# Tagged Questions

The tag has no usage guidance.

17 views

### Properties of non-commuting (and particularly anti-commuting) operators

The commutator of 2 operators describes in some sense "how much" do they commute or actually its more about "how far" are they from commuting. The case where the commutator of 2 operators (say ...
42 views

65 views

### Derivation of Fermions anticommutation rule

How one might derive fermions anticommutation rule? For bosonic particles, there is no ordering issue, and its commutation relation could be easily derived. However, for fermion, is there any easy way ...
94 views

230 views

### Does This Really “Prove” Spin-statistics Theorem?

In quantization of scalar field theory we impose commutation relation between the field operators by hand and similarly we impose anti-commutation relation between Dirac field operators by hand. As a ...
399 views

### Schroedinger field operators and their commutation relations

I've got several questions regarding the so called second quantization of the Schroedinger equation. My professor introduced the field operators for the Schroedinger field by simply stating them as ...
241 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 ...
366 views

### Quantizing the Dirac Field: which commutation relations are more fundamental?

When quantizing a system, what is the more (physically) fundamental commutation relation, $[q,p]$ or $[a,a^\dagger]$? (or are they completely equivalent?) For instance, in Peskin & Schroeder's ...
837 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 ...
114 views

### Fock state and corresponding relations for continuous momentum label

In Wikipedia I found following relation for Fock state: $$\hat {a}_i| \{n_j\}_j\rangle ~=~ \sqrt{n}_i| \{n_j-\delta_{ij}\}_j\rangle,$$ where $n_j$ refers to the number of $j$'th particles. This ...
340 views

713 views

185 views

1k views

### The implication of anti-commutation relations in quantum mechanics

All the textbooks I saw are very clear about the implications of commutating operators in quantum mechanics. However, much less is said about anti-commutation relations. Does it have a general ...
2k views

### Why are anticommutators needed in quantization of Dirac fields?

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