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

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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:	Publisher
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

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