克利福德代数
- What is the periodicity of spinors?
- How do spinors relate to Clifford algebras?
- In what sense is {$SO(n)$} not simply connected? And what is the relationship between its covering group {$\textrm{Spin}(n)$} and the special unitary group?
读物
Spinor
Harvey, F. Reese (1990), "Chapter 2: The Eight Types of Inner Product Spaces", Spinors and calibrations, Academic Press, pp. 19–40, ISBN 0-12-329650-1
MacMahon Master Theorem
- The coefficient of {$x_1^{k_1}\cdots x_m^{k_m}$} in {$\frac{1}{\det (I_m - TA)}$} equals its coefficient in {$\prod_{i=1}^m \bigl(a_{i1}x_1 + \dots + a_{im}x_m \bigl)^{k_i}$}
- My thesis has combinatorial interpretations for the generating function {$\frac{1}{\det (I - A)} = \sum_{n=0}^{\infty}x^nh_n(\xi_1,...,\xi_n)$}
- Julian Schwinger: It is the MacMahon Master Theorem that unifies the angular momentum properties of composite systems in the binary build-up of such systems from more elementary constituents.
- In the Standard Model, fermions are not their own antiparticles, but in some theories they can be. Among other things, this involves the question of whether the relevant spinor representations of the groups Spin(p,q) are complex, real (‘Majorana spinors’) or quaternionic (‘pseudo-Majorana spinors’). The options are well-understood, and follow a nice pattern depending on the dimension and signature of spacetime modulo 8.
Twistors
https://en.wikipedia.org/wiki/Twistor_theory
- Do twistors relate the threesome and the foursome?
- Is there an eight-dimensional concept that expands on spinors and twistors?