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15

With one minor qualification, the answer is yes: the CPT theorem holds for all spacetime dimensions. The qualification is that the P in CPT should be interpreted as a reflection of an odd number of spatial dimensions. (The simplest choice is to reflect just one spatial dimension.) If the total number of spatial dimensions is odd, then this is the same as ...

6

So this is really the twist in the construction of QFT that is still sometimes misunderstood. Historically, people like Dirac noticed that solutions to relativistic field equations such as the spinor equation for $\psi(x)$ admitted apparent negative mass-energy densities. However, once you go into QFT, either from a "second quantization" or a Fockian bottom-...

3

In QED, for example, charge conjugation commutes with the Lorentz group. It's an "internal" symmetry, not part of Lorentz (or Poincaré) symmetry. However, a different kind of connection exists between charge conjugation and the Lorentz group, via the CPT theorem. The CPT theorem says that every relativistic QFT (satisfying certain axioms) has a symmetry ...

2

A Higgs boson can be endowed with a VEV entailing both CP even (scalar) and CP odd (pseudscalor) sectors, reflected as a "complex" fermion mass term as: $$m\bar{\psi} e^{\theta i\gamma_5} \psi = m\cos\theta \bar{\psi} \psi + m\sin\theta \bar{\psi} i\gamma_5\psi.$$ The fun fact is that after a global rotation of the fermion field $$\psi \rightarrow e^{... 1 When you time-reverse a black hole, you get a white hole. Therefore you don't see black holes as antimatter fountains. White holes would be antimatter fountains, but that doesn't say much because everything falls out of white holes anyway. 1 I think it would be useful to make a distinction between two different, but related concepts. On one side, you have what is called reversibility, information conservation or determinism (unitarity in the context of quantum mechanics). On the other side, you have time-reversal symmetry. Let's start with reversibility. It is an essential feature of our ... 1 In reality there is no physical way to show that all processes are CPT symmetric, though you could in principle show that it's not by showing CPT-violation in an experiment. You can prove mathematically that a given physical theory is CPT-symmetric. The CPT-theorem does this for (Lorentz-invariant) quantum field theories. Since the standard model of ... 1 I believe you're correct. Another reference here gives the identity$$CPT: \qquad \bar{\chi}\psi \rightarrow \bar{\psi}\chi$$which is$$ -(\bar{\chi}\psi)^\dagger = \psi^\dagger \gamma_0 \chi = \bar{\psi} \chi$$The error in the reference you are working from is in the second-to-last equality. They have used the fermion anticommutation relation in the ... 1 This may not be the answer you’re looking for, but your sense of what is probable may have something to do with the way in which you categorize the states. Sure, it’s more likely to end up with a huge cascade, but there are many many different outcomes which you would call a “huge cascade”. The probability of one specific cascade, with a particular ... 1 The statement that antimatter is matter going back in time is usually associated with Feynman diagrams in QED, so we're talking about electrons, and electrons have parity +1, so:$$ CPT = C1T = CT = 1  So the parity part doesn't come into play, but it is required in general.

1

CPT symmetry (described as a dynamical symmetry) means that a dynamical evolution$s=s(t)$ is mapped into another possible dynamical evolution $s'=s'(t)$ if you transform under CPT every single state $s'(t) := CPTs(-t)$ connected by the initial dynamical evolution (reversing also the chronological order due to the presence of $T$). In other words, $s'$ ...

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