Questions tagged [cpt-symmetry]
The cpt-symmetry tag has no usage guidance.
124
questions
24
votes
4
answers
3k
views
What is CPT, really?
The naive statement for the "CPT theorem" one usually finds in the literature is "relativistic theories should be CPT invariant". It is clear that this statement is not true as written, e.g. ...
21
votes
2
answers
19k
views
Charge conjugation in Dirac equation
According to Dirac equation we can write,
\begin{equation}
\left(i\gamma^\mu( \partial_\mu +ie A_\mu)- m \right)\psi(x,t) = 0
\end{equation}
We seek an equation where $e\rightarrow -e $ and which ...
user12906
18
votes
2
answers
13k
views
How to prove $(\gamma^\mu)^\dagger=\gamma^0\gamma^\mu\gamma^0$?
Studying the basics of spin-$\frac{1}{2}$ QFT, I encountered the gamma matrices. One important property is $(\gamma^5)^\dagger=\gamma^5$, the hermicity of $\gamma^5$. After some searching, I stumbled ...
- 16.4k
17
votes
2
answers
1k
views
How can we detect antihydrogen?
From a mathematical standpoint (CPT symmetry) it is most probable that antihydrogen has the same spectra (absorption and emission) as hydrogen. The CERN confirmed this hypothesis to a high accuracy ...
- 723
17
votes
0
answers
1k
views
Time Reversal, CPT, spin-statistics, mass gap and chirality of Euclidean fermion field theory
In Minkowski space even-dim (say $d+1$ D) spacetime dimension, we can write fermion-field theory as the Lagrangian:
$$
\mathcal{L}=\bar{\psi} (i\not \partial-m)\psi+ \bar{\psi} \phi_1 \psi+\bar{\psi} ...
- 7,848
13
votes
2
answers
1k
views
What are the assumptions that $C$, $P$, and $T$ must satisfy?
I am not asking for a proof of the $CPT$ theorem. I am asking how the $CPT$ theorem can even be defined.
As matrices in $O(1,3)$, $T$ and $P$ are just
$$
T = \begin{pmatrix} -1 & 0 & 0 & ...
- 11.6k
13
votes
1
answer
527
views
What feature of QFT requires the C in the CPT theorem?
Classical tensor field theories have a PT theorem, so what changes in a QFT to require charge conjugation to be a part of the theorem? Charge conjugation seems a bit unrelated to space-time, but is an ...
- 133
13
votes
1
answer
1k
views
Can the CPT theorem be valid if Lorentz invariance is only spontaneously broken?
Earlier, I asked here whether one can have spontaneous breaking of the Lorentz symmetry and was shown a Lorentz invariant term that can drive the vacuum to not be Lorentz invariant. How relaxed are ...
- 8,800
11
votes
2
answers
1k
views
Spin-Statistics Theorem (SST)
Please can you help me understand the Spin-Statistics Theorem (SST)? How can I prove it from a QFT point of view? How rigorous one can get? Pauli's proof is in the case of non-interacting fields, how ...
- 111
10
votes
1
answer
2k
views
Neutron electric dipole moment and $T$ symmetry violation
Our textbook (and other sources I have found) says that non-zero electric dipole moment of neutron would violate $T$ symmetry. They prove this statement by first assuming $\boldsymbol{D}=\beta\...
- 4,962
9
votes
1
answer
1k
views
Does the CPT theorem hold for all spacetime dimensions?
I can't find any reference which mentions the dependence of the theorem on spacetime dimension, but it would be very interesting to know what if any it has!
- 3,514
7
votes
1
answer
747
views
What makes *electric* charge special (wrt. CPT theorem)?
I'm wondering why the 'C' in CPT - charge conjugation - refers specifically to electric charge. Of course you could say that C is just defined as $e^+ \leftrightarrow e^-$... but there has to be ...
- 4,217
7
votes
2
answers
2k
views
What is the definition of the charge conjugation?
I seem to have troubles finding definitions of the charge conjugation operator that are independant of the theory considered.
Weinberg defined it as the operator mapping particle types to ...
- 16.5k
7
votes
1
answer
7k
views
Maxwell equations and symmetry
Do the full inhomogeneous Maxwell equations obey parity (P) and time reversal (T) symmetry separately or only the full CPT symmetry?
I believe the homogeneous Maxwell equations obey parity and time ...
- 5,925
7
votes
2
answers
1k
views
C, T, P transformation mistakes in ``Peskin&Schroeder's QFT''?
I suppose the right way to do C (charge), T (time reversal), P(parity) transformation on the state $\hat{O}| v \rangle$ with operators $\hat{O}$ is that:
$$
C(\hat{O}| v \rangle)=(C\hat{O}C^{-1})(C| ...
- 7,848