All Questions
Tagged with anticommutator dirac-equation
20
questions
0
votes
0
answers
26
views
Canonical Variables in Dirac Spinor Field Theory
In S.Weinberg [QFT V1][1] section 7.1, in eq (7.1.15) and (7.1.16), he states that in order to be consistent with the previous-derived anti-commutator relation, we should take $\psi_{\text{n}}$ and $\...
- 529
-1
votes
1
answer
24
views
Deriving the equal time anti-commutator of the Dirac fields [closed]
I am trying to solve an exercise on deriving the equal-time anti-commutator of the Dirac fields. But I got stuck somewhere and couldn't get the desired result.
I would like to show that
$$
\{\psi(x), \...
- 41
1
vote
1
answer
35
views
Does the anticommutator of two spinors affect the transpose of their product?
My lecture notes claim that for an anticommutation relation
$$[ \psi_{\mu}(\bf{x},t),{\psi_{{\nu}}^{*}}(\bf{y},t)] = \delta_{\mu \nu} \delta^3(\bf{x}-\bf{y})$$
between two spinors, the transpose of ...
- 337
2
votes
1
answer
74
views
Product of spinors in Dirac field anticommutators
I am reading a "A modern introduction to quantum field theory" by Maggiore and on page 88 it shows the anticommutators of the Dirac field:
$$
\{\psi_a(\vec{x},t),\psi_{b}^{\dagger}(\vec{y},t)...
- 613
1
vote
0
answers
18
views
Adding a surface term to Dirac action modifies the canonical anticommutation relations [duplicate]
I'm dealing with the following issue: when describing a fermionic field, one can use the typical Dirac Lagrangian $$\mathcal{L}=\bar\psi(i\gamma^\mu\partial_\mu-m)\psi,\tag{1}$$ or the more symmetric ...
- 503
1
vote
1
answer
122
views
Can the operator field Dirac equation be expressed as Heisenberg's equation?
The Dirac equation of the operator spinor field is:
$$(i\gamma ^{\mu}\partial _{\mu} -m)\psi =0$$
where $\psi$ is interpreted to be a quantum field.
I'm wondering, can this be derived from the ...
- 6,355
1
vote
0
answers
117
views
Anticommutation relation for the Weyl spinors in Minkowski space+time
For $D$-dimensional Minkowski space+time, I suppose that the Dirac spinor has the following anticommutation relation:
$$
\{ \psi(x_1), \psi(x_2)\}=\{ \psi^\dagger(x_1), \psi^\dagger(x_2)\}=0
$$
$$
\{ \...
- 593
0
votes
1
answer
241
views
On the normal ordering of Fermi fields
From my understanding, the normal ordering of Klein-Gordon fields in QFT is valid because of the ambiguity that comes with quantizing a classical theory, in the sense that the conmutator of fields is ...
- 11
3
votes
1
answer
534
views
Why is the anti-commutation relation $\lbrace \psi_a(x), \bar{\psi}_b(y) \rbrace = 0$ enough to ensure causality?
In quantum field theory, it is crutial that two experiments can not effect each other at space-like seperation. Thus $[\mathcal{O}_1(x), \mathcal{O}_2(y)] = 0 $ if $(x-y)^2 < 0$.
For the Klein-...
- 1,219
3
votes
2
answers
3k
views
Propagator for Dirac spinor field
I am currently trying to learn Quantum Field Theory through David Tong's notes which only talk about canonical quantisation for the scalar field and Dirac spinor field.
In Chapter 2, the propagator ...
- 522
0
votes
1
answer
371
views
Fierz identities and anticommutation relations
Let us consider the following term
$$\bar\psi(p_1)M\psi(p_2) \bar\psi(p_3)N\psi(p_4)$$
According to Ortin's book (equation (D.65)), from the Fierz identity we would have something like
$$\bar\psi(...
0
votes
1
answer
110
views
Dirac spinor and field quantization
Can we simplify $$ Σ_s Σ_r [b_p^s u^s(p)\mathrm e^{ipx} (b_q^r)^†(u^r)^†(q)\mathrm e^{-iqy} + (b_q^r)^†(u^r)^†(q)\mathrm e^{-iqy} b_p^s u^s(p)\mathrm e^{ipx}]\tag{1}$$ as $$Σ_sΣ_r[ \{b_p^s, (b_q^r)^†...
- 369
0
votes
0
answers
583
views
Anti-commutator in Quantization of Dirac field
Can anyone explain while calculating $\left \{ \Psi, \Psi^\dagger \right \} $, set of equation 5.4 in david tong notes lead us to
$$Σ_s Σ_r [b_p^s u^s(p)e^{ipx} b_q^r†u^r†(q)e^{-iqy}+ b_q^r †u^r†(q)e^{...
- 369
0
votes
0
answers
175
views
Commutation relations in QFT [duplicate]
So I have just started learning QFT. So you take a classical field and turn the degrees of freedom into operators. All fine, just like normal quantum.
However I am confused about the commutation ...
- 1,933
1
vote
2
answers
2k
views
Deriving anti-commutation relation between creation/annihilation operators for Dirac fermions
Starting from Dirac fields:
$$\Psi(x) = \dfrac{1}{(2\pi)^{3/2}} \int \dfrac{d^3k}{\sqrt{2\omega_k}}\sum_r\left[ c_r(k)u_r(k)e^{-ikx}+d^\dagger_r(k)v_r(k)e^{-ikx} \right]_{k_0=\omega_k}$$
$$\Psi^\...
- 23