All Questions
Tagged with anticommutator superalgebra
9
questions
-1
votes
1
answer
100
views
Confusion about whether a fermion field and its conjugate as an Grassmann number
I'm confused about what "a Grassmann-odd number" really means and how does it apply to fermions.
In some text, it says that "if $\varepsilon \eta+\eta \varepsilon =0 $, then $\...
- 368
3
votes
0
answers
93
views
Derivation of anti-commutation relations of massive supermultiplet generators [closed]
In almost all intro to supersymmetry notes the commutation relations are given between the generators and their conjugates however, I can not find any proofs of them anywhere and am struggling to ...
2
votes
1
answer
585
views
Right derivative of Grassmann number and associated anti-commutation relation
I am reading chapter 3 of Anomalies in quantum field theory by Reinhold Bertlmann and I found one statement that I don't know how to prove. First of all he defined the right derivative on the ...
- 766
2
votes
2
answers
324
views
How do fermionic operators transform?
In quantum mechanics, if we have an operator $\Omega$, then under the transformation $T$, with infinitesimal generator $G$ (i.e. $T(\epsilon)=1-i\epsilon G + \ldots$), then operator transforms as
$$\...
- 857
3
votes
1
answer
103
views
$\mathcal{N} \ge 2$ Supersymmetry massive supermultiplets
In Bertolinis SUSY notes [https://people.sissa.it/~bertmat/susycourse.pdf] we have defined:
$$
\{Q^I_\alpha,\bar{Q}_\dot{\beta}^J\}=2m\delta_{\alpha\dot{\beta}}\delta^{IJ}\tag{3.24}
$$
$$
\{Q^I_\alpha,...
- 2,035
4
votes
1
answer
323
views
Canonical Quantisation vs the Dirac Field, why does it even work?
Using the "Dirac Prescription", we can preserve the format of a differential equation in its QM form. If we define the canonical variables s.t. they have the same commutation relations times $i$ as ...
- 267
1
vote
1
answer
228
views
Commutation relations of symmetry generators in SUSY
It is well known that the generators
$$ Q_\alpha = \frac{\partial}{\partial \theta^\alpha} - i \sigma^\mu_{\alpha \dot \beta} \bar{\theta}^\dot{\beta} \partial_\mu $$
and
$$ \bar{Q}_\dot{\alpha} = -\...
- 13
1
vote
2
answers
425
views
How to prove the translation generator commutes with the spinors in SUSY algebra?
I was reading Modern Supersymmetry by John Terning, the book starts with SUSY algebra and says
$$
\left[ P_{\mu} , Q_{\alpha} \right] = \left[ P_{\mu} , Q_{\alpha}^{\dagger} \right] = 0
$$
I am ...
- 247
2
votes
2
answers
499
views
How to change a commutator of SUSY super-charges into an anti-commutator?
I would like to understand an apparently rather simple calculation which checks the closure of the Supersymmetry algebra via the commutator of 2 supersymmetric variations of the type:
$$\delta \phi = ...
- 9,778