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Why do we only consider commutators and anticommutators in QFT?

While studying canonical quantization in QFT, I observed that we quantize fields either by a commutation or an anticommutation relation \begin{equation} [\phi(x), \phi(y)]_\pm := \phi(x) \phi(y) \pm \...
Ishan Deo's user avatar
  • 1,588
1 vote
0 answers
117 views

Is there a bosonic representation of Clifford algebra in (1,3) spacetime?

By a suitable combination of Dirac's $\gamma_\mu$ matrices one can define creation and destruction operators satisfying fermionic anticommutators. Is there a similar result for bosons in the context ...
Dharam Vir Ahluwalia's user avatar
1 vote
1 answer
406 views

Importance of position of Bosonic and Fermionic operators in quantum mechanics

In quantum mechanics if (Fermionic or Bosonic) operators do not commute with each other, one cannot swap position of two operators easily. For example, let $(c^\dagger, c)$ are Fermionic operators, ...
Sana Ullah's user avatar
3 votes
1 answer
241 views

Generalized commutator/anticommutator via phase factor

We know that the commutator between two operators $A$ and $B$ reads $[A,B]_{-}=AB - BA$, while the anticommutator reads $[A,B]_+=AB + BA$. I am wondering if someone has ever used a generalized ...
linello's user avatar
  • 1,277
1 vote
2 answers
338 views

Canonical quantization of bosons

During my studies on QFT a fundamental question occurred concerning the canonical quantization. In our course, we mentioned that: "The canonical quantization of a field with values in the complex ...
Hamilcar's user avatar
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