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I asked my professor but he didnt/couldnt answer. Google is no help either.

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In summary, the conversation discusses the exchange symmetry in Quantum Mechanics and the conservation of certain properties when this symmetry is demanded. Noether's theorem is not applicable in this case and there is no infinitesimal generator that is conserved. The exchange symmetry can be formulated in terms of a continuous and differentiable unitary group, but it must be done in a way that recovers the discrete symmetry. The American Journal of Physics has an article that discusses the explicit construction of the exchange operator in terms of position and momentum, but the link is not available.

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I asked my professor but he didnt/couldnt answer. Google is no help either.

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Science Advisor

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Mentor

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I think you mean "That's not a differentiable symmetry ..."DrDu said:That's not a discrete symmetry so Noether's theorem is not applicable

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Ok got it. Thanks.

I find this helpful too

http://ajp.aapt.org/resource/1/ajpias/v64/i7/p840_s3?isAuthorized=no [Broken]

I find this helpful too

http://ajp.aapt.org/resource/1/ajpias/v64/i7/p840_s3?isAuthorized=no [Broken]

Last edited by a moderator:

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Cheers,

Jazz

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DaleSpam said:I think you mean "That's not a differentiable symmetry ..."

Of course, thanks!

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Jazzdude said:

Cheers,

Jazz

I remember having seen in American Journal of Physics an explicit construction of the exchange operator in terms of x and p.

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DrDu said:I remember having seen in American Journal of Physics an explicit construction of the exchange operator in terms of x and p.

I would like to read that paper. Can you give the link?

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Ravi Mohan said:I would like to read that paper. Can you give the link?

I fear not as I no longer have access to Am J Phys.

The Noether current for exchange symmetry is a mathematical concept in physics that describes the conservation of a physical quantity related to the symmetry of exchanging two identical particles in a system. It is based on the Noether's theorem, which states that for every continuous symmetry of a system, there exists a corresponding conserved quantity.

The Noether current for exchange symmetry is directly related to the exchange symmetry of particles in a system. This means that if the physical laws governing the system remain unchanged when two identical particles are exchanged, then there exists a conserved quantity associated with this symmetry, known as the Noether current.

The Noether current for exchange symmetry is significant because it provides a way to understand and analyze the conservation laws in physical systems where there is an exchange symmetry present. It helps to explain the conservation of certain quantities, such as energy and momentum, in these systems.

Yes, the Noether current for exchange symmetry can be applied to all physical systems that exhibit exchange symmetry. This includes systems in classical mechanics, quantum mechanics, and field theory.

The Noether current for exchange symmetry is calculated using the Noether's theorem, which involves finding the continuous symmetry transformation of the Lagrangian of a system. This transformation will lead to the conserved quantity associated with the exchange symmetry, which is the Noether current.

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