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qsa
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Why is it that when we combine SR with QM we are lead directly to the multiparticle picture. I know about the standard textbooks, I need to know EXACTLY why? What is it in SR that produces the multiparticle picture.
clem said:The appearance of negative energy states requires a multiparticle picture.
Also the appearance of a second time derivative prevents |psi|^2 from being a probability, so psi must become an operator.
I suspect that what you have in mind is the fact that the Klein-Gordon field can't be interpreted as a wavefunction, already mentioned by clem. If that field is promoted to an operator, by imposing commutation relations on its Fourier coefficients, the Fourier coefficients can be interpreted as operators that change the number of particles of the state they act on. This is a very weak argument at best, so you might as well forget about it. If you want to read about it anyway, I think it's explained in Mandl & Shaw. (Not 100% sure...it's been a long time since I read it).qsa said:Why is it that when we combine SR with QM we are lead directly to the multiparticle picture. I know about the standard textbooks, I need to know EXACTLY why? What is it in SR that produces the multiparticle picture.
arkajad said:Quantized fields are not irreducible representations. But one-particle subspaces, for stable particles, carry nearly irreducible representations of the Poincare group. Why only "nearly"? Because we have to leave the room for parities, charges, other internal degrees of freedom. So, irreducible representations of the Poincare group enter with some (usually finite) multiplicity.
The connection between Special Relativity (SR) and the multiparticle picture in Quantum Mechanics (QM) lies in the way that both theories describe the behavior of particles at a fundamental level. SR deals with the behavior of particles moving at high speeds, while the multiparticle picture in QM deals with the behavior of particles at a microscopic level. Both theories rely on the concept of spacetime and the idea of particles as wave-like entities.
SR affects the multiparticle picture in QM by providing a framework for understanding the behavior of particles at high speeds. The principles of SR, such as time dilation and length contraction, are taken into account when describing the behavior of particles in the multiparticle picture. This allows for a more accurate and comprehensive understanding of the behavior of particles at a fundamental level.
The connection between SR and the multiparticle picture in QM has significant implications for our understanding of the universe. It helps to bridge the gap between the macroscopic and microscopic worlds, providing a more unified and comprehensive understanding of the behavior of particles. It also allows for the development of new technologies and advancements in fields such as quantum computing.
The multiparticle picture in QM is used in a wide range of practical applications, including the development of new materials, medical imaging technologies, and quantum computing. It is also used in fields such as astrophysics, where it helps to explain the behavior of particles in extreme environments and the formation of structures in the universe.
There is still much research needed to fully understand the connection between SR and the multiparticle picture in QM. This includes further experiments and observations to test the theories, as well as the development of new mathematical frameworks to better describe the behavior of particles at a fundamental level. Additionally, more research is needed to explore the potential applications of this connection and its implications for our understanding of the universe.