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1323
bio website sites.google.com/site/…
location Cambridge, MA
age 25
visits member for 1 year, 11 months
seen 7 hours ago

Physics Graduate student at Harvard University.


12h
comment The Spin Connection
Here's a quick motivation (maybe not an answer). In the tetrad formalism, the metric is replaced by tetrads $e^a_\mu$ satisfying $g^{\mu\nu} e^a_\mu e^b_\nu = \eta^{ab}$. The original 16 d.o.f. of the tetrad are constrained by 10 equations above, thereby giving 6 new independent d.o.f. The metric $g_{\mu\nu}$ starts out with 10 d.o.f. Thus, we must have 4 new d.o.f. to completely describe the theory. These are precisely the spin connection coefficients.
12h
answered Where does this term “shell” with prefix “on-/off-” come from?
19h
comment Why gravity is a spin-2 field? How can I read the spin from Einstein-Hilbert action?
For massless states, helicity is the correct quantum number (people often use spin and helicity interchangeably and this causes confusion). To compute helicity, one does not go to the rest frame. (since there isn't any!)
1d
reviewed Close Change in volume of air held at the top of a tube with upper end closed and holding some liquid
1d
reviewed Leave Open Is there any distinction between these products: scalar, dot, inner?
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reviewed Close Loop-the-loop question
1d
reviewed Close Why does light seem so slow when compared to everyday observations here on Earth?
1d
comment Finding the creation/annihilation operators
For example, in the case of Minkowski space, it is standard to choose $\phi_k^\pm = e^{ \mp i k \cdot x }$. The creation and annihilation operators are then defined as $a^\dagger_k = (\phi^+_k, \phi)$ and $a_k = (\phi_k^-, \phi)$. Working out all these explicitly, one obtains the formula that I have described.
1d
comment Finding the creation/annihilation operators
One starts by consider the classical space of solutions of the wave equation, and define an inner product on this space $(\phi_1, \phi_2) = \int d^3 x \phi_1 {\overleftrightarrow \partial_0} \phi_2$. It can be shown that this is a conserved inner product. One then chooses an orthonormal basis on this space $\phi_k$ satisfying $(\phi_k \phi_{k'} ) = \delta_{k, k'}$. This basis is then broken into positive freq. and negative freq modes $\phi_k^\pm$. This distinction (and the basis) is not unique in general and depends on the coordinates and the space-time.
1d
comment Finding the creation/annihilation operators
@user13223423 I know this was the main problem you were having, and I gave you an explicit formula. All you have to do is plugin the various expansions and derive this. I essentially used step 3. More generally, I used a more generalized technique to define creation-annihilation operators in terms of some inner product on the classical field space.
1d
revised Finding the creation/annihilation operators
added 76 characters in body
1d
answered Finding the creation/annihilation operators
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reviewed Close Stationary wave on a string
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reviewed Close How much smaller will be human body, when we hypothetically get of every space between particles
2d
reviewed Approve suggested edit on Kinematics - Find theta with Coefficient of Friction?
Apr
13
reviewed Close If 'pure energy' is photons, and energy is conserved, how can matter and antimatter (electrons and positrons) annihilate into photons and vice-versa?
Apr
13
reviewed Close Elongation of a beam
Apr
10
reviewed Leave Open Covariant derivative of a vanishing tensor component
Apr
10
reviewed Approve suggested edit on Finding power with Drag Force equation
Apr
10
awarded  Nice Answer