The Tao of Physics interested and very open, and he told me something that I think is not known publicly because he never published it. He said that he was well aware of these parallels. While he was working on quantum theory he went to India to lecture and was a guest of Tagore. He talked a lot with Tagore about Indian philosophy. Heisenberg told me that these talks had helped him a lot with his work in physics, because they showed him that all these new ideas in quantum physics were in fact not all that crazy. He realized there was, in fact,
Heisenberg group group of a locally compact abelian group "K", equipped with a Haar measure. Such a group has a Pontrjagin dual formula_101, consisting of all continuous formula_102-valued characters on "K", which is also a locally compact abelian group if endowed with the compact-open topology. The Heisenberg group associated with the locally compact abelian group "K" is the subgroup of the unitary group of formula_103 generated by translations from "K" and multiplications by elements of formula_101. In more detail, the Hilbert space formula_103 consists of square-integrable complex-valued functions formula_106 on "K". The translations in "K" form a unitary representation of "K" as