Abstract
The transformations in space and in time which belong to the Galilei group play an important role in quantum theory. In some respect and for some aspects, their role is new as compared to classical mechanics. Rotations, translations, and space reflection induce unitary transformations of those elements of Hilbert space which are defined with respect to the physical space ℝ3 and to the time axis ℝt. Reversal of the arrow of time induces an antiunitary transformation in ℋ. Invariance of the Hamiltonian H of a quantum system under Galilei transformations implies certain properties of its eigenvalues and eigenfunctions which can be tested in experiment. This chapter deals, in this order, with rotations in ℝ3, space reflection, and time reversal. A further and more detailed analysis of the rotation group is the subject of Chap. 6 in Part Two.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
The series (4.27) is named after the mathematicians A. Clebsch (1833–1872) and P. Gordan (1837–1912).
In view of Jacobi coordinates for N particles I choose here r to point from particle 1 to particle 2. Note, however, that in [Scheck (2005)], Sects. 1.7.1 and 1.7.3, I used r = x (1) − x (2) instead.
K. G. J. Jacobi, Crelles Journal für reine und angewandte Mathematik XXVI, 115–131 (1843).
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
(2007). Space-Time Symmetries in Quantum Physics. In: Quantum Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-49972-5_4
Download citation
DOI: https://doi.org/10.1007/978-3-540-49972-5_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-25645-8
Online ISBN: 978-3-540-49972-5
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)