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Suppose $V$ is a vector bundle with structure group $SO(3)$, and suppose that it can be lifted to a $\text{Spin}(3) = SU(2)$ bundle (i.e. $w_2(V) = 0$). Let us call the lifted bundle $E$. Then it is s …

Let $M$ be a complex manifold, and $\omega$ be a $(p,q)$-form. Then $d\omega$ is an element of $\Omega^{p+1,q}(M)\oplus\Omega^{p,q+1}(M)$, so that $d = \partial + \overline{\partial}$, where $\partial …

I am currently trying to understand the BV-formalism, which makes heavy use of the functional derivative. Let us consider the functional derivative, as defined in for example its Wikipedia article. Le …

Consider a smooth vector bundle $\pi: E\rightarrow M$, the associated infinite jet bundle $J^\infty(\pi)$, and evolutionary vector fields $\partial_\varphi = \sum_{i,\sigma}(D_\sigma\varphi^i)\frac{\p …

I believe I have found the answer. I think it works like this, but I still have to verify it. In case of any other people that might have the same question, I will outline it here. It relies on the fo …