All Questions
19
questions
1
vote
1
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65
views
Parity operator action on quantized Dirac field
I am stuck on equation 3.124 on p.65 in Peskin and Schroeder quantum field theory book.
There they are claiming that:
$$P\psi(x)P=\displaystyle\int\frac{d^3p}{(2\pi)^3}\frac{1}{\sqrt{2E_{\bf p}}}\...
- 413
1
vote
0
answers
75
views
What does a quantized field in QFT do? [duplicate]
I'm studying for an exam called Introduction to QFT. One of the main topics in this class is the quantized free fields.
I can now find the fields that solve the Klein-Gordon equation and the Dirac ...
- 19
0
votes
0
answers
56
views
Adjoint of the Dirac equation, and hermiticity of the momentum operator
I'm trying to derive the adjoint of the Dirac equation in standard relativistic quantum mechanics. We have the Dirac equation as follows :
$$(i\gamma^{\mu}\partial_\mu -m)\psi=0$$
To find it's adjoint,...
- 1,791
1
vote
2
answers
137
views
Motivation behind introducing creation/annihilation operators into the Dirac equation
When studying the Klein-Gordon equation, the introduction of creation/annihilation operators was justified by recognizing a harmonic-oscillator-like equation which we know how to quantize. Is there a ...
- 3,350
1
vote
1
answer
155
views
How to take hermitian conjugate of an operator containing multiple elements?
The annihilation operator in the Dirac field could be written as
$$
a_p^s = \frac{e^{iE_pt}}{\sqrt{2E_p}}u^s(p)^\dagger\int d^3xe^{-ipx}\psi(t,x)
$$
Where
\begin{equation*}
\begin{split}
\psi(t, x) = \...
- 1,783
2
votes
1
answer
140
views
Confused with computing causality for Dirac field
In Peskin and Schroeder's QFT book, P.56 Eq.(3.95) mentions that
$$\begin{align}
\langle 0|\bar\psi(y)_b\psi(x)_a|0\rangle = (\gamma \cdot p -m)_{ab}\int\frac{d^3p}{(2\pi)^3}\frac{1}{2E_p}Be^{ip(x-y)}\...
- 169
2
votes
0
answers
359
views
Momentum of the Dirac field in terms of creation/annhilation operators [closed]
In Peskin & Schroeder, the Momentum operator of the Dirac field is given as:
$$
{\bf P}=\int d^3x \psi^\dagger \left(-i\nabla\right) \psi=\int \frac{d^3p}{(2\pi)^3}\sum_s {\bf p}(a_p^{s\dagger}a_p^...
- 129
4
votes
1
answer
494
views
Explicit form of Dirac field creation/annihilation operators?
The explicit form of the creation and annihilation operators for the complex scalar field seems to be shown in all QFT lecture notes, but not those for the Dirac field (instead they tend to only give ...
- 2,604
-1
votes
1
answer
107
views
Problems in computing commutators in quantizing Dirac field
When I read articles on how to quantize Dirac Field, like on page 53 of An introduction to Quantum Field Theory written by Michael E. Peskin and Daniel V. Schroeder, it is defined as
$$\psi(\vec{x})=\...
- 326
0
votes
1
answer
327
views
Commutator of Dirac field operators
If we let field operators
$$\psi(x)=\int\frac{d^3p}{(2\pi)^3}\frac{1}{\sqrt{2E_p}}e^{ip\cdot x}\sum_s(a^s_pu^s(p)+b^{s}_{-p}v^s(-p)).$$
Then the commutator of field operators will be
$$[\psi,\psi^{\...
- 29
0
votes
1
answer
139
views
Confusion about Dirac field operators
I have a little confusion about Dirac field operator. Field operator can be written as
$$\psi(x)=\int\frac{d^3p}{(2\pi)^3}\frac{1}{\sqrt{2E_p}}\sum_s(a^s_pu^s(p)e^{-ip\cdot x}+b^{s\dagger}_pv^s(p)e^{...
- 29
-1
votes
1
answer
126
views
Dealing with $\delta^{(3)}(0)$ using normal ordering
On page 109 of David Tong's lecture notes on QFT, equations (5.11) and (5.12) read:
$$ H = \int \frac{d^{3}p}{(2\pi)^{3}} E_{\vec{p}}[(b_{\vec{p}}^{s})^{\dagger}b_{\vec{p}}^{s}-c_{\vec{p}}^{s}(c_{\vec{...
- 1,131
0
votes
1
answer
241
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On the normal ordering of Fermi fields
From my understanding, the normal ordering of Klein-Gordon fields in QFT is valid because of the ambiguity that comes with quantizing a classical theory, in the sense that the conmutator of fields is ...
- 11
4
votes
3
answers
1k
views
Dirac fields: Do particle and antiparticle creation operators act differently on the vacuum?
Given a Dirac field $$\Psi(x):=\int\frac{d^4k}{(2\pi)^4}\delta\left(p_0-\omega(\mathbf{k})\right)\sum_s\left(a_s(k)u_s(k)e^{-ikx}+b^\dagger_s(k)v_s(k)e^{ikx}\right)$$
with the creation operators $a^\...
- 1,187
1
vote
1
answer
179
views
Transformation matrix for Dirac equation
The Dirac wavefunction $\psi(x)$, a four component spinor, transforms under Lorentz transformations according to
$$\psi'(x')=S\psi(x)$$
where $S$ is the transformation matrix.
In Ashok Das' QFT book, ...
- 4,235