Hamiltonian Formalism of General Relativity

Independent Research with Dr. Syed Moeez Hassan (Google Scholar profile)

Institution: Department of Physics, Lahore University of Management Sciences

Abstract:

Canonical gravity, a framework that uses Dirac’s method for constrained Hamiltonian systems, to derive the Hamiltonian for General Relativity, and then quantize it. In canonical gravity one usually reduces the system by symmetry arguments and then solves these Hamiltonians to get “wave functions” for the universe. This comes under Quantum Cosmology.

I derived the ADM formalism and then expressed the Einstein’s Field equations as a constrained Hamiltonian system in terms of new variables, called the ADM variables after Arnowitt, Deser, Miser, and their canonically conjugate momenta.

Picture Credits: Suat Dengiz
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