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Classical notions on super Riemann surfaces

A super Riemann surface $M$ is a complex supermanifold of dimension 1|1 with a superconformal structure given locally by an odd vector field ...
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Examples of Supergroups: U(n | m), SU(N, n|m) and PSU(N, n|m).

Looking for explicit forms of group elements in the supergroups: (1) U(n | m), (2) SU(N, n|m), (3) PSU(N, n|m), (4) PSL(n|m), (5) OSp(n|m). We can simply take $N=2$, $n=1$ and $m=1$. Partial ...
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1answer
50 views

The exterior algebra is a superalgebra?

Can someone explain how the exterior algebra of a vector space or a module over a commutative ring is a superalgebra? The exterior algebra has an obvious $\mathbb{Z}$-grading, but I don't see ...
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1answer
41 views

Sign convention for derivatives in a $\mathbb{Z}_2$ graded space

Suppose $V=V_0\oplus\theta V_1$ is a $\mathbb{Z}_2$ graded super vector space. Note: Since $\theta^2=0$, this implies $\theta\mathrm{d}\theta=-\mathrm{d}\theta\cdot\theta$. However, I wish to know ...
3
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1answer
172 views

Geometric interpretation of Supersymmetry

Is there a geometric interpretation of supersymmetry? I.e., if one has a manifold $\mathcal {M} $, and there are $\mathcal {N} $ SUSY generators, then is there a geometric interpretation of the SUSY ...
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A good reference for learning about super-differentiation & super-integration?

I've looked at a couple of books for basic information for super-differentiation & super-integration - Rogers Supermanifolds, and Khrennikovs Superanalysis. Unfortunately both books lack a clear ...
2
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1answer
86 views

Question about the parity of the ghost number operator in BRST quantization

Given a Lie algebra $[K_i,K_j]=f_{ij}^k K_k$, and ghost fields satisfying the anticommutation relations $\{c^i,b_j\}=\delta_j^i$, the ghost number operator is then $U=c^ib_i$ (duplicate indices are ...
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888 views

Grassmann numbers as eigenvalues of nilpotent operators?

The following question is motivated by the construction of the fermionic path/field integral, as done for example in Altland & Simons "Condensed Matter Field Theory". Consider the vector space ...