2
votes
1answer
84 views

Intrinsic parity of particle and antiparticle with spin zero

I need to prove that the intrinsic parities of a particle and antiparticle with spin zero are the same. Can I prove that by an argument that operator of $P$-inversion commutes with charge conjugation ...
1
vote
0answers
49 views

What is the definition of a charge-neutral operator?

What is the definition of a charge-neutral operator? I guess it means something like: it is invariant under charge conjugation. It that correct?
9
votes
2answers
309 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 ...
5
votes
1answer
214 views

Derivation of a gamma matrices identity

While studying Srednicki's book on quantum field theory, I encountered a particular identity that is of interest to me (equation 36.40): $$\mathcal{C}^{-1}\gamma^\mu\mathcal{C}=-(\gamma^\mu)^T$$ where ...
3
votes
2answers
141 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| ...
1
vote
0answers
49 views

Time reversal invariance and statistics

To what extend does the behaviour of time reversal invariance depend on the statistics of the particle under consideration? More explicitly: To what extend does the action of the time reversal ...
4
votes
0answers
237 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} ...
8
votes
2answers
1k 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 ...
0
votes
1answer
525 views

Charge conjugation in Dirac equation

I need to know the mathematical argument that how the relation is true $(C^{-1})^T\gamma ^ \mu C^T = - \gamma ^{\mu T} $ . Where $C$ is defined by $U=C \gamma^0$ ; $U$= non singular matrix , $T$= ...
1
vote
2answers
138 views

matter anti-matter world

let us suppose the gedanken experiment a man isolated into a room he ask if he is made of matter oder of antimatter could he set some experiments to see if he is made of matter or if he is made of ...
2
votes
0answers
203 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 ...
7
votes
1answer
349 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 ...
11
votes
1answer
297 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 ...