# On Simple Spinors, Null Vectors and the Orthogonal Group O(n)

@article{Budinich2020OnSS, title={On Simple Spinors, Null Vectors and the Orthogonal Group O(n)}, author={Marco Budinich}, journal={arXiv: Mathematical Physics}, year={2020} }

We explore the three separate isomorphisms that link together simple spinors, null vectors and the orthogonal group O(n) and exploit them to look back at these arguments from a unified viewpoint.

## One Citation

### The Clifford algebra of $R^{n,n}$ and the Boolean Satisfiability Problem

- Mathematics
- 2021

We formulate a Boolean algebra in the set of idempotents of Clifford algebra Cl(R) and within this frame we examine different formulations of the Boolean Satisfiability Problem in Clifford algebra.…

## References

SHOWING 1-8 OF 8 REFERENCES

### The Boolean SATisfiability Problem and the orthogonal group $O(n)$

- Mathematics
- 2019

We explore the relations between the Boolean Satisfiability Problem with $n$ literals and the orthogonal group $O(n)$ and show that all solutions lie in the compact and disconnected real manifold of…

### Fock space description of simple spinors

- Mathematics
- 1989

Cartan’s simple—often called pure—spinors corresponding to even‐dimensional complex vector spaces are defined in terms of the associated maximal totally null planes. Their geometrical properties are…

### Clifford Algebra As a Bridge Between Discrete and Continuous Worlds

- MathematicsAdvances in Applied Clifford Algebras
- 2018

There are several topics of Clifford algebra where discrete and continuous worlds are deeply intertwined, one for all the Cartan theorem that expresses continuous automorphisms by a succession of…

### The Theory of Spinors

- Physics
- 2012

The concept of a “spinor” emerged from the work of E. Cartan on the representations of simple Lie algebras. However, it was not until Dirac employed a special case in the construction of his…

### Topological geometry

- 1981

### On spinors transformations

- Mathematics
- 2016

We begin showing that for even dimensional vector spaces V all automorphisms of their Clifford algebras are inner. So all orthogonal transformations of V are restrictions to V of inner automorphisms…

### On Spinor Transformations

- Mathematics
- 2016

We begin observing that, if a vector space $V$ is even dimensional, all automorphisms of its Clifford algebra are inner. So all orthogonal transformations of $V$ can be seen as restrictions to $V$ of…

### Pivoting in Cayley transform-based optimization on orthogonal groups

- In Proceedings of the Second APSIPA Annual Summit and Conference, Biopolis, Singapore,
- 2010