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193 views

Trace of the number operator in second quantization

I would like to find the helmholtz free energy of a system $F=-T ln(Tr[e^{\frac{-H}{T}}])$ namely a bcs superconductor (using Annett's notation) $H=\sum E_k (b_{k\uparrow}^\dagger ...
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24 views

Scale invariance and stress energy tensor

I have seen in a paper [1] that in a quantum field theory scale invariance takes place provided the stress energy tensor is traceless. How this is true? References: "INFINITE CONFORMAL SYMMETRY IN ...
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68 views

On shell and off shell simultaneously?

I am considering the following one loop virtual correction in the DIS process: where I have a quark of momentum $p$ coming in, emitting a gluon before interacting with a photon of momentum $q$ to ...
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19 views

could we obtain the potential (in one dimension) from the Gutzwiller trace?

to solve and obtain the potential of a 1-D Hamiltonian we must solve an integral equation $$ N(E)= A \int_{0}^{E}\frac{V^{-1}(x)}{\sqrt{E-x}}$$ fro a some constant 'A' , then my question is since ...
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48 views

Solving non scalar integrals in loop calculations

Consider the following integral that comes out of a loop calculation along with some fermionic propagators (e.g virtual one loop correction to a $p \gamma^* \rightarrow p'$ process such as in DIS): $$ ...
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44 views

Cyclicity of trace with fermionic arguments

I think this is a non-question, but it has me considerably worried. Consider the piece of a Lagrangian density given by, $$\mathcal{L} = ...
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36 views

Problem getting a product of traces out of a single trace in a chiral perturbation theory computation

I am stuck at a computation and I would appreciate any help. $U$ is the pion matrix in chiral perturbation theory $$U=e^{i\sigma_a\phi_a/f}$$ where $\sigma_a$ are Pauli matrices, $\phi_a$ are three ...