The grassmann-numbers tag has no wiki summary.
4
votes
1answer
82 views
Strange Grassmann double integration
I can unterstand why because the integration over Grassman variables has to be translational invariant too, one has
$$
\int d\theta = 0
$$
and
$$
\int d\theta \theta = 1
$$
but I dont see where ...
1
vote
0answers
89 views
Why are differential forms on a n-dimensional manifold a Grassmann algebra?
This is stated as an obvious example of a Grassmann algebra on page 32 in this tutorial I am trying to read, but to me it is unfortunately not so obvious.
So can somebody expand this comment a bit ...
6
votes
1answer
230 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 ...
1
vote
3answers
134 views
Constructing Supersymmetric Lagrangians
It is a very trivial doubt but somehow I am not able to figure it out. While constructing a supersymmetric lagrangian we always even number of fermionic fields.
One reason is of course the product ...
1
vote
1answer
129 views
dimensional analysis of Grassmann integration/differentiation
There is another paradox that I need to resolve:
The Berezin integration rules for Grassmann odd variables give the same result as differentiation:
If $f=x+\theta\psi$ is a superfunction, the ...
1
vote
0answers
103 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 ...
7
votes
3answers
465 views
Grassmann paradox weirdness
I'm running into an annoying problem I am unable to resolve, although a friend has given me some guidance as to how the resolution might come about. Hopefully someone on here knows the answer.
It is ...
1
vote
1answer
116 views
Superspace Uncertainty Principle
Do the "operator for translations in superspace" and the "position in superspace operator" follow an uncertainty principle? How "real" is superspace? Aside from being weird (and possibly just a ...
1
vote
2answers
253 views
Nature of Derivatives of Anticommuting Variables
This may be a noob question but I've tried searching about this and haven't been able to put things into the context of what I've been studying.
(Dot means the usual derivative w.r.t. time)
If $c$ ...
3
votes
2answers
291 views
A different type of Gaussian Grassmann Integral
Let $A$ be an antisymmetric matrix.
Usually, one proves that for a Grassmann integral of the type,
$$\int d\psi d\theta \exp( \psi^T A \theta) = \det(A)$$
where $\psi$ and $\theta$ are vectors of ...
3
votes
1answer
242 views
Basic Grassmann/Berezin Integral Question
Is there a reason why $\int\! d\theta~\theta = 1$ for a Grassmann integral? Books give arguments for $\int\! d\theta = 0$ which I can follow, but not for the former one.
0
votes
1answer
195 views
what are grassmanian (even/odd) numbers used in superalgebras?
are grassmaniann numbers a concept of graded lie algebras or is something specific to superalgebras? what are they (i.e: how are they defined, important properties, etc.)? is there a reasonable ...
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votes
4answers
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“Velvet way” to Grassmann numbers
In my opinion, the Grassmann number "apparatus" is one of the least intuitive things in modern physics.
I remember that it took a lot of effort when I was studying this. The problem was not in the ...
