Projective Representation of the Poincaré Group in a Quaternionic Hilbert Space
1968; Elsevier BV; Linguagem: Inglês
10.1016/b978-1-4832-3188-4.50011-9
Autores Tópico(s)Advanced Mathematical Theories and Applications
ResumoPublisher Summary This chapter discusses the concepts of quantum mechanics, complex Hilbert space, the Lattice structure of general quantum mechanics, the group of automorphisms in a proposition system, and projective representation of the Poincare group in quaternionic Hilbert space. Theoretical physics in the first half of the 20th century is dominated by two major developments—the discovery of the theory of relativity and the discovery of quantum mechanics. Both have led to profound modifications of basic concepts. Relativity in its special form has proclaimed the invariance of physical laws with respect to Lorentz transformations and led to the inevitable consequence of the relativity of spatial and temporal relationships. On the other hand, quantum mechanics recognizes as basic the complementarity of certain measurable quantities for microsystems and the concomitant indeterminism of physical measurements. From the mathematical point of view, the central object in the special theory of relativity is a group, the Lorentz group, or more generally, the Poincare group. For quantum mechanics, the most important mathematical object is the Hilbert space and its linear operators.
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