Linked Questions

24 votes
1 answer
4k views

Classical Fermion and Grassmann number

In the theory of relativistic wave equations, we derive the Dirac equation and Klein-Gordon equation by using representation theory of Poincare algebra. For example, in this paper http://arxiv.org/abs/...
Xiaoyi Jing's user avatar
  • 1,078
10 votes
2 answers
2k views

What conserved quantity does Supersymmetry imply?

According to Noether's theorem, for every continuous symmetry there is a conserved quantity. What is the quantity that corresponds to Supersymmetry?
Nemo's user avatar
  • 1,679
9 votes
3 answers
2k views

Is the fermion mass Lagrangian term imaginary instead of real?

This seems to be an absurd question, but bear with me. In quantum field theory, the Dirac fermion mass Lagrangian term reads $$ m\bar\psi \psi = m(\bar\psi_L \psi_R + \bar\psi_R \psi_L) = m(\psi_L^\...
MadMax's user avatar
  • 3,832
10 votes
3 answers
982 views

Why are Grassmann fields never classical?

I see this statement in many QFT books (e.g. Altland & Simons' Condensed Matter Field Theory) but the author never explains why. Can you briefly explain why Grassmann fields never have a ...
Medulla Oblongata's user avatar
14 votes
1 answer
2k views

What is the value of a quantum field?

As far as I'm aware (please correct me if I'm wrong) quantum fields are simply operators, constructed from a linear combination of creation and annihilation operators, which are defined at every point ...
Siraj R Khan's user avatar
  • 1,958
7 votes
1 answer
4k views

A few simple questions about Grassmann numbers: commutation relations and derivatives

I'm trying to learn about Grassmann numbers from the book "Condensed Matter Field Theory" by Altland and Simons, but I am currently encountering some difficulties. I have several smaller questions ...
RogueDodecahedron's user avatar
5 votes
3 answers
2k views

Completing the square for Grassmann variables

When working with path integrals of both bosonic and fermionic field variables, I'm a bit unsure of how to do the usual complete the square trick when an interaction between the two is concerned. Say ...
TeeJay's user avatar
  • 538
0 votes
1 answer
2k views

What is the meaning of a Grassmann variable?

I don't seem to understand the concept of a Grassmann-variable. When studying superspaces and superfields I am told that the coordinates being used are $$(x^\mu, \theta_\alpha, \bar{\theta}_\alpha)$$ ...
user7077252's user avatar
2 votes
2 answers
1k views

Using Grassmann variables on fermionic theories

I think the best way to put my question is the following: what (fermionic) theories make use of Grassmann variables? Let me clarify my question a little further. I remember some discussions in quantum ...
JustWannaKnow's user avatar
7 votes
1 answer
2k views

What exactly are "Grassmann-valued fields"?

Peskin & Schroeder define a Grassmann field $\psi(x)$ as a function whose values are anticommuting numbers, that can be written as : [p.301 eq. 9.71] $$\psi(x) = \sum\psi_i \phi_i(x),\tag{9.71}$$ ...
user341440's user avatar
3 votes
2 answers
692 views

How are supersymmetry transformations even defined?

I am just starting to read about supersymmetry for the first time, and there is something bothering me. Supersymmetry transformations transform between bosonic fields and fermionic fields, but I don't ...
user1379857's user avatar
  • 11.5k
5 votes
1 answer
408 views

Dirac Lagrangian in Classical Field Theory with Grassmann numbers

The concept of the Grassmann number makes me confused. It is used to describe fermionic fields, especially path integral quantization. Also, it is used to deal with the classical field theory of ...
Jaeok Yi's user avatar
14 votes
0 answers
1k views

Where does a fermionic coherent state live (which Hilbert space)? [duplicate]

There have been a couple of questions on fermionic coherent states, but I didn't find any that covered the following question: If I define a coherent fermionic state in the 2-level-system spanned by $...
LFH's user avatar
  • 730
5 votes
1 answer
788 views

Number of Grassmann generators for Dirac field?

How many Grassmann generators are sufficient for the description of a Dirac spinor in 4 dimensions? i.e. The Dirac field is a map to $\Lambda_N$, the space of supernumbers with $N$ real Grassmann ...
QuantumDot's user avatar
  • 6,301
5 votes
1 answer
343 views

What is the Grassmann parameter $\epsilon$ in the BRST transformation?

Whenever I learn about anything involving fermions and the path integral, I get confused about Grassmann numbers. I'm currently following Weigand's notes, specifically the section on BRST symmetry. ...
knzhou's user avatar
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