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| bio | website | en.wikipedia.org/wiki/… |
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A Sufi prayer of love
O love, O pure deep love, be here, be now, be all.
Dissolve me into your stainless endless radiance,
Make me your servant, your breath, your core.
:- by sufi mystic Rumi
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Nov 30 |
comment |
Example of two linearly independent, nowhere vanishing vector fields in $\mathbb{R}^{2}$ Did you mean $V_2=x\partial_x+\partial_y$ ? I mean your $V_1$ and $V_2$ are not independent everywhere (specifically they are not independent at $x=0$). |
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Nov 30 |
comment |
Example of two linearly independent, nowhere vanishing vector fields in $\mathbb{R}^{2}$ $\partial/\partial x +f(x,y)\partial/\partial y$ and $\partial/\partial y$ are linearly independent vector fields for any choice of smooth function $f$. We can choose $f$ such that commutators do not vanish. For $f=0$ commutators vanish. |
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Nov 28 |
answered | Is there a default notation for 4-vectors while handwriting? |
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Nov 28 |
answered | Special Relativity |
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Nov 26 |
awarded | Caucus |
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Nov 25 |
comment |
How electric currents can flow between 2 points at the same potential? Potential drop across connecting wires is never really zero. However it is so small compared to other impedances in the circuit, that for practical purposes it can be taken to be zero. |
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Nov 18 |
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Interacting representation of the Poincaré group Hmm.. the conditions on H are I think given by equations 3.3.19, and 3.3.21 in Weinberg's book (note that in these equation he denotes (integral of) H(x) as V). |
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Nov 18 |
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Interacting representation of the Poincaré group then I guess (as @Arnold says) its still an unsolved problem :) |
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Nov 18 |
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Interacting representation of the Poincaré group What level of rigorousness do you want ? I think arguments given by Weinberg in section 3.3. make a fairly complete proof of his statements (at least at heuristic level). |
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Nov 18 |
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How do I define time-ordering for Wightman functions? @user1504 you are right, but is this one fine ? :- $$T(\hat\phi_1(f_1)..\hat\phi_n(f_n))≡ Lim_{\{\epsilon_i\}\rightarrow0}\int dx_1..dx_n\, f_1(x_1)...f_n(x_n) T(\hat\phi_1(g_{x_1,\epsilon_1})...\hat\phi_n(g_{x_n,\epsilon_n}))$$ where for each $i$, $g_{x_i,\epsilon_i}(y)$ converges to $\delta(y-x_i)$ when $\epsilon_i$ is taken to zero. |
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Nov 18 |
comment |
How do I define time-ordering for Wightman functions? Is there anything wrong with this definition : - $T(\hat\phi_1(f_1)..\hat\phi_n(f_n))≡\int dx_1..dx_n\, f_1(x_1)..f_n(x_n) T(\hat\phi_1(x_1)..\hat\phi_n(x_n))$ ? |
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Nov 15 |
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Noether's charge due to lorentz transformation Hmm.. I think Noether charge corresponding to a continuous symmetry of action is just the generator of that symmetry. Whether it is conserved or not depends upon whether it commutes with Hamiltonian or not. The Noether charge corresponding to boosts doesn't commute with Hamiltonian and hence changes with time. |
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Nov 15 |
comment |
Noether's charge due to lorentz transformation Boosts do not commute with Hamiltonian so there can be no conserved quantity corresponding to them. |
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Nov 14 |
answered | Why is electric field zero inside a hollow metal sphere ? |
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Nov 14 |
revised |
Why is electric field zero inside a hollow metal sphere ? modified the title, and the main body of question, and included a picture |
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Nov 14 |
suggested | suggested edit on Why is electric field zero inside a hollow metal sphere ? |
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Nov 13 |
revised |
How to compute the expectation value $\langle x^2 \rangle$ in quantum mechanics? added 396 characters in body |
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Nov 13 |
revised |
How to compute the expectation value $\langle x^2 \rangle$ in quantum mechanics? added 396 characters in body |
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Nov 13 |
answered | How to compute the expectation value $\langle x^2 \rangle$ in quantum mechanics? |
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Nov 13 |
comment |
The role of representation theory in QM/QFT? Hi @Nick i was not trying to be very rigorous in this answer. All i meant was that elements of group/algebra G of observables should be expressible in terms of elements of algebra A of fields. This of course follows from requirement of cyclicity of vacuum wrt A and as i think cyclicity of the vacuum wrt A is not a physical requirement but just one (though possibly only ?) way of implementing the requirement that observables be local expressions in terms of quantum fields. In algebraic approach too observables are required to be constructed out of elements of A in more abstract terms (right ?). |
