Pauli's exclusion principle

In summary, the conversation discusses the proof of Pauli's exclusion principle, which states that identical particles must be described either as bosons or fermions. The first step to understanding this is a proof in both relativistic and non-relativistic quantum theory, while the second step involves the connection between spin and statistics in relativistic quantum field theory. This is explained in detail in the book "Quantum Theory of Fields" by Weinberg and the paper "Feynman Functional Integrals for Systems of Indistinguishable Particles" by Laidlaw and DeWitt.
  • #1
Ravi Mohan
196
21
How do we prove Pauli's exclusion principle? My professor makes a Slater determinant and then merrily shows how it disappears when two columns or rows are same.
That is not Pauli's principle, is it? It is based on an assumption that certain particles are described by certain states.
So my question translates to why fermions (half integral spin particles) are described by antisymmetric states while bosons (integral spins) are described by symmetric states?
 
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  • #2
This is a pretty deep question. The first step to understand the answer is the proof that in both relativistic an non-relativistic quantum theory for particles in spaces with dimension [itex]d \geq 3[/itex] identical particles must be described either as bosons or fermions, i.e., with states in the Fock space spanned by totally symmetrized (bosons) or antisymmetrized (fermions) product bases. This is shown in the paper

Laidlaw, M. G. G., DeWitt, Cécile Morette: Feynman Functional Integrals for Systems of Indistinguishable Particles, Phys. Rev. D 3, 1375 (1970)
http://link.aps.org/abstract/PRD/v3/i6/p1375

The second step is to understand the connection between spin and statistics in relativistic quantum field theory. The spin-statistics theorem tells us that for any local Poincare symmetric qft with a stable ground state (spectrum of the Hamiltonian bounded from below) particles with integer spin are bosons and those with half-integer spin fermions. The best book about QFT is

Weinberg, Quantum Theory of Fields, Cambridge University Press

For the very clear and careful treatment of the representation theory of the Poincare group, see vol. 1.
 
  • #3
Thank you Vanhees. I will read the literature you mentioned.
 

1. What is Pauli's exclusion principle?

Pauli's exclusion principle is a fundamental principle in quantum mechanics that states that no two identical fermions (particles with half-integer spin) can occupy the same quantum state simultaneously.

2. How does Pauli's exclusion principle affect the behavior of electrons in an atom?

Pauli's exclusion principle plays a crucial role in determining the electronic configuration of atoms. It states that each electron in an atom must have a unique set of quantum numbers, which determines its energy level, orbital, and spin.

3. Why is Pauli's exclusion principle important in understanding the properties of matter?

Pauli's exclusion principle is essential in understanding the stability and properties of matter at the atomic and subatomic level. It explains why atoms have distinct energy levels and why electrons do not collapse into the nucleus.

4. What is the difference between bosons and fermions according to Pauli's exclusion principle?

Bosons, unlike fermions, can occupy the same quantum state simultaneously, as they have integer spin. This is known as Bose-Einstein statistics, which is in contrast to the Fermi-Dirac statistics governing fermions.

5. Can Pauli's exclusion principle be violated?

No, Pauli's exclusion principle is considered a fundamental law of nature and has been experimentally verified countless times. It is a crucial part of our understanding of quantum mechanics and the behavior of matter at the atomic level.

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