Quantum field theory and the renormalization group

In summary, the paper discusses how particle number is not conserved in non-relativistic physics, and how relativistic quantum mechanics relates mass, momentum, and energy by using the speed of light.
  • #1
Naty1
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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??
 
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  • #2
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.
 
  • #3
Naty1 said:
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.

Naty1 said:
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.

Naty1 said:
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.


Naty1 said:
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.
 
  • #4
atyy...appreciate you help...thank you.
 

FAQ: Quantum field theory and the renormalization group

1. What is quantum field theory?

Quantum field theory is a theoretical framework that combines the principles of quantum mechanics and special relativity to describe the behavior of subatomic particles. It is a mathematical formalism that allows us to calculate the probabilities of different particle interactions and the properties of elementary particles.

2. What is the renormalization group in quantum field theory?

The renormalization group is a mathematical tool used in quantum field theory to study the behavior of physical systems at different length scales. It involves rescaling the parameters of a theory to account for the effects of short-distance fluctuations and interactions. This allows us to understand the behavior of a system at different energy scales.

3. How is the renormalization group used in quantum field theory?

The renormalization group is used to study the behavior of physical systems at different energy scales. By analyzing how the parameters of a theory change as we zoom in or out on a system, we can understand how the system behaves at different length scales and make predictions about its behavior at high or low energies.

4. Why is renormalization necessary in quantum field theory?

Renormalization is necessary in quantum field theory because it allows us to account for the effects of virtual particles and short-distance fluctuations. These effects can lead to infinities in the calculations, which must be removed through a process of renormalization. Without renormalization, the theory would not be able to make accurate predictions about physical phenomena.

5. What are some applications of quantum field theory and the renormalization group?

Quantum field theory and the renormalization group have many applications in modern physics, including in the study of particle physics, condensed matter physics, and cosmology. They are used to make predictions about the behavior of subatomic particles, the properties of materials, and the evolution of the universe. They also have practical applications in technologies such as transistors and superconductors.

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