Relativistic Quantum Mechanics

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Discussion Overview

The discussion centers on the spin-statistics theorem in the context of relativistic quantum mechanics, particularly regarding the classification of particles as bosons or fermions based on their spin. Participants are seeking references and proofs related to this theorem, as well as discussing various resources for understanding the topic.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant is looking for a proof of the spin-statistics theorem, which states that particles with integer spin are bosons and those with half-integer spin are fermions.
  • Another participant suggests a Wikipedia page as a starting point for finding information on the spin-statistics theorem.
  • A different participant mentions the book "PCT, Spin and Statistics, and All That" by Streater & Wightman as a potential source for the proof, noting the difficulty of the material.
  • One participant proposes that an alternative approach to understanding the theorem is through the canonical quantization of classical field theories, specifically mentioning the Dirac field and the implications of anti-commutation relations.
  • Another participant asserts that a proof can be found in serious axiomatic quantum field theory books and recommends Pauli's 1940 article for preliminary understanding.
  • One participant recalls finding the proof in Franz Schwabl's advanced Quantum Mechanics book.

Areas of Agreement / Disagreement

Participants express varying opinions on the resources available for understanding the spin-statistics theorem, with no consensus on a single definitive source or proof. Multiple references and approaches are suggested, indicating a lack of agreement on the best path to understanding the theorem.

Contextual Notes

Some participants mention the complexity of the materials and the mathematical rigor required to fully grasp the theorem, indicating that prior knowledge may be necessary to engage with the proofs effectively.

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Hey guys, I am attending my second course in quantum mechanics. At the moment we are studying two-particle-systems using Dirac notation. In our book (An introduction to quantum mechanics - Griffiths) the author wrote that one can prove from relativisitic quantum mechanics that particles with integer spin are always bosons and particles with half integer spin are always fermions.
I've been googling, trying to find this prove, but I can't find it. Does anyone here know a book or web page in which this is explained/proved?
Thanks in advance!
 
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Here is the wikipedia page: http://en.wikipedia.org/wiki/Spin-statistics_theorem" google spin statistics theorem proof and you'll find a few links.
 
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There has to be a proof somewhere in "PCT, spin and statistics, and all that" by Streater & Wightman, but I have only read a small part of that book. The book is really hard, so I expect the proof of the spin-statistics theorem to be too. (I haven't actually studied the theorem or its proof. I have only read a small part of that book).

An alternative to proving it rigorously as a theorem is to consider the canonical quantization of a few classical field theories. For the Dirac field, the usual quantization procedure only makes sense if the creation and annihilation operators satisfy an anti-commutation relation instead of the usual commutation relation. A consequence of that is that if you apply two creation operators to the vacuum state, you get the zero vector instead of a two-particle state. I think you can find this argument in most quantum field theory books that use the canonical quantization approach. I know you can find it in Mandl & Shaw.
 
A proof for the spin-statistics theorem in the general case can be found in any serious axiomatic QFT book. However, before venturing in heavy maths, I would advise people go through Pauli's 1940 article in the Physical Review.
 
Hello, Agree on Wikepedia.
 
I remember coming across the proof somewhere in Franz Schwabl's advanced Quantum Mechanics book (Ch.13).
 

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