4
votes
1answer
74 views

The correspondence between Grassmann number and 4-spinor

In canonical quantization, we view the Dirac field $\psi$ as a $4\times1$ matrix of complex number. While in path integral quantization, we view the Dirac field $\psi$ as a Grassmann number. For two ...
2
votes
2answers
96 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 ...
0
votes
1answer
269 views

Matrix representation for fermionic annihilation operator

My guess it should look something like this: $ c_\sigma = ...
0
votes
0answers
95 views

Time ordering and Fermions

Having time ordering operator for fermions, should it reverse sign if it swaps operators with opposite spin variable? In other words should $T[c_{t_1,\uparrow}c_{t_2,\downarrow}^\dagger]$ return ...
7
votes
1answer
388 views

What is the value of a quantum field?

As far as I'm aware (please correct me if I'm wrong) quantum fields are simply operators, constructed from a linear combination of creation and annihilation operators, which are defined at every point ...