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I am reading the first chapter of Akhiezer, Berestetskii QED (1981). They state that Dirac was wrong to assume that the evolution of the wave function is described by

$\psi(t) = e^{-iHt} \psi(t_0)$

They say that in relativity it is also not legit to try to write a single particle formalism; that we only can describe an ensemble of the particles. Why is that?

Actually, why do we assume time reversal invariance in QM at the first place?

MsTais
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  • sorry but you seem to be asking three different and independent questions, right? In that case, consider breaking your post up into three different posts. For example, the first question is essentially answered in http://physics.stackexchange.com/questions/257787; in short: no, Dirac was not wrong, and your first equation is correct. – AccidentalFourierTransform Jan 19 '17 at 19:20
  • @ AccidentalFourierTransform Yes, but I think they should be deeply interconnected on the level of QED axiomatics. Ex., time reversal is the reason for demanding unitarity in QM; QM axiomatics was adopted by Dirac when he was working out his spin-1/2 theory; and his logic was faulty because his theory appeared to be relativistic, where for some reason single particle approach is not applicable. – MsTais Jan 19 '17 at 19:26
  • @ AccidentalFourierTransform Nobody says that he was wrong in his final results. I am talking about the axiomatics which he used initially and which apparently was wrong. To begin with, he was solving negative energy problem and didn't even have a clue about spin-1/2... – MsTais Jan 19 '17 at 19:27
  • No, time reversal has nothing to do with unitarity. There are plenty of healthy (read, unitary) quantum theories that break the time-reversal symmetry. 2) What I meant is that "They state that Dirac was not* wrong to assume that the evolution of the wave function is described by*..."
  • – AccidentalFourierTransform Jan 19 '17 at 19:28
  • @ AccidentalFourierTransform what does unitarity mean then? Why do we demand the time evolution operator to be unitary? – MsTais Jan 19 '17 at 19:31
  • @ AccidentalFourierTransform I guess my question was why in Akhiezer, A. I., and V. B. Berestetskii. "Quantum Electrodyrmmics." Naulm, Moscow (1981) the authors state that he was wrong... – MsTais Jan 19 '17 at 19:33
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  • see http://physics.stackexchange.com/questions/65793 and http://physics.stackexchange.com/questions/191034 2) without the context, I don't know. For example, in QED there are no wave-functions, so maybe it has to do with that. Or maybe because the Hamiltonian is time-dependent, and so the exponential has to be time-ordered. There are many possibilities.
  • – AccidentalFourierTransform Jan 19 '17 at 19:37
  • @ AccidentalFourierTransform thank you for the useful links=) – MsTais Jan 19 '17 at 19:47
  • Your first statement is very very important to me. ("They state that Dirac was wrong to assume..."). But I don't have the book. I found Russian version and I couldn't find this statement. It would be very appreciated if help me to read this argument. (may be by addressing number of equation around it so that I could find argument in russian edition, or send me some thing to my gmail mojtabanadery@gmail.com or any other way) @MsTais – moshtaba Aug 04 '23 at 06:06