The Hamiltonian formulation in relativity.

Like any major breakthrough in thinking, the theory of relativity caused a great upheaval in our attitude to science. Seventy years after the advent of relativity we are still coming to terms with the changes it has brought in our outlook. Part of this process is simply the valid translation of pre-relativistic laws and concepts into the 4-dimensional language of relativity - a problem by no means as easy as would at first seem; the aim of this thesis is to survey the ways in which the methods of analytical mechanics may be translated into a relativistic setting. Chapter 1 provides an introduction to the work in the form of a non-rigorous discussion of the historical and mathematical development of electromagnetism, analytical mechanics and relativity, and ends with a presentation of the basics of the functional calculus. This is needed in the presentation of field theory given in chapter 2. We see two possibilities for the relativistic formulation of analytical mechanics, and field theory represents the first of these possibilities. In the absence of any real grounds for continuing on this tack we then move on to the other possibility in chapter 3, where we review the attempts of a number of authors to formulate relativistic particle mechanics as a Hamiltonian system. This then leads in chapter 4 to our own such attempt, based mainly on the work of Synge, which we have named homogeneous mechanics. After the main exposition of the theory the work of the remaining chapters 5 and 6 is then to apply the above theory (not always successfully) to a number of cases where analytical mechanics has in the past proven itself an invaluable tool: namely, the areas of symmetries and quantum theory.