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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^{\...
Didier's user avatar
  • 16.2k
1 vote

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 ...
Daniel Teixeira's user avatar
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^...
Bence Racskó's user avatar
1 vote

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}(\...
Nicholas Todoroff's user avatar

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