Your diagram is unphysical as a standalone diagram as it violates unitarity. This is being hinted by the condition that Ward identity as an operation of Polarization vector on amplitude does not vanish. Since there are no other diagrams at level \alpha, you can not consider this diagram with...
I am not sure what you are searching for but if you look at Holonomy group generated by covariant constant spinor, it gives you SU(N) (N=3 for the case you are considering) rather than SO(N). So the notion of Complex space rather than Real space need to be used. An even dimensional real manifold...
b^{s\dagger}b^s is some sort of occupation number and counts the number of particles. More number of particles created with b^{\dagger} will increase this occupation number and will give negative contribution to Hamiltonian.
An example of a zero dimensional qft are quantum gauge theories of matrix models. The basic field involved is a N dimensional matrix M with a gauge symmetry $$M\rightarrow UMU^\dagger$$, where U is a U(N) matrix. The partition function for this gauged matrix model involves a Haar measure dM and...
##x →x+ i \theta \sigma \bar{\theta}## is precisely the shift which makes covariant derivative a simple derivative against ##\bar{\theta}## for left chiral superfield and hence make sure that there is no explicit dependence on ##\bar{\theta}## of the superfield. So it is not in any sense...
There is quite a subtlety with putting bare mass equal to zero for photon. In fact, if you will put bare mass of photon equal to zero, you will find that with a convergence factor included physical mass of photon goes quadratic with the cut-off !
This is as bad as it sounds, the 1 loop...
What you are looking for is not angular momentum conservation, you need to know about C-parity. You need to concentrate on ground state of Positronium here, this is where you prefer singlet and triplet state as para-positronium and ortho-positronium.
Transformation of triplet state under...
It is meaningful to talk about masses of particles in a supersymmetric theory even when the SUSY breaking has not taken place if you don't have requirement of gauge invariance.
You use this on original superpotential treating Φ as φ and you get right result.
If you write it in terms of F's like,
then you need to use eqn. of motion for F's to get the same thing ( with F*F term included), you get by directly differentiating superpotential with respect to scalar part...
The differentiation is performed with respect to scalar part as opposed to superfield as you have written in OP.
For the same reason you don't take VEV of spinor fields because it's zero.
Write the most general form of chiral superfield with it's expansion in terms of the scalar field, fermionic and auxiliary field. Constructing a superpotential consists of some expression like Φn with different values of n and a number of superfields and writing a general expression.
You need...
Be careful here, it is possible to have a supersymmetric theory of scalars and fermions which does not have gauge interactions. In this case, a supersymmetric multiplet necessarily have the same mass because supercharges commute with the momentum operator, so a supercharge acting on a state does...
You can evaluate the integral in closed form here, it will not be negative. Saddle point method is approximate, also which charge are you talking about? Are you using a scalar field theory with Wick rotation and coupling as charge, then it does not have a critical point.