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Results tagged with clifford-algebras
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user 69531
3
votes
1
answer
125
views
Classification of $2k$-vectors modulo orthogonal transformations
Consider the following chain $\{A_1,A_2,A_3,\cdots,A_{n}\}$ of orbit spaces of even-rank anti-symmetric tensors, where
$$A_k:=\frac{\Lambda^{2k}(\mathbb{R}^{2n})}{e_{i_1}\wedge \cdots \wedge e_{i_{2k} …
- 605
3
votes
Accepted
Why does the Bogolyubov transformation work? - In language of Clifford Algebras?
There is an elegant formulation of the Bogolyubov transformation in terms of Clifford algebras. Note that a quadratic Hamiltonian (noted by a hat), is a hermitian element of the representation of a Cl …
- 605
4
votes
1
answer
503
views
Why does the Bogolyubov transformation work? - In language of Clifford Algebras?
Letting the standard Clifford algebra of dimension $2k$ be denoted by $Cl_{2k}$, let's denote the corresponding complex Clifford algebra via $$\mathbb{C}l_{2k}\equiv Cl_{2k}\otimes_{\mathbb{R}}\mathbb …
- 605