3
votes
2answers
149 views
+50

Grassmann 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? $$ ...
4
votes
1answer
99 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
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 ...
0
votes
1answer
341 views

Matrix representation for fermionic annihilation operator

My guess it should look something like this: $ c_\sigma = ...
0
votes
0answers
111 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
416 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 ...