Haldane gave a talk on his 2012 ICTP Dirac Medal, of which the
corresponding presentation can be retrieved online from <https://physics.princeton.edu//~haldane/talks/dirac.pdf>. On the
page 6 of this talk in the above-mentioned file, he wrote the
following formula:
\left|\partial_{\mu} \Psi(\boldsymbol{x})\right\rangle \equiv
\sum_{i} \frac{\partial u_{i}(\boldsymbol{x})}{\partial x^{\mu}}|i\rangle
But I'm confused on the symbols used here. Any more hints/explanations
willl be highly appreciated.
Regards,
HY
On 21/07/13 3:06 AM, Hongyi Zhao wrote:
Haldane gave a talk on his 2012 ICTP Dirac Medal, of which the corresponding presentation can be retrieved online from <https://physics.princeton.edu//~haldane/talks/dirac.pdf>. On the
page 6 of this talk in the above-mentioned file, he wrote the
following formula:
\left|\partial_{\mu} \Psi(\boldsymbol{x})\right\rangle \equiv
\sum_{i} \frac{\partial u_{i}(\boldsymbol{x})}{\partial x^{\mu}}|i\rangle
But I'm confused on the symbols used here. Any more hints/explanations willl be highly appreciated.
Regards,
HY
It seems to be factoring of the total wave function
Psi into a spinor part |i> and a spatial part u_i(x),
where the summation index i is then over the number
of spin states.
It is then assumed that the space-time-dependence is
through the u_i(x) and that the |i> are fixed in time.
On Tuesday, July 13, 2021 at 4:49:08 PM UTC+8, Jos Bergervoet wrote:
On 21/07/13 3:06 AM, Hongyi Zhao wrote:
Haldane gave a talk on his 2012 ICTP Dirac Medal, of which theIt seems to be factoring of the total wave function
corresponding presentation can be retrieved online from
<https://physics.princeton.edu//~haldane/talks/dirac.pdf>. On the
page 6 of this talk in the above-mentioned file, he wrote the
following formula:
\left|\partial_{\mu} \Psi(\boldsymbol{x})\right\rangle \equiv
\sum_{i} \frac{\partial u_{i}(\boldsymbol{x})}{\partial x^{\mu}}|i\rangle >>>
But I'm confused on the symbols used here. Any more hints/explanations
willl be highly appreciated.
Regards,
HY
Psi into a spinor part |i> and a spatial part u_i(x),
How do you deduce that |i> is a spinor part and u_i(x) is a spatial
part?
Based on the talk file given on the website, I can only see
that |i> is a set of fixed orthonormal basis and u_i(x) is the i-th
expanding coefficient of "\Psi x" on this basis.
where the summation index i is then over the number
of spin states.
Again, based on the context of the formula, I can not see where the
author speaks of a "spin state".
It is then assumed that the space-time-dependence is
through the u_i(x) and that the |i> are fixed in time.
I really can't find this implication too.
On 21/07/13 3:06 AM, Hongyi Zhao wrote:
Haldane gave a talk on his 2012 ICTP Dirac Medal, of which the corresponding presentation can be retrieved online from <https://physics.princeton.edu//~haldane/talks/dirac.pdf>. On the
page 6 of this talk in the above-mentioned file, he wrote the
following formula:
\left|\partial_{\mu} \Psi(\boldsymbol{x})\right\rangle \equiv
\sum_{i} \frac{\partial u_{i}(\boldsymbol{x})}{\partial x^{\mu}}|i\rangle
But I'm confused on the symbols used here. Any more hints/explanations willl be highly appreciated.
Regards,
HY
It seems to be factoring of the total wave function
Psi into a spinor part |i> and a spatial part u_i(x),
where the summation index i is then over the number
of spin states.
It is then assumed that the space-time-dependence is
through the u_i(x) and that the |i> are fixed in time.
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