As it is well known, the Reality, incl. its real space form, is only a hypothesis.

@ Nathalie

Yes the theory of elementary particle physics is in real space, that is why by the discovery of Higgs boson, one can predicted the confirmation of Standard Model.

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Please read this web link

http://science.howstuffworks.com/higgs-boson.htm

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Particle physics usually has a hard time competing with politics and celebrity gossip for headlines, but the Higgs boson has garnered some serious attention. That's exactly what happened on July 4, 2012, though, when scientists at CERN announced that they'd found a particle that behaved the way they expect the Higgs boson to behave. Maybe the famed boson's grand and controversial nickname, the "God Particle," has kept media outlets buzzing. Then again, the intriguing possibility that the Higgs boson is responsible for all the mass in the universe rather captures the imagination, too. Or perhaps we're simply excited to learn more about our world, and we know that if the Higgs boson does exist, we'll unravel the mystery a little more.

Mohammad: the theory of elementary particles (the Standard Model) uses calculations in a space of functions, thus it acts not in real space (x,y,z,t). Of course, experimental particle physics has results in real space.

Maybe my question was not clear.

Ok, Thanks a lot dear Nathalie Olivi-Tran

I will think in about this.

Actually, it is in the configuration space. Second quantization isn't in the function space, but in an internal space at every point of the "real space."

Nathalie,

also classical fluid dynamics and electro dynamics works with functions of (x,y,z,t), the components of vector fields and tensor fields. So, according to your understanding, these are not 'theories in real space'. This observation should make you think whether your thoughts are on the right track.

Ulrich, there is a difference between using functions of (x,y,z,t) and working in a space of functions....

Nathalie,

the state space of a hydro-dynamical system (viewed as a dynamical system) is a space of functions (velocity field, density field, pressure field, stress tensor field).

Don't we 'work in the state space'? If not, please explain the difference.

Other topic: your 'Higgs paper' certainly is unrelated to Higgs particles/fields. It is a way to understand that the 'virtual particles' of perturbative interaction description are 'off mass shell' since they are, in a sense, time-wise localized for which your time-box is a reasonable idealization.

@Nadeem, researchers follow unexplored tracks even if it's difficult. How could we know whether it gives any new observations if we do not make the calculations in real space?

Nathalie Olivi-Tran

Hopefully this might be of some help. I tried to make an internally constant semi-classical physics model for undergraduates that could introduce concepts from more advanced fields of physics.

https://www.academia.edu/1118589/Undergraduate_Thesis_A_relativistic_quantum_model_of_atomic_structures_from_particles_to_the_atom_

Thus it is based in 3 dimensions plus time, and may have some relevance. Not technically advanced, being for undergraduate use, but I hope it helps.

As for how the Higgs is treated in the model, Maxwell's equations are also used in the model for pair production, and the "Mass particles" produces from the vacuum energy can represent the Higgs.

I really need to update the paper and upload it to this site, just been too busy.