Craig McRae

collaborators

5 papers

math-ph2026

Parity Oddness of $Spin (1, 4)$ Dirac Mass Terms

Craig McRae

In the representation theory of Lorentzian orthogonal groups there are well known arguments as to why the parity operator $P$ and the time reversal operator $T$ …

math-ph2025

The Anti-Unitarity of Time Reversal & Co-representations of Lorentzian Pin Groups

Craig McRae

In the representation theory of Lorentzian orthogonal groups, there are well known arguments as to why the parity inversion operator $P$ and the time reversal operator $\…

math-ph2025

A Convenient Representation Theory of Lorentzian Pseudo-Tensors: $P$ and $T$ in $O (1, 3)$

Craig McRae

A novel approach to the finite dimensional representation theory of the entire Lorentz group $O (1, 3)$ is presented. It is shown how the entire Lorentz group may be u…

math.RT2025

Sporadic Isogenies to the Quaternionic Orthogonal Groups $SO^{*} (2 n)$

Craig McRae

For small dimensional Lie algebra's there are many so-called accidental isomorphisms which give rise to double covers of special orthogonal groups - Spin groups - which happen to c…

math.RT2025

Exploring Triality Explicitly: Convenient bases for $SO (8)$ , $Spin (1, 7)$ , and $G_{2}$

Craig McRae

The property of triality only appears in one linear simple Lie algebra: $D_{4}$ , a.k.a. $so (8, C)$ . Though often explored in abstract, it is desirable to have an…

Parity Oddness of Spin(1,4) Dirac Mass Terms

The Anti-Unitarity of Time Reversal & Co-representations of Lorentzian Pin Groups

A Convenient Representation Theory of Lorentzian Pseudo-Tensors: P and T in O(1,3)

Sporadic Isogenies to the Quaternionic Orthogonal Groups SO∗(2n)

Exploring Triality Explicitly: Convenient bases for SO(8), Spin(1,7), and G2​

Parity Oddness of $Spin (1, 4)$ Dirac Mass Terms

A Convenient Representation Theory of Lorentzian Pseudo-Tensors: $P$ and $T$ in $O (1, 3)$

Sporadic Isogenies to the Quaternionic Orthogonal Groups $SO^{*} (2 n)$

Exploring Triality Explicitly: Convenient bases for $SO (8)$ , $Spin (1, 7)$ , and $G_{2}$