The higgs boson and its scalar field.

[Sorcerer]

Just reading up on the higgs.

Since scalar fields have a value over every point in space, when space expands and more points in space are created, does that mean that the higgs field and its corresponding particle is the only particle of the standard model for which energy density remains constant and doesn't decrease as space expands?

What does it mean when they say the higgs does not transform under Lorentz transformations? Is it independant of time?

Also what does it mean to have a point in space, is it the mathematical 1 dimensional space time point or are points in space measured by a planck length?

If it is the 1 dimensional point, since there is an infinte ammount of points between any 2 points (or greater number of points). How is the energy of the higgs field retained at a non infinite value when measured cumulatively over any distance, area or volume? Does that matter at all to anything though?

Edited June 8, 2015 by Sorcerer

[ajb]

Since scalar fields have a value over every point in space, when space expands and more points in space are created, does that mean that the higgs field and its corresponding particle is the only particle of the standard model which energy density remains constant and doesn't decrease as space expands?

You don't think about more points being created as space expands, rather the distance between two chosen points increases as a function of time.

 

 

What does it mean when they say the higgs does not meaning it does not transform under Lorentz transformations? Is it independant of time?

It means that it transforms as a scalar; it is invariant under the Lorentz transformations.

[Sorcerer]

You don't think about more points being created as space expands, rather the distance between two chosen points increases as a function of time.

 

Yes but if it has a value at every point, at which scale does this matter, does it make any sense going past certain sizes? Because if it's meaningless at certain scales, as the distance between 2 points increase, points on a scale which would otherwise be too small to be meanigful would cross that threshold.

[ajb]

I don't understand the question.

 

A scaler field assigns a value to each point on space-time really and not just space. More generally a field in physics is a section of a fibre bundle over space-time.

[Sorcerer]

I don't understand the question.

 

A scaler field assigns a value to each point on space-time really and not just space. More generally a field in physics is a section of a fibre bundle over space-time.

Is that value changeable or is it the same for every point?

 

Is there a minimum period that can be set for a moment in time, or is time infinitely reducible? The same applies for space.

 

If time is infinitely reducible, then when summing the value over any non zero period of time (or space), the result would be infinite. I however don't know if this is a problem at all, or means anything.

 

Could the minimum scale for the higgs field be set at the minimum size/time interval for a fermion, since this would be the minimum interaction that can be measured? (and fermions obey the pauli exclusion principle)

 

_________________________________________

 

I am also wondering am I correct that the higgs field and its corresponding particle is the only particle of the standard model for which energy density remains constant and doesn't decrease as space expands?

 

(as asked but not answered in the OP)

 

[ajb]

Is that value changeable or is it the same for every point?

Generally the value will depend on the point; that is the whole reason for using fibre bundles and their sections as fields.

 

Is there a minimum period that can be set for a moment in time, or is time infinitely reducible? The same applies for space.

Not if we assume that space-time is smooth, as we do in standard quantum field theory and semi-classical gravity. Provided we are not near the energy scale of quantum gravity this assumption is harmless.

 

If time is infinitely reducible, then when summing the value over any non zero period of time (or space), the result would be infinite. I however don't know if this is a problem at all, or means anything.

Everything is assumed to be smooth. There is no trouble here with the theory.

 

Could the minimum scale for the higgs field be set at the minimum size/time interval for a fermion, since this would be the minimum interaction that can be measured? (and fermions obey the pauli exclusion principle)

 

What is the scale of the Higgs? Energy wise one could say the electroweak scale, which gives us an energy, which we can then get a length scale. However, I don't see that this can be interpreted as you suggest.

 

I am also wondering am I correct that the higgs field and its corresponding particle is the only particle of the standard model for which energy density remains constant and doesn't decrease as space expands?

 

You can examine this yourself; look up inflation. You can find the expressions for the energy density and so on for scalar fields in an expanding Universe. It looks similar to the flat space-time case, but the Hubble constant acts as a friction term in the equations of motion. You can compare all this with a perfect fluid and get the expressions you are looking for.

 

In short, I don't see that the energy density of the Higgs is constant, I could be mistaken here.

[Sorcerer]

thank you ajb

[Mordred]

The Higgs field changes potential at higher temperatures. It has a Mexican hat potential (metastability). These articles show the metastability

Higg's inflation possible dark energy

 

http://arxiv.org/abs/1402.3738

http://arxiv.org/abs/0710.3755

http://arxiv.org/abs/1006.2801

 

 

The low end of the Mexican hat is the vacuum expectation value at 246 GeV. The top of the hat is when the Higgs field no longer gives mass to elementary particles. This is roughly just above [latex]10^{16}[/latex] GeV.

https://en.m.wikipedia.org/wiki/Vacuum_expectation_value

This lecture shows the related formulas and has a decent image of the Mexican hat potential.

 

https://www.google.ca/url?sa=t&source=web&cd=2&ved=0CB4QFjABahUKEwiI3YKOq4rGAhXJlYAKHV07AIs&url=http%3A%2F%2Fwww2.ph.ed.ac.uk%2F~playfer%2FPPlect17.pdf&rct=j&q=vacuum%20expectation%20value&ei=vOh6VYiPCMmrggTd9oDYCA&usg=AFQjCNHgQwFmLTdYGa3h5OM_fL4mdAexgA&sig2=__TDScPUTdBe7hyvBnKLGQ

Edited June 12, 2015 by Mordred