# Tagged Questions

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### Are Fock spaces just a special type of tensor algebra?

Are Fock spaces just a special type of tensor algebra? The definitions I am using: http://en.wikipedia.org/wiki/Fock_space http://en.wikipedia.org/wiki/Tensor_algebra From what I can tell, the ...
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### Reference on Lie superalgebras

I wish to study Lie superalgebras, in particular how they are involved with the superconformal symmetry of N=4 SYM in D=4. I have a solid background in Lie algebras from a pure mathematical ...
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### The super Grassmannian $G_{2|2}(4|4)$

In the paper, the super Grassmannian $G_{2|2}(4|4)$ is defined by (12)--(18). An element of $G_{2|2}(4|4)$ can be written as a $(2 | 2) \times (4 | 4)$ matrix of full rank modulo the left action by ...
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### Notation of supermatrices

I am trying to understand supermatrices. First I want to know the notation of supermatrices. In the paper, it is mentioned $(2|4|2) \times (2|2)$ supermatrices. What are $(2|4|2) \times (2|2)$ ...
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### Under what cases is the Batalin-Vilkovisky (BV) operator nilpotent?

It is understood that when we deal with gauge algebras which close on-shell only after using equations of motion or where the space-time is curved, we can no longer just do away with BRST quantization....
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### Multivariable functions of Grassmann numbers

I'm trying to derive the closed form of the fermionic coherent state defined by the relation: $$f_i|\vec{\eta}\rangle = \eta_i |\vec{\eta}\rangle \tag{4.10}$$ My book (Atland and Simons, Condensed ...
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### Representations of subalgebra in the super virasoro algebra

In the Virasoro algebra, which is generated by $L_n$, one has the obvious subalgebra spanned by $L_{-1}$ ,$L_{1}$ and $L_{0}$ which is isomorphic to the Lie algebra $\mathfrak{sl}(2,\mathbb{R})$. The ...
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### New Supersymmetry Algebra

We know that SUSY generators commute with translation $$[P_\mu,Q_\alpha]=0$$ I have some questions: What is this equation physical meaning? Is it possible to make "SUSY-like" generators that do ...
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### Does the commutator of anything with itself not vanish?

In a quantum mechanics exam one question was to write the commutator of a couple of operators. Everybody got points taken away since they did not write $[Q_i, Q_i] = 0$ for all the operators $Q_i$ in ...
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### Highest weight unitary representations of $psl(2|2)$

I'm having some trouble understanding how to extend representation theory from Lie algebras to super Lie algebras, in particular with $psl(2|2)$. Ultimately I'm interested in 2D quantum sigma models ...
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### What is a supermultiplet?

In Quantum field theory by Lewis H. Ryder, a supermultiplet is mentioned with no explanation as to what one is.
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### Embedding of $F(4)$ in $OSp(8|4)$?

Is the superconformal algebra in five dimensions, $F(4)$, a subalgebra of the (maximal) six-dimensional superconformal algebra $OSp(8|4)$?
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### Grassmann Variables Representation?

It might be a silly question, but I was never mathematically introduced to the topic. Is there a representation for Grassmann Variables using real field. For example, gamma matrices have a ...
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### What are Grassmann (even/odd) numbers used in superalgebras?

Are Grassmann 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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### What do the supercharges in extended supersymmetry do?

What do the supercharges in extended supersymmetry do? In $N=1$ supersymmetry there are a certain number of fermions and and equal number of bosons. You can transform all fermions to the bosons (and ...
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.
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 ...