5
votes
0answers
60 views

Is $\overline{\psi_{L}^{c}}\psi_{R}^{c}=\overline{\psi_{R}}\psi_{L}$ true for two different spin 1/2 fermions?

In the context of seesaw mechanism or Dirac and Majorana mass terms, one often see the following identity $$ \overline{\psi_{L}^{c}}\psi_{R}^{c}=\overline{\psi_{R}}\psi_{L}. $$ Here, I am using 4 ...
1
vote
1answer
116 views

Observables still commute even if fields only anti-commute

In Peskin & Schroeder page 56, after introducing anti commutation relations for the fields instead of commutation relations (in order to fix the negative energy problem as well as to have proper ...
1
vote
1answer
263 views

A few simple questions about Grassmann numbers: commutation relations and derivatives

I'm trying to learn about Grassmann numbers from the book "Condensed Matter Field Theory" by Altland and Simons, but I am currently encountering some difficulties. I have several smaller questions ...
0
votes
1answer
203 views

Fock state and Slater determinant

Let's have Fock state for fermions: $$ | \mathbf p_{1} , \mathbf p_{2}\rangle = \frac{1}{\sqrt{2}}\hat {a}^{+}(\mathbf p_{1})\hat {a}^{+}(\mathbf p_{2})| \rangle , \quad | \mathbf p_{2} , \mathbf ...
2
votes
2answers
100 views

Quantum operator catastrophe

Assume we look at an interaction between 2 fermions $V \sum_{k_i,k_j,k_m,k_n} c_{k_i}^\dagger c_{k_j}^\dagger c_{k_m} c_{k_n} \delta_k $ where $\delta_k$ conserves momentum. We can directly write ...
1
vote
1answer
264 views

Physical implications behind the exchange antisymmetry condition of fermions

Explain the Physical implications behind the exchange antisymmetry condition of fermions. This condition forms the basis of the pauli principle but I can't find/understand what happens physically that ...
3
votes
3answers
671 views

Fermionic anti-commutation relations

For Pauli's exclusion principle to be followed by fermions, we need these anti-commutators $$[a_{\lambda},a_{\lambda}]_+=0 $$ and $$[a_{\lambda}^{\dagger},a_{\lambda}^{\dagger}]_+=0 $$ Then ...
1
vote
1answer
146 views

Anticommutation relations and bispinor field

In a case of free Dirac field we have $$ \hat {H} = \int \epsilon_{\mathbf p}\left( \hat {a}^{+}_{s}(\mathbf p )\hat {a}_{s}(\mathbf p ) - \hat {b}_{s}(\mathbf p )\hat {b}_{s}^{+}(\mathbf p ) ...
4
votes
2answers
316 views

Imposing anti-commutation relations on fermionic quasi-particles

In many theories of CMT, we assume the nature of quasi-particles (without giving proper justifications). For example, we assume nature of quasi-particles to be fermionic in case of a interacting ...
5
votes
2answers
795 views

Why are anticommutators needed in quantization of Dirac fields?

Why is the anticommutator actually needed in the canonical quantization of free Dirac field?