History of subatomic physics indestructible. But when the nucleus change its charge and/or mass (by emitting or capturing a particle), the atom can become the one of another element. Special relativity explained how the "mass defect" is related to the energy produced or consumed in reactions. The branch of physics that studies transformations and the structure of nuclei is now called nuclear physics, contrasted to atomic physics that studies the structure and properties of atoms ignoring most nuclear aspects. The development in the nascent quantum physics, such as Bohr model, led to the understanding of chemistry in terms of the arrangement of electrons in
Heisenberg group operators on formula_103: for formula_109. So too do the multiplications by characters: for formula_111. These operators do not commute, and instead satisfy multiplication by a fixed unit modulus complex number. So the Heisenberg group formula_113 associated with "K" is a type of central extension of formula_114, via an exact sequence of groups: More general Heisenberg groups are described by 2-cocyles in the cohomology group formula_116. The existence of a duality between formula_117 and formula_101 gives rise to a canonical cocycle, but there are generally others. The Heisenberg group acts irreducibly on formula_103. Indeed, the continuous characters separate points so any