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I'm dealing with this paper from C. Bär and A. Strohmeier about a rigorous derivation of the chiral anomaly. I'm not quite familiar with the physical context of chirality and its anomaly. What actually happens physically when an eigenvalues of the Dirac operator "flips" the sign? Are there any pictures like the Dirac sea explaining it intuitively? Are there any good references about that topic?

EDIT: So far, I have consulted two papers. One is by Ambjørn and the other by Manton. Thanks to mike stone. Now, I understand it this way:

Assume there is no zero energy eigenvalue. In terms of the Dirac sea all negative energies are occupied. Then, a change of sign brings an occupied state "up" or a hole "down" and causes a creation of a particle or antiparticle. Or is it a pair, one per handedness?

What really bothers me, are the zero eigenvalues in the massless case. Are they occupied or not and what is the physical meaning of these? Moreover, what does a change to a non-zero energy state actually mean?

And anyway, what is the description in terms of creation and annihilation operators?

I'm dealing with this paper from C. Bär and A. Strohmeier about a rigorous derivation of the chiral anomaly. I'm not quite familiar with the physical context of chirality and its anomaly. What actually happens physically when an eigenvalues of the Dirac operator "flips" the sign? Are there any pictures like the Dirac sea explaining it intuitively?

EDIT: So far, I have consulted two papers. One is by Ambjørn and the other by Manton. Thanks to mike stone. Now, I understand it this way:

Assume there is no zero energy eigenvalue. In terms of the Dirac sea all negative energies are occupied. Then, a change of sign brings an occupied state "up" or a hole "down" and causes a creation of a particle or antiparticle. Or is it a pair, one per handedness?

What really bothers me, are the zero eigenvalues in the massless case. Are they occupied or not and what is the physical meaning of these? Moreover, what does a change to a non-zero energy state actually mean?

And anyway, what is the description in terms of creation and annihilation operators?

I'm dealing with this paper from C. Bär and A. Strohmeier about a rigorous derivation of the chiral anomaly. I'm not quite familiar with the physical context of chirality and its anomaly. What actually happens physically when an eigenvalues of the Dirac operator "flips" the sign? Are there any pictures like the Dirac sea explaining it intuitively? Are there any good references about that topic?

EDIT: So far, I have consulted two papers. One is by Ambjørn and the other by Manton. Thanks to mike stone. Now, I understand it this way:

Assume there is no zero energy eigenvalue. In terms of the Dirac sea all negative energies are occupied. Then, a change of sign brings an occupied state "up" or a hole "down" and causes a creation of a particle-particle or antiparticle-antiparticle pair (one for each handedness). Did I get it right so far?

What bothers me now, are the zero eigenvalues in the massless case. Are they occupied or not and what is the physical meaning of these? Moreover, what does a change to a non-zero energy state actually mean?

I'm dealing with this paper from C. Bär and A. Strohmeier about a rigorous derivation of the chiral anomaly. I'm not quite familiar with the physical context of chirality and its anomaly. What actually happens physically when an eigenvalues of the Dirac operator "flips" the sign? Are there any pictures like the Dirac sea explaining it intuitively? Are there any good references about that topic?

EDIT: So far, I have consulted two papers. One is by Ambjørn and the other by Manton. Thanks to mike stone. Now, I understand it this way:

Assume there is no zero energy eigenvalue. In terms of the Dirac sea all negative energies are occupied. Then, a change of sign brings an occupied state "up" or a hole "down" and causes a creation of a particle or antiparticle. Or is it a pair, one per handedness?

What really bothers me, are the zero eigenvalues in the massless case. Are they occupied or not and what is the physical meaning of these? Moreover, what does a change to a non-zero energy state actually mean?

And anyway, what is the description in terms of creation and annihilation operators?

I'm dealing with this paper from C. Bär and A. Strohmeier about a rigorous derivation of the chiral anomaly. I'm not quite familiar with the physical context of chirality and its anomaly. What actually happens physically when an eigenvalues of the Dirac operator "flips" the sign? Are there any pictures like the Dirac sea explaining it intuitively? Are there any good references about that topic?

EDIT: So far, I have consulted two papers. One is by Ambjørn and the other by Manton. Thanks to mike stone. Now, I understand it this way:

Assume there is no zero energy eigenvalue. In terms of the Dirac sea all negative energies are occupied. Then, a change of sign brings an occupied state "up" or a hole "down" and causes a creation of a particle-particle or antiparticle-antiparticle pair (one for each handedness). Did I get it right so far?

What bothers me now, are the zero eigenvalues in the massless case. Are they occupied or not? And what does a change to a non-zero energy state actually mean?

I'm dealing with this paper from C. Bär and A. Strohmeier about a rigorous derivation of the chiral anomaly. I'm not quite familiar with the physical context of chirality and its anomaly. What actually happens physically when an eigenvalues of the Dirac operator "flips" the sign? Are there any pictures like the Dirac sea explaining it intuitively? Are there any good references about that topic?

EDIT: So far, I have consulted two papers. One is by Ambjørn and the other by Manton. Thanks to mike stone. Now, I understand it this way:

Assume there is no zero energy eigenvalue. In terms of the Dirac sea all negative energies are occupied. Then, a change of sign brings an occupied state "up" or a hole "down" and causes a creation of a particle-particle or antiparticle-antiparticle pair (one for each handedness). Did I get it right so far?

What bothers me now, are the zero eigenvalues in the massless case. Are they occupied or not and what is the physical meaning of these? Moreover, what does a change to a non-zero energy state actually mean?