Bosons and Fermions in a rigorous QFT

In summary, there is still a sharp distinction between Bosons and Fermions in a rigorous QFT, if exists.
  • #71
Isn't it possible to construct a Fock space from the asymptotic in and out states of an interacting theory? E.g. if there are bound states, I don't see how it could be unitarily equivalent to the Fock space constructed from the free particles.
 
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  • #72
DrDu said:
Isn't it possible to construct a Fock space from the asymptotic in and out states of an interacting theory? E.g. if there are bound states, I don't see how it could be unitarily equivalent to the Fock space constructed from the free particles.

That's precisely what is being done in S-matrix theory. You get in- and out- Fock spaces that are the direct sum of free Fock spaces, one for each stable bound state. These are the only physical Fock space that exists, as it contains the physical particles. The Fock space in which the Lagrangian is expressed has no physical meaning and is only a crutch to ensure a correct classical limit, as it is composed of bare particles with masses that diverge during the renormalization procedure.

The problem is that this gives a free particle description at t=-inf and another one at t=+inf, but no dynamics for in between times. To get the dynamics right, one needs a representation that, by Haag's theorem, cannot be a Fock representation. (There are additional problems in case of gauge theories or massless fields; the above is just the simplest version.)
 
<h2>1. What are bosons and fermions in a rigorous QFT?</h2><p>Bosons and fermions are two types of elementary particles that make up the building blocks of matter. They are described by quantum field theory (QFT), which is a mathematical framework that combines quantum mechanics and special relativity to explain the behavior of particles at a subatomic level. In QFT, bosons are particles with integer spin, while fermions have half-integer spin.</p><h2>2. What is the significance of bosons and fermions in QFT?</h2><p>Bosons and fermions play a crucial role in QFT as they have different properties and interactions. Bosons, such as photons and gluons, are responsible for mediating fundamental forces, while fermions, such as electrons and quarks, make up matter. The behavior of these particles is governed by the principles of quantum mechanics, which allows for the prediction of their properties and interactions.</p><h2>3. How do bosons and fermions differ from each other?</h2><p>The main difference between bosons and fermions lies in their spin. Bosons have integer spin, which means they have a whole number of units of angular momentum, while fermions have half-integer spin. This difference in spin also leads to distinct behaviors, such as bosons being able to occupy the same quantum state, while fermions cannot.</p><h2>4. Can bosons and fermions be created or destroyed?</h2><p>According to the principles of QFT, particles can be created or destroyed through interactions with other particles. However, there are certain conservation laws that must be followed, such as the conservation of energy and momentum. This means that while bosons and fermions can be created or destroyed, the total number of particles must remain constant.</p><h2>5. How does QFT explain the behavior of bosons and fermions in different environments?</h2><p>QFT provides a mathematical framework for understanding the behavior of bosons and fermions in different environments, such as in the presence of strong magnetic fields or at high energies. By using mathematical equations and principles, QFT can predict how these particles will interact and behave in these different environments, allowing scientists to make accurate predictions and observations in experiments.</p>

1. What are bosons and fermions in a rigorous QFT?

Bosons and fermions are two types of elementary particles that make up the building blocks of matter. They are described by quantum field theory (QFT), which is a mathematical framework that combines quantum mechanics and special relativity to explain the behavior of particles at a subatomic level. In QFT, bosons are particles with integer spin, while fermions have half-integer spin.

2. What is the significance of bosons and fermions in QFT?

Bosons and fermions play a crucial role in QFT as they have different properties and interactions. Bosons, such as photons and gluons, are responsible for mediating fundamental forces, while fermions, such as electrons and quarks, make up matter. The behavior of these particles is governed by the principles of quantum mechanics, which allows for the prediction of their properties and interactions.

3. How do bosons and fermions differ from each other?

The main difference between bosons and fermions lies in their spin. Bosons have integer spin, which means they have a whole number of units of angular momentum, while fermions have half-integer spin. This difference in spin also leads to distinct behaviors, such as bosons being able to occupy the same quantum state, while fermions cannot.

4. Can bosons and fermions be created or destroyed?

According to the principles of QFT, particles can be created or destroyed through interactions with other particles. However, there are certain conservation laws that must be followed, such as the conservation of energy and momentum. This means that while bosons and fermions can be created or destroyed, the total number of particles must remain constant.

5. How does QFT explain the behavior of bosons and fermions in different environments?

QFT provides a mathematical framework for understanding the behavior of bosons and fermions in different environments, such as in the presence of strong magnetic fields or at high energies. By using mathematical equations and principles, QFT can predict how these particles will interact and behave in these different environments, allowing scientists to make accurate predictions and observations in experiments.

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