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Nov
18
comment 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.
Nov
18
comment How do I define time-ordering for Wightman functions?
Is there anything wrong with this definition : - $T(\hat\phi_1(f_1)..\hat\phi_n(f_n))≡\int dx_1..dx_n\, f_1(x_1)..f_n(x_n) T(\hat\phi_1(x_1)..\hat\phi_n(x_n))$ ?
Nov
15
comment 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.
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.
Nov
14
answered Why is electric field zero inside a hollow metal sphere ?
Nov
14
revised Why is electric field zero inside a hollow metal sphere ?
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Nov
14
suggested approved edit on Why is electric field zero inside a hollow metal sphere ?
Nov
13
revised How to compute the expectation value $\langle x^2 \rangle$ in quantum mechanics?
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Nov
13
revised How to compute the expectation value $\langle x^2 \rangle$ in quantum mechanics?
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Nov
13
answered How to compute the expectation value $\langle x^2 \rangle$ in quantum mechanics?
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 ?).
Nov
13
revised The role of representation theory in QM/QFT?
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Nov
13
revised The role of representation theory in QM/QFT?
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Nov
13
answered The role of representation theory in QM/QFT?
Nov
12
comment Have I discovered how to calculate the proton's mass using only integers?
Nice! but the problem here is that mass is a dimensionful quantity so the same integer representation may not hold in other units. It could perhaps be more useful if one can try to represent (say) the ratio of proton and electron mass as some such expression in terms of integers.
Nov
10
comment Does the axiom of choice appear to be “true” in the context of physics?
I think that Banach - Tarski theorem which depends crucially upon choice axiom may have some physical meaning - e.g. in terms of creation of more than one particles out of one when given with enough energy. However, the question of whether this is so or not belongs more to the domain of philosophy than physics.
Nov
4
answered Translations of field operators in QFT
Oct
24
comment Can someone identify this Landau reference?
This could be helpful.
Oct
22
comment What do I see if I move quickly past a charge surrounded by iron filings?
If 4-force in one inertial frame is zero then it will be zero in any other inertial frame too (simply because a zero vector is preserved under a linear transformation). For simplification replace iron fillings with a tiny magnet. Then in the rest frame this magnet doesn't feel any force because i) it can not respond to its own magnetic field ii) it is not moving relative to the charge. So the total 4-force on it is zero as observed in rest frame. Hence in any other frame too it will remain zero.
Oct
22
comment Do Christoffel symbols commute?
Do Christoffel symbols commute? As matrices they do not. See @Ron's answer. does $\Gamma^{e}_{db}\Gamma^{c}_{ea} = \Gamma^{c}_{ea}\Gamma^{e}_{db}$? Yes, because they are just numbers.