QFT and renormalization

In summary, the conversation is about the speaker's attempt to understand the history of Quantum Mechanics and how the introduction of Quantum Field and renormalization addressed the issue of infinity. They are seeking input and resources for further understanding.
  • #1
crisis
1
0
Hi all,

I'm an amateur with some knowledge on the surface and actually am trying to make sense of the history of QM evolution and try to put things in place by trying to understand their 'raison d'être, at the time.
So I'm back in:
1. 1926-28 with the question: how the introduction of Quantum Field solve the problem of QM and relativity with regard to simultaneously.

2. and 20 years later, at Shelter Island, with renormalization-I cannot understand it...how come does the 'forced' introduction of mass and charge resolve the problem of infinity in a satisfying manner?

Any input, links, advise will be highly appreciated,

Cheers
 
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  • #2
crisis said:
with renormalization-I cannot understand it...how come does the 'forced' introduction of mass and charge resolve the problem of infinity in a satisfying manner?

See Chapter B5 ''Divergences and renormalization'' of my theoretical physics FAQ at http://arnold-neumaier.at/physfaq/physics-faq.html#B5
 

1. What is QFT and how does it differ from classical field theory?

Quantum field theory (QFT) is a theoretical framework that combines the principles of quantum mechanics and special relativity to describe the behavior of subatomic particles. Unlike classical field theory, which treats particles as classical objects with definite positions and momenta, QFT describes particles as excitations of quantum fields that permeate space and time.

2. What is the role of renormalization in QFT?

Renormalization is a mathematical technique used in QFT to remove infinities that arise in certain calculations. In QFT, the interactions between particles are described by Feynman diagrams, which involve integrals that can have infinite values. Renormalization allows us to redefine the parameters of the theory to absorb these infinities and make meaningful predictions.

3. How does QFT explain the behavior of particles at the quantum level?

In QFT, particles are described as excitations of quantum fields, which are mathematical objects that pervade all of space and time. These fields can be in a state of low energy (vacuum state) or can be excited by the presence of particles. The behavior of particles is then described by the interactions between these fields, which are governed by the principles of quantum mechanics.

4. What are the main challenges in renormalization?

One of the main challenges in renormalization is dealing with the infinities that arise in certain calculations. These infinities can lead to nonsensical results and need to be carefully removed through renormalization techniques. Another challenge is finding the appropriate parameters to absorb these infinities, as there is no unique way to do so.

5. What are the real-world applications of QFT and renormalization?

QFT and renormalization have numerous applications in modern physics, including particle physics, condensed matter physics, and cosmology. QFT is used to describe the behavior of subatomic particles, while renormalization is essential for making accurate predictions in these theories. Additionally, QFT and renormalization have also been applied to other fields, such as quantum computing and information theory.

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