2
votes
Sign of the $n$-form
Counterexample: $dx^3\wedge dx^2 \wedge dx^1 = - dx^1\wedge dx^2 \wedge dx^3 \neq (-1)^{1+3} dx^1\wedge dx^2\wedge dx^3$ in $\Bbb R^3$.
What is true is that for $\sigma\in \mathfrak{S}_n$, $\alpha^{\...
- 16.2k
1
vote
Accepted
Is Fock space a symmetric/exterior algebra?
There are two ways of looking at the symmetrization of $H$:
as the quotient $S^n(H) = H^{\otimes n}/I$, where $I$ is the ideal generated $I$ by sums of the form $v\otimes w - w\otimes v$;
as the ...
- 1,967
1
vote
Where is the magical sign change under change of basis ? Not pseudotensor?
Let $g$ be an inner product on the $n$ dimensional vector space $V$ (not necessarily positive definite). Suppose that an orientation has been chosen on $V$. Then there is an $n$-form $\mu_g\in\Lambda^...
- 6,742
1
vote
Accepted
How do simple bivectors in $\mathbb{R^4}$ generate rotations?
$
\newcommand\Ext{\mathop{\textstyle\bigwedge}}
\newcommand\MVects[1]{\mathop{\textstyle\bigwedge^{\mkern-1mu#1}}}
\newcommand\Cl[1]{\mathrm{Cl_{#1}}(\mathbb R)}
\newcommand\ClE[1]{\mathrm{Cl}^+_{#1}(\...
- 3,630
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