Visualize the Hamiltonian

[Nusc]

"Once, Dirac asked me whether I thought geometrically or algebraically? I said I did not know what he meant, could he tell me how he, himself, thought. He said his thinking was geometrical. I was taken aback by this because Dirac, with his transformation theory, represented for my generation the algebraic movement in physics par excellence. So, I said: 'I still don't understand.' He said: 'I will ask you a question. How do you picture de Sitter space?' I said, 'I write down the metric and then think about the structure of the terms in the expression.' He said, 'Precisely as I thought. You think algebraically, as most people from the Indian sub-continent do. I picture, without effort, the de Sitter space as a four-dimensional surface in a five-dimensional space.' (Kursunoglu 1990)

Dirac's hidden geometry: what about the Hamiltonian?

 

[pat_connell]

Dirac's approach to physics was heavily based on the Hamiltonian, which is an algebraic expression that describes the total energy of a physical system. Dirac believed that this expression could be used to describe the geometry of the system. This idea of hidden geometry was at the heart of his transformation theory and it allowed him to make predictions about how particles interact with fields and other particles. By picturing the Hamiltonian as a geometrical object, Dirac was able to develop a greater understanding of the structure of the universe.