1,720,987 research outputs found
Square-integrable imprimitivity systems
No full textWe give a definition of square-integrability for imprimitivity systems and we provethat the square-integrable ones share most of the properties of square-integrablerepresentations of group
Galilei invariant wave equations
No full textWe describe the quantum states of an elementary particle invariant with respect to asymmetry group as solutions of an invariant wave equation. From the mathematical point ofview the wave equation is a set of differential operators on the space of vector-valued dis-tributions over the space-time. As an application, we consider the Galilei invariant particlesboth in 3 + 1 and in 2 + 1 dimensions
The Theory of Symmetry Actions in Quantum Mechanics: with an application to the Galilei group
No full textThis is a book about representing symmetry in quantum mechanics. The book is on a graduate and/or researcher level and it is written with an attempt to be concise, to respect conceptual clarity and mathematical rigor. The basic structures of quantum mechanics are used to identify the automorphism group of quantum mechanics. The main concept of a symmetry action is defined as a group homomorphism from a given group, the group of symmetries, to the automorphism group of quantum mechanics. The structure of symmetry actions is determined under the assumption that the symmetry group is a Lie group. The Galilei invariance is used to illustrate the general theory by giving a systematic presentation of a Galilei invariant elementary particle. A brief description of the Galilei invariant wave equations is also given
Symmetry groups in quantum mechanics and the theorem of Wigner on the symmetry transformations
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