A question about Heizenberg uncertainty.

[ndung200790]

In some QFT books they say:If we consider momentum p of particle being very great,then the physics is at short scale.Then how can we apply Heizenberg uncertainty principle when the momentum p of particle having a certain value?What do they imply when they say that?

 

[mfb]

p is not an exact value, but for large p (as distribution, if you like) this can be negligible.
Consider a particle, confined in a space of 1cm: It has a corresponding minimal momentum uncertainty of ~0.1 meV. If the particle has a momentum of 1 MeV (10 billion times more than this uncertainty), you just don't care.

 

[ndung200790]

Is there any relation between great value p and great value of uncertainty in p?This(relation) explains why with the great p we have short scale physics as they say.

 

[Graniar]

Is there any relation between great value p and great value of uncertainty in p?

Great value of p is necessary for the great uncertainty in p.

Let's say, we have a particle with the well-known p^→, scuttering on the target (also well-known p^→).
Therefore there is a big uncertainty in x

But, after the scuttering, x may get well measured (x_space by affecting the lattice, x_time by energy dissipation), thus p^→ should get big uncertainty.

In case of almost elastic scattering, x_time remain uncertain, and p^→ uncertainty rely mostly on the angle uncertainty (p_time → E≈const ; p_x²+p_y²+p_z²≈const)

 

[ndung200790]

By the way,are there any difference between particle and quantum of field?Do the value of field coincide with the wave function or not?

 

[mfb]

By the way,are there any difference between particle and quantum of field?Do the value of field coincide with the wave function or not?

Particles are excitations of fields in quantum field theory, but I don't see the relation to the original question.

 

[ndung200790]

Is that correct if I say c$^{+}$exp{p.x}/vacum> is the value of field of representation of a quantum of field.This quantum corresponds with a particle having the mean value of momentum equalling p.

 

[ndung200790]

I mean a well defined momentum of a quantum of field corresponds with uncertainty of momentum of a particle having that momentum.

 

[ndung200790]

I was wrong!Each ''quantum field value'' corresponds with a plane wave of particle!