39 ms·

As a physicist: where can you spot the physicist accent?

mturmon 7y ago
Guessing, but: > ...one can multiply any eigenvector by a phase e^{iθ}... and: > As a consistency check...
jordigh 7y ago
You use \equiv for definitions instead of :=, ^* for complex conjugation instead of \overline, you refer to the Hermitian transpose as the adjoint, and you implicitly assume all matrices are over the complex numbers. There are also other little things like some of the phrases as pointed out in a sibling comment. Physicists really do have their own distinct style.
- pmiller2 7y ago
  Hermitian matrices are always complex matrices, and A^* is a standard notation for the conjugate transpose of a Hermitian matrix. I didn’t find either of those strange, and I studied math, not physics. Nor did I notice any use of \equiv anywhere. https://en.m.wikipedia.org/wiki/Hermitian_matrix https://en.m.wikipedia.org/wiki/Hermitian_matrix https://en.wikipedia.org/wiki/Conjugate_transpose https://en.wikipedia.org/wiki/Conjugate_transpose
  - ramshorns 7y ago
    > and A^* is a standard notation for the conjugate transpose This seems strange. I didn't realize A† was mainly only used in quantum mechanics, but it seems better to have a distinct notation, since A* could mean a matrix with all the entries conjugated but in the same places. So, from a physics standpoint it appears to have a bit of a mathematics accent, which is a bit like how real accents are perceived: someone who has lived in two countries will have a foreign accent according to natives of each.
  - jordigh 7y ago
    No, Hermitian matrices can be over p-adics too. You just need an inner product so you can define a matrix to be self-adjoint, and you can define that inner product over p-adics. And the result is kind of funny, because although the statement of the result doesn't make any reference to complex numbers nor to adjoints, the proofs do. I do wonder if the result is still valid over other fields. There are other notations for the Hermitian transpose, such as the dagger or the H. The asterisk is particularly physicist, I think. And you might have studied physicist-accented mathematics; a lot of the accent often carries over into PDEs, functional analysis and related fields. The \equiv usage is in D \equiv diag(...)
    - cshimmin 7y ago
      In my experience (as a physicist), the dagger is much more common in physics literature to represent adjoint; A^* for adjoint is confusing because it could just mean complex conjugation in many contexts. Overlines are practically never used physics notation.
      - jordigh 7y ago
        I figured the notational confusion between the Hermitian transpose and the complex conjugate is kind of intentional, since moving from one side to the other of an inner product both conjugates scalars and is the adjoint of matrices, plus AA* is "real squaring" for both matrices and scalars.

Guessing, but: > ...one can multiply any eigenvector by a phase e^{iθ}... and: > As a consistency check...

You use \equiv for definitions instead of :=, ^* for complex conjugation instead of \overline, you refer to the Hermitian transpose as the adjoint, and you implicitly assume all matrices are over the complex numbers. There are also other little things like some of the phrases as pointed out in a sibling comment. Physicists really do have their own distinct style.

pmiller2 7y ago
Hermitian matrices are always complex matrices, and A^* is a standard notation for the conjugate transpose of a Hermitian matrix. I didn’t find either of those strange, and I studied math, not physics. Nor did I notice any use of \equiv anywhere. https://en.m.wikipedia.org/wiki/Hermitian_matrix https://en.m.wikipedia.org/wiki/Hermitian_matrix https://en.wikipedia.org/wiki/Conjugate_transpose https://en.wikipedia.org/wiki/Conjugate_transpose
- ramshorns 7y ago
  > and A^* is a standard notation for the conjugate transpose This seems strange. I didn't realize A† was mainly only used in quantum mechanics, but it seems better to have a distinct notation, since A* could mean a matrix with all the entries conjugated but in the same places. So, from a physics standpoint it appears to have a bit of a mathematics accent, which is a bit like how real accents are perceived: someone who has lived in two countries will have a foreign accent according to natives of each.
- jordigh 7y ago
  No, Hermitian matrices can be over p-adics too. You just need an inner product so you can define a matrix to be self-adjoint, and you can define that inner product over p-adics. And the result is kind of funny, because although the statement of the result doesn't make any reference to complex numbers nor to adjoints, the proofs do. I do wonder if the result is still valid over other fields. There are other notations for the Hermitian transpose, such as the dagger or the H. The asterisk is particularly physicist, I think. And you might have studied physicist-accented mathematics; a lot of the accent often carries over into PDEs, functional analysis and related fields. The \equiv usage is in D \equiv diag(...)
  - cshimmin 7y ago
    In my experience (as a physicist), the dagger is much more common in physics literature to represent adjoint; A^* for adjoint is confusing because it could just mean complex conjugation in many contexts. Overlines are practically never used physics notation.
    - jordigh 7y ago
      I figured the notational confusion between the Hermitian transpose and the complex conjugate is kind of intentional, since moving from one side to the other of an inner product both conjugates scalars and is the adjoint of matrices, plus AA* is "real squaring" for both matrices and scalars.