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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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### Question about the expression of Witten Index

I am studying supersymmetry by myself. I do not understand the expression of Witten index, which is ${\rm Tr}(-1)^{F}$. What does it mean by writing $-1$ to the power of an operator $F$? Is this ...
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### What are anticommuting spinor parameters $\zeta^\alpha$?

I'm reading Martin F.Sohnius, Introducing supersymmetry, page 82. It is the first time he introduces the anticommuting spinor parameters $\zeta^\alpha$ to calculate the supersymmetry variations of a ...
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### Why should an generator acts on an operator with the Lie bracket?

When we deal with ordinary symmetries which form a Lie group, we have an corresponding Lie algebra with a structure of Lie bracket $[,]$. A infinitesimal transformation can act on a state or an ...
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### Supersymmetric variation of $F$ term using super Jacobi identity [closed]

Basically, i am solving problems in note with a slightly different notation. \begin{align} [Q_\alpha F] = -i \lambda_\alpha (x), \quad [ \bar{Q}_{\dot{\alpha}},F] = -i \bar{\chi}_{\dot{\alpha}} \...
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### Why $\delta F = B\epsilon$ and not $F=B \epsilon$ in supersymmetry?

We can express supersymmetric transformations as $$\delta F = B\epsilon, \tag{1}$$ $$\delta B = F\bar{\epsilon},\tag{2}$$ where $B$ and $F$ denote the bosons and fermions, respectively, in the theory ...
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Given the complete supersymmetric lagrangian of a free abelian gauge multiplet $$\mathcal{L} = -\frac{1}{4} F_{\mu\nu} F^{\mu\nu} + i \bar{\lambda} \bar{\sigma}^\mu \partial_\mu \lambda + \frac{1}{2} ... 1answer 125 views ### Under what cases is the Batalin-Vilkovisky (BV) operator nilpotent? It is understood that when we deal with gauge algebras which close on-shell only after using equations of motion or where the space-time is curved, we can no longer just do away with BRST quantization.... 2answers 82 views ### Multivariable functions of Grassmann numbers I'm trying to derive the closed form of the fermionic coherent state defined by the relation:$$ f_i|\vec{\eta}\rangle = \eta_i |\vec{\eta}\rangle \tag{4.10} $$My book (Atland and Simons, Condensed ... 1answer 113 views ### Representations of subalgebra in the super virasoro algebra In the Virasoro algebra, which is generated by L_n, one has the obvious subalgebra spanned by L_{-1} ,L_{1} and L_{0} which is isomorphic to the Lie algebra \mathfrak{sl}(2,\mathbb{R}). The ... 0answers 92 views ### New Supersymmetry Algebra We know that SUSY generators commute with translation$$ [P_\mu,Q_\alpha]=0 $$I have some questions: What is this equation physical meaning? Is it possible to make "SUSY-like" generators that do ... 2answers 1k views ### Does the commutator of anything with itself not vanish? In a quantum mechanics exam one question was to write the commutator of a couple of operators. Everybody got points taken away since they did not write [Q_i, Q_i] = 0 for all the operators Q_i in ... 0answers 68 views ### Highest weight unitary representations of psl(2|2) I'm having some trouble understanding how to extend representation theory from Lie algebras to super Lie algebras, in particular with psl(2|2). Ultimately I'm interested in 2D quantum sigma models ... 1answer 318 views ### What is a supermultiplet? In Quantum field theory by Lewis H. Ryder, a supermultiplet is mentioned with no explanation as to what one is. 1answer 493 views ### What do the supercharges in extended supersymmetry do? What do the supercharges in extended supersymmetry do? In N=1 supersymmetry there are a certain number of fermions and and equal number of bosons. You can transform all fermions to the bosons (and ... 4answers 1k views ### Dirac equation as Hamiltonian system Let us consider Dirac equation$$(i\gamma^\mu\partial_\mu -m)\psi ~=~0$$as a classical field equation. Is it possible to introduce Poisson bracket on the space of spinors \psi in such a way that ... 1answer 312 views ### dimensional analysis of Grassmann integration/differentiation There is another paradox that I need to resolve: The Berezin integration rules for Grassmann odd variables give the same result as differentiation: If f=x+\theta\psi is a superfunction, the ... 3answers 222 views ### Embedding of F(4) in OSp(8|4)? Is the superconformal algebra in five dimensions, F(4), a subalgebra of the (maximal) six-dimensional superconformal algebra OSp(8|4)? 1answer 380 views ### Grassmann Variables Representation? It might be a silly question, but I was never mathematically introduced to the topic. Is there a representation for Grassmann Variables using real field. For example, gamma matrices have a ... 1answer 2k views ### Why/How is this Wick's theorem? Let \phi be a scalar field and then I see the following expression (1) for the square of the normal ordered version of \phi^2(x).$$T(:\phi^2(x)::\phi^2(0):) ~=~ 2<0|T(\phi(x)\phi(0))|0>^2 ...
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.