# Questions tagged [grassmann-numbers]

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### Integration by parts in functional field integrals

In QFT one often encounters expressions of the form $$\displaystyle Z = \int \mathscr{D}(\bar{\psi}, \psi) \, \mathrm{exp} \, S [ \bar{\psi}, \psi ]$$ with complex-valued (in the bosonic case) or ...
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### About constants in fermionic path integral in Peskin and Schroeder

I am confused by fermionic path integral used in Peskin and Schroeder. Equation (9.69) gives $$\Big(\prod_n\int d\bar{\theta}_nd\theta_n\Big)e^{-\bar{\theta}_iM_{ij}\theta_j}=\det M\tag{9.69}$$ But ...
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### Expanding superfields: inconsistency of notation?

If I have a wavefunction of a fermion field $\Psi[\psi]$ I can expand it like so about some vacuum: $$\Psi[\psi] = \Psi_0[\psi]( a + \int a(x)\psi(x)dx+\int a(x,y)\psi(x)\psi(y)dxdy+...)$$ Now all ...
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### Representing quaternionic algebra with creation and annihilation operators?

The paper "Quantized Grassmann variables and unified theories" says given creation and annihilation operators $b$ and $b^\dagger$ one can represent quaternionic imaginary units $q_1$, $q_2$ and $q_3$ ...
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### Show: $\langle n \vert \psi \rangle \langle \psi \vert n \rangle = \langle -\psi \vert n \rangle \langle n \vert \psi \rangle$ [closed]

The book (Altland and Simons, Condensed Matter Field Theory, Ch. 4.2) I am reading makes use of the identity \begin{equation} \langle n \vert \psi \rangle \langle \psi \vert n \rangle = \langle -\psi \...