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- TL;DR Summary
- Are we able to think about positions of particles in QFT?

A lecturer today told the class that relativistic QM for single particles is flawed by showing us that for a state centered at the origin, it was possible that ##Pr(\vec{x}>ct)>0##.

He said that this was down to the fact that we should be considering multi-particle states in relativistic situation, before introducing Fock-space states. He then mentioned that

a) We have evaded the ##\vec{x}>ct## problem as "we can't"/"it doesn't make sense to" think about localised particles in such situations.

b) In relativistic QM, it is not the particles that are localised, but the measurements given by ##\hat{\phi}(x)##. He then made an analogy to the calorimeters found in the LHC being localised, rather than the particles(?), which I couldn't really understand.

I can't make out the specifics of what he was trying to bring across;

For a), why can't we / doesn't it make sense to think about localised, relativistic particles? Does this have anything to do the the Fock-space states? As for b), suppose I take the mean value ##\langle n_1 , n_2, ...|\hat{\phi}(x,t)| n_1, n_2 ... \rangle##. What are the measurements given by ##\hat{\phi}(x,t)## made on, if not particles? And doesn't the calorimeter measure the energy deposited by particles that are in its locality (ie localised)?

Thanks in advance.

He said that this was down to the fact that we should be considering multi-particle states in relativistic situation, before introducing Fock-space states. He then mentioned that

a) We have evaded the ##\vec{x}>ct## problem as "we can't"/"it doesn't make sense to" think about localised particles in such situations.

b) In relativistic QM, it is not the particles that are localised, but the measurements given by ##\hat{\phi}(x)##. He then made an analogy to the calorimeters found in the LHC being localised, rather than the particles(?), which I couldn't really understand.

I can't make out the specifics of what he was trying to bring across;

For a), why can't we / doesn't it make sense to think about localised, relativistic particles? Does this have anything to do the the Fock-space states? As for b), suppose I take the mean value ##\langle n_1 , n_2, ...|\hat{\phi}(x,t)| n_1, n_2 ... \rangle##. What are the measurements given by ##\hat{\phi}(x,t)## made on, if not particles? And doesn't the calorimeter measure the energy deposited by particles that are in its locality (ie localised)?

Thanks in advance.