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# Questions tagged [grassmann-numbers]

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### Wick's theorem proof for fermions

This is my first question. I am trying to prove Wick's theorem for fermions. I am currently using Peskin and Schroeder's discussion, which is in section 4.7 (and uses section 4.3, where Wick's ...
37 views

### Should Faddeev-Popov ghosts (in path integral) belong to infinite-dimensional Grassmann (Banach) algebra?

Many years ago, I had the opportunity to study gauge theories based on the book by Faddeev and Slavnov. The Faddeev-Popov ghost fields in the path integral for the Yang-Mills (YM) theory did not ...
• 101
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### $2\pi$-rotation of fermionic states vs. fermionic operators

Given a fermionic state $|\Psi\rangle$, a $2\pi$ rotation should transform it as $$|\Psi\rangle \quad\to\quad -|\Psi\rangle \,,$$ On the other hand, given a fermionic ...
• 707
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### Trace formula for fermionic variables

I am using Bravyi's paper "Lagrangian representation of fermionic linear optics" and one formula that stumbled me is the trace formula in Eq. (15) in the picture below: I do not see how to ...
97 views

### Commuting/anticommuting properties of fermionic ghost fields in BRST Quantization

I was reading the paper "Batalin-Vilkovisky analysis of supersymmetric systems" (by Laurent Baulieu and others). I am struggling to understand how commutation/anticommutation relations of ...
17 views

### N=4 Supersymmetric Ward identity

(This question pertains to exercise 4.13 of Elvang and Huang's textbook (which used to be lecture notes). This is not for a class, just to learn some new tools for work). Consider the expansion of the ...
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### Explicit form of Noether current for Majorana equation

I am looking for an explicit form of the Noether current for the Majorana equation.
• 2,271
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### Strange definition of the fermion number operator in Polchinski

In Polchinski's exposition of the RNS formalism for the superstring (String Theory: Volume II, chapter 10), in page 8, he mentions the worldsheet fermion number operator, which he calls $F$. He then ...
• 917
1 vote
82 views

### Fermionic path integral with boundary

Given a path integral: $$K(\eta,\xi) = \int\limits_{\psi(0)=\eta}^{\psi(1)=\xi} e^{\int_0^1\dot{\psi}(t)\psi(t) dt} D\psi\tag{1}$$ where $\psi(t)$ are a real Grassmann fields. I get two answers ...
54 views

1 vote
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