A NAME="188"></A> ] but what about the rest
of physics!!? </FONT></P>
<P><FONT SIZE=+1>We now extend this idea by introducing more general coordinate
independent quantities called Tensors<A NAME="190"></A> . In this
section we will confine our discussion to Minkowski spacetime<A NAME="191"></A> ,
although the concepts will apply to curved spacetime and General Relativity.
</FONT><BR>
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<LI><A NAME="tex2html51"></A><FONT SIZE=+1><A HREF="node1.html#SECTION00010000000000000000" NAME="tex2html51">Metrics
and forms</A> </FONT></LI>
<LI><A NAME="tex2html52"></A><FONT SIZE=+1><A HREF="node2.html#SECTION00020000000000000000" NAME="tex2html52">One-
forms</A> </FONT></LI>
<UL>
<LI><A NAME="tex2html53"></A><FONT SIZE=+1><A HREF="node3.html#SECTION00021000000000000000" NAME="tex2html53">Gradients</A>
</FONT></LI>
<LI><A NAME="tex2html54"></A><FONT SIZE=+1><A HREF="node4.html#SECTION00022000000000000000" NAME="tex2html54">The
metric as a mapping of vectors onto one- forms</A> </FONT></LI>
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<LI><A NAME="tex2html55"></A><FONT SIZE=+1><A HREF="node5.html#SECTION00030000000000000000" NAME="tex2html55">More
general tensors</A> </FONT></LI>
<UL>
<LI><A NAME="tex2html56"></A><FONT SIZE=+1><A HREF="node6.html#SECTION00031000000000000000" NAME="tex2html56">Tensors
of type 0/2</A> </FONT></LI>
<LI><A NAME="tex2html57"></A><FONT SIZE=+1><A HREF="node7.html#SECTION00032000000000000000" NAME="tex2html57">Tensors
of type 0/<I>N</I></A> </FONT></LI>
<LI><A NAME="tex2html58"></A><FONT SIZE=+1><A HREF="node8.html#SECTION00033000000000000000" NAME="tex2html58">Tensors
of type 2/0</A> </FONT></LI>
<LI><A NAME="tex2html59"></A><FONT SIZE=+1><A HREF="node9.html#SECTION00034000000000000000" NAME="tex2html59">Tensors
of type <I>M</I>/0</A> </FONT></LI>
<LI><A NAME="tex2html60"></A><FONT SIZE=+1><A HREF="node10.html#SECTION00035000000000000000" NAME="tex2html60">Tensors
of type <I>M</I>/<I>N</I></A> </FONT></LI>
<LI><A NAME="tex2html61"></A><FONT SIZE=+1><A HREF="node11.html#SECTION00036000000000000000" NAME="tex2html61">Index
``raising'' and ``lowering''</A> </FONT></LI>
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<LI><A NAME="tex2html62"></A><FONT SIZE=+1><A HREF="node12.html#SECTION00040000000000000000" NAME="tex2html62">General
properties of tensors</A> </FONT></LI>
<LI><A NAME="tex2html63"></A><FONT SIZE=+1><A HREF="node13.html#SECTION00050000000000000000" NAME="tex2html63">Tensor
derivatives and gradients</A> </FONT></LI>
<LI><A NAME="tex2html64"></A><FONT SIZE=+1><A HREF="node14.html#SECTION00060000000000000000" NAME="tex2html64">Index</A>
</FONT></LI>
<LI><A NAME="tex2html65"></A><FONT SIZE=+1><A HREF="node15.html#SECTION00070000000000000000" NAME="tex2html65">About
this document ... </A></FONT></LI>
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<I>postscript</I> file of chapter 3.</A> </FONT></LI>
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<I>dvi</I> file of chapter 3.</A> </FONT></LI>
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<ADDRESS><I><FONT SIZE=+1>Peter Dunsby <BR>
Sat Jun 8 15:29:35 ADT 1996</FONT></I><FONT SIZE=+1> </FONT></ADDRESS>
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