Understanding Spacetime in QM and QFT: Time Treatment and Particle Tracking

[lucas_]

spacetime is classical and continuous.. so when quantum system form superposition or entanglement, how is time treated esp in qft? how does spacetime keep track of the particles of fields? or how does the fields or particles able to jump in spacetime.. how is this handle in qm or qft?

 

[atyy]

Spacetime is classical and continuous in relativistic qft.

 

[lucas_]

Spacetime is classical and continuous in relativistic qft.

but particles are connected to spacetime.. how can particles just appear and disappear anywhere in spacetime.. isn't it spacetime are supposed to where particles or fields can move

 

[wabbit]

You should find quite a few discussions around this theme in the "Beyond the Standard Model" section (that is, if you are interested in treatments of spacetime in QFT beyond flat spacetime, not sure if this is the case).

A paper that seems relevant is (copied from the biblio thread there)
http://arxiv.org/abs/1502.06539
Fields as Bodies: a unified presentation of spacetime and internal gauge symmetry
David Wallace
(Submitted on 23 Feb 2015)
Using the parametrised representation of field theory (in which the location in spacetime of a part of a field is itself represented by a map from the base manifold to Minkowski spacetime) I demonstrate that in both local and global cases, internal (Yang-Mills-type) and spacetime (Poincaré) symmetries can be treated precisely on a par, so that gravitational theories may be regarded as gauge theories in a completely standard sense.

 

[lucas_]

for now.. I just want to understand how qft deals with flat spacetime... so when the fields are in superposition, how did they treat the time and space in the equation, as superposition too? or did they untangle or separate the 2 (fields from and spacetime)?

 

[atyy]

for now.. I just want to understand how qft deals with flat spacetime... so when the fields are in superposition, how did they treat the time and space in the equation, as superposition too? or did they untangle or separate the 2 (fields from and spacetime)?

The fields are not in superposition. In quantum theory, the field are observables, so they basically correspond to where classical observers can be in classical spacetime. There is still the quantum state which can be in superposition, and this state is not anywhere in space, but is in Hilbert space, and assigned to an entire surface of simultaneity.

 

[lucas_]

The fields are not in superposition. In quantum theory, the field are observables, so they basically correspond to where classical observers can be in classical spacetime. There is still the quantum state which can be in superposition, and this state is not anywhere in space, but is in Hilbert space, and assigned to an entire surface of simultaneity.

What is the difference between the quantum states in terms of eigenvalues etc between QM and QFT? For example, do we have the same position, momentum, energy? and why does QFT put operator in every point of space instead of values?

 

[Sonderval]

@lucas
The difference between QM and QFT is discussed here:
https://www.physicsforums.com/threa...m-field-theory-yet-again.654697/#post-4173697
https://www.physicsforums.com/threads/second-quantization-for-fermions.653803/#post-4169414

 

[lucas_]

@lucas
The difference between QM and QFT is discussed here:
https://www.physicsforums.com/threa...m-field-theory-yet-again.654697/#post-4173697
https://www.physicsforums.com/threads/second-quantization-for-fermions.653803/#post-4169414

Please reply in the quantum forum here for an inquiry so as not to be off topic https://www.physicsforums.com/threads/from-observable-to-operators-in-qft.803189/