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Thanks!

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- Thread starter copernicus1
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Thanks!

- #2

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An example in the standard model is the photon, which is its own antiparticle. It's not clear yet whether neutrinos are their own antiparticles or not. In the standard model they are treated as Dirac particles and thus are different from the antiparticles, but they could as well be Majorana fermions. The question, what's right is unsettled. There are experiments looking for the socalled neutrinoless double-beta decay of nuclei, but there's no conclusive evidence for this yet.

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The electron and positron have different creation operators, so they don't seem to be identical in this picture. Really identical particles should have identical creation operators (above other things).

Anyway, I have seen something similar, but I'm not sure if it's what you are looking for. Check out Robert Klauber's online book, chapter 3, page 63, botom of the page. He says:

[itex]\phi[/itex] acts as a total particle number lowering operator, because it destroys particles (via a(k)) and creates antiparticles (via b†(k)).

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- #6

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- While the creation/annihilation operators don't work the way you described, the
*field*operators do. The operator [itex]\psi[/itex] contains both [itex]a[/itex] and [itex]b^\dagger[/itex], so it will both create an electron and annihilate a positron, and vice versa. - Particles and antiparticles do behave very similarly in a lot of ways--they have the same mass, and the same coupling constant to other fields, etc. So in many cases it makes sense to talk about them as being identical, if you are able to ignore the areas where they do differ. These things are consequences of the U(1) symmetry that connects them (and which is responsible for the charge quantum number being a conserved quantity). In a similar way, one often talks about protons and neutrons as being identical particles, because of their SU(2) isospin symmetry.

- #7

Bill_K

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Whoa! There is no U(1) symmetry connecting particles with antiparticles. Certainly not the U(1) symmetry of electromagnetic gauge invariance.Particles and antiparticles do behave very similarly in a lot of ways--they have the same mass, and the same coupling constant to other fields, etc. So in many cases it makes sense to talk about them as being identical, if you are able to ignore the areas where they do differ. These things are consequences of the U(1) symmetry that connects them (and which is responsible for the charge quantum number being a conserved quantity).

- #8

tiny-tim

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- #9

Bill_K

Science Advisor

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Sorry, tiny-tim, this is popsci horseradish!an anti-particle is identical to its particle, except that it "lives backwards"

- #10

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Whoa! There is no U(1) symmetry connecting particles with antiparticles. Certainly not the U(1) symmetry of electromagnetic gauge invariance.

Sorry, I think I mixed up some concepts here. I guess the symmetry that shows that particles and anti-particles have the same mass and coupling constants is symmetry under charge conjugation, not the U(1) gauge symmetry. Is that right, or am I just spouting nonsense now?

- #11

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The free-field operator of a Dirac field can be written as a superposition of creation and annihilation operators wrt. to the single-particle momentum-spin eigenstates:

[tex]\psi(t,\vec{x})=\int_{\mathbb{R}^3} \sum_{\sigma=\pm 1/2} \frac{\mathrm{d}^3 \vec{p}}{(2 \pi)^{3/2} \sqrt{2 E(\vec{p})}} \left [\hat{a}(\vec{p},\sigma) u(\vec{p},\sigma)\exp(-\mathrm{i} p \cdot x) + \hat{b}^{\dagger}(\vec{p},\sigma) v(\vec{p},\sigma) \exp(+\mathrm{i} p \cdot x) \right]_{p^0=+E(\vec{p})}.[/tex]

It is crucial that the particles come with an annihilation an the antiparticles with a creation operator. This reinterprets the modes with negative frequency as antiparticles with positive frequency.

Particle or anti-particle number is by itself not a "good quantum number", because it's not conserved. This is the case for net-particle number (or charge), i.e., the particle number - the antiparticle number. The field operator changes lowers this net-particle number by 1.

- #12

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ψ=ψ

ψ

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