Physics and Beyond people could do big things" are gone. But the people who had been there continue to speak to us through this book. The book was published first in German 1969, in English as "Physics and Beyond" (1971) and in French in 1972 (La partie et le tout). Physics and Beyond Physics and Beyond () is a book by Werner Heisenberg, the German physicist who discovered the uncertainty principle. It tells, from his point of view, the history of exploring atomic science and quantum mechanics in the first half of the 20th century. As the subtitle "Encounters and Conversations" suggests, the
Heisenberg group the special property that the exponential map is a one-to-one and onto map from the Lie algebra formula_16 to the group formula_1. More general Heisenberg groups formula_31 may be defined for higher dimensions in Euclidean space, and more generally on symplectic vector spaces. The simplest general case is the real Heisenberg group of dimension formula_32, for any integer formula_33. As a group of matrices, formula_31 (or formula_35 to indicate this is the Heisenberg group over the field formula_36 of real numbers) is defined as the group formula_37 matrices with entries in formula_36 and having the form: where This is indeed