# Questions tagged [clifford-algebra]

The tag has no usage guidance.

174 questions
Filter by
Sorted by
Tagged with
20 views

### Rotor of a rotor in Geometric Algebra

I was reading Geometric Algebra for Physicists, by Doran and Lasenby, and, in section 5.5.2, they calculate the Thomas Precession. However, at a certain point, they have the exponential of an ...
41 views

### Intuition about analogy of spinors in Clifford Algebra

I've been studying the application of Clifford Algebra in quantum mechanics, more specifically in spin, but I'm stuck in a basic analogy that is part of the basics before starting to do things using ...
54 views

### Symplectic Majorana spinors in 5D

According to the book "Supergravity" written by Freedman & van Proeyen in 5D for the existence of Majorana spinors it is necessary to introduce so called sympletic ones which requires ...
34 views

### Confusion in linear independence of matrices argument in Bjorken and Drell

In Bjorken and Drell, Relativistic Quantum Mechanics, the following argument is constructed to show that a set of matrices derived from the $\gamma$ matrices are linearly independent. The matrices of ...
62 views

336 views

### Conflicting definitions of a spinor

I'm moving my question from math.stackexchange over here because it got no attention over there, even after 3 weeks and a 50-point bounty, and also because this is a very physics-oriented math ...
43 views

### What is the definition of a Majorana fermion in conformal field theory?

Majorana spinors background According to Eq. (4.84) and (4.85) of these notes, charge conjugation of the spinor $\Psi$ is defined as $$\Psi^{(c)} = C \Psi^*,$$ where $C$ is the unitary charge ...
36 views

### Majorana fermions in Euclidean and Minkowski signatures - contradiction with Wikipedia Table

In this wonderful lecture note on Clifford Algebra and Spin(N) Representations, http://hitoshi.berkeley.edu/230A/clifford.pdf Somehow I find some inconsistency with his Tables of Euclidean and ...
33 views

### The 'mutual' and the 'self' in terms of the 'conjugacy' of Euclidean and Minkowski Weyl fermions

Euclidean and Minkowski fermions are shown in the Table of Wikipedia. (see the bottom https://en.wikipedia.org/wiki/Spinor#Summary_in_low_dimensions) My question is that what does the conjugacy mean ...
65 views

### Does $\{\gamma^\mu,\gamma^\nu\}=2g^{\mu\nu}\mathbb1$ determine the hermiticity of the gamma matrices?

If I remember correctly, the derivation of the Dirac equation requires that $\gamma^0$ is Hermitian while $\gamma^i$ for $i=1,2,3$ is anti-Hermitian. This is clearly true for the standard Dirac ...
52 views

96 views

### Help understanding Clifford/Geometric Algebra on curved spacetimes

Geometric Algebra on curved spacetimes. I seem to come across a lot of mentions of “spacetime algebra” (especially by Hestenes). As I understand it, this is simply the Clifford algebra $Cl(3,1)$. I'm ...
109 views

### How do you compute the successive action of two angular momentum operators on a multivector in geometric algebra?

I'm trying to compute the action of two angular momentum operators $J_i$ on some multivector $\psi$ in geometric algebra as in page 290 of Doran & Lasenby (Geometric Algebra for Physicists). ...
56 views

### How do I normalize the relativistic wavefunction in general?

https://en.wikipedia.org/wiki/Spacetime_algebra#Relativistic_quantum_mechanics claims that the wave-function can be written using geometric algebra as follows: $$\psi=R(\rho e^{i\beta})^{1/2}$$ ...