Quantum field theory and the renormalization group

[Naty1]

The following statements are from the paper with the above title, recommended in another
thread, are from here:

http://fds.oup.com/www.oup.co.uk/pdf/0-19-922719-5.pdf

An interpretion of these statements would be appreciated:

1.

..a field is characterized by its values at all space points, which thus constitutes an infinite number of data. The non conservation of the number of particles in hgh energy collisions is a manifestation of such a property.

[first paragraph, page 3] What is 'conservation of the number of particles'?? Am I supposed to expect that outcome??

2.

...Moreover the field theories that describe microscopic physics have a locality property, a notion that generalizes the notion of point like particles: they display no short distance structure.

[second paragraph, page 3]
What is 'short distance structure'...or the lack thereof?

3.Following these,still page 3, under the title 'Gauge Symmetries' a discussion ensues regarding non relativistic quantum mechanics but suddenly the final sentence switches to a relativistic interpretation of vector potential. What's happening here? Is the prior discussion
not relevant??

and following immediately in "Units of relativistic Quantum theory" we have this statement:

..in a relativistic theory mass scales M, momenta p and energies E can be related
by the speed of light c...E = Mc²...

Is this considered 'relativistic'?? why would they not use
E² = [pc]² + m²c⁴

or do you think they are just interested in 'units'??

4. Has anyone read the whole paper...IS it worthwhile??

 

[Bill_K]

I haven't read the whole thing but I've glanced through it. I'd say it's unusually well written, and succeeds in describing some rather advanced topics without delving into too much mathematics.

 

[atyy]

1. [first paragraph, page 3] What is 'conservation of the number of particles'?? Am I supposed to expect that outcome??

In non-relativisitic physics, particle number is conserved. In relativistic physics, colliding 2 particles together can create more than 2 particles, because kinetic energy can be changed into matter, so particle number is not conserved.

2. [second paragraph, page 3]
What is 'short distance structure'...or the lack thereof?

Short distance structure means a point particle that cannot be broken into constituent parts. In quantum field theory, this means that the field is a fundamental "thing" (not made of other fields). Locality also refers to the fact that waves of the field must travel at less than the speed of light, so a disturbance at one point in space is local, since it cannot affect a far away region immediately.

3.Following these,still page 3, under the title 'Gauge Symmetries' a discussion ensues regarding non relativistic quantum mechanics but suddenly the final sentence switches to a relativistic interpretation of vector potential. What's happening here? Is the prior discussion not relevant??

He's just giving a bunch of different examples in physics of "gauge" which just means the same physics is represented by many different mathematical expressions.

Is this considered 'relativistic'?? why would they not use

E² = [pc]² + m²c⁴

or do you think they are just interested in 'units'??

Yes, he was just interested in units.

 

[Naty1]

atyy...appreciate you help...thank you.