Relative Minus signs from different Feynman Diagrams
I have a problem understanding the occurrence of a the relative minus signs between contributions, coming from different Feynman diagrams, involving fermions. A simple example is Bhabha scattering $e^+...
View ArticleMinimization of a quaradic-like expression when calculating the generating...
The generating functional for a free Dirac field is $$Z_0[eta,bar{eta}]=int Dbar{psi}Dpsi mathrm{exp}{iint [bar{psi}(x)S^{-1}psi(x)+bar{eta}(x)psi(x)+bar{psi}(x)eta(x)]dx}$$ where...
View ArticleGrassmann number representation for fermions
How one can simultaneously represent fermionic operators and its corresponding Grassmann variables, so that all the anticommutation relations between them and also states would take place? $$...
View ArticleBasic question about superspace, Grassmann numbers and world sheet supersymmetry
So, I’m trying to read the section on superspace from the book on string theory by Becker, Becker and Schwarz, and I realized that I’ve been stuck on something simple for a while. Some relevant...
View ArticleWhy must the supersymmetry generators be spinors?
I have read in a few places (for example, at page 5 here) that the supersymmetry generators must be spinors. Quoting the reference mentioned The generator of the symmetry must relate two types of...
View ArticleIs it possible to write the fermionic quantum harmonic oscillator using $P$...
The Hamiltonian of the quantum harmonic oscillator is $$mathcal{H}=frac{P^2}{2m}+frac{1}{2}momega^2X^2$$ and we can define creation and annihilation operators...
View ArticleAbout the definition of super Hilbert Spaces
I have founded in the literature at leas two different definition of Hilbert spaces: Definition 1: A super Hilbert space is a complex super-vector space $mathcal{H}=mathcal{H}_0oplus mathcal{H}_1$ with...
View ArticleDerivative of effective action with respect to classical fields [on hold]
I have some trouble with the effective action involving fermions. Consider the following effective action (QED): $$varGamma = int mathrm{d}^4 x left( j_mu mathcal{A}_mu + bar{varPsi} eta + bar{eta}...
View ArticleNon-hermiticity of Dirac Lagrangian: null momentum?
The usual Dirac Lagrangian is $L(psi,barpsi)=barpsi(inotpartial-m)psi$. The canonical momenta are $$ pi=frac{partial L}{partial psi_{,0}}=ipsi^dagger \ bar pi=frac{partial L}{partial barpsi_{,0}}=0 $$...
View ArticleWhy is this proof that all $overline{psi}psioverline{psi}psi$ interactions...
This is a homework question for my quantum field theory class. I haven’t been able to figure out the answer, and neither has anybody I asked. The homework was due two days ago. Consider a spinor...
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