Dolan, Brian P. (2021) On the group generated by C, P and T: I 2 = T 2 = P 2 = ITP = −1, with applications to pseudo-scalar mesons. Journal of Physics A: Mathematical and Theoretical, 54 (30). p. 305401. ISSN 1751-8121
Download (655kB)
|
Abstract
We study faithful representations of the discrete Lorentz symmetry operations of parity P and time reversal T, which involve complex phases when acting on fermions. If the phase of P is a rational multiple of π then P2n = 1 for some positive integer n and it is shown that, when this is the case, P and T generate a discrete group, a dicyclic group (also known as a generalised quaternion group) which are generalisations of the dihedral groups familiar from crystallography. Charge conjugation C introduces another complex phase and, again assuming rational multiples of π for complex phases, TC generates a cyclic group of order 2m for some positive integer m. There is thus a doubly infinite series of possible finite groups labelled by n and m. Demanding that C commutes with P and T forces n = m = 2 and the group generated by P and T is uniquely determined to be the quaternion group. Neutral pseudo-scalar mesons can be simultaneous C and P eigenstates, T commutes with P and C when acting on fermion bilinears so neutral pseudo-scalar mesons can also be T eigenstates. The T-parity should therefore be experimentally observable and the CPT theorem dictates that T = CP.
Item Type: | Article |
---|---|
Keywords: | Lorentz group; parity; time reversal; fermions; quaternions; |
Academic Unit: | Faculty of Science and Engineering > Theoretical Physics |
Item ID: | 18429 |
Identification Number: | https://doi.org/10.1088/1751-8121/abe831 |
Depositing User: | Dr. Brian Dolan |
Date Deposited: | 25 Apr 2024 13:28 |
Journal or Publication Title: | Journal of Physics A: Mathematical and Theoretical |
Publisher: | Institute of Physics Publishing Ltd |
Refereed: | Yes |
URI: | |
Use Licence: | This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here |
Repository Staff Only(login required)
Item control page |
Downloads
Downloads per month over past year