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8h
comment Wave/particle-duality as result of taking different limits of a QFT
@JohnRennie: k. As stated in the question, I'm interested in the explicit construction of the two different limits of one QFT claimed to exist in the article n page 4, i.e. this. Math is no barrier to me.
2d
comment Does water maintain equal level in connected vessels?
I'm not in the position to answer the question, butI have no feeling for how big your construction is - the American units are somewhat alienating. I offer 250 Vietnamese dong to anyone who translates it.
2d
comment Can interacting Hamiltonians always be written in second quantized form?
Why the downvote? Is my solution just too much outside the box or is it wrong? Going passed that, does the discrete sum remark not give a negative answer to the question?
Dec
23
comment Wave/particle-duality as result of taking different limits of a QFT
OP here. The paper suggestion you have two limits, a particle limit and another field limit. I'd like to know/see both different limits, and explicitly with some QFT.
Dec
22
asked Wave/particle-duality as result of taking different limits of a QFT
Dec
21
comment Making precise the statement “particles are excitations in a quantum field”
Passing away from non-relativistic QM, as you say, to high energy physics isn't where things move from a single wave function $ψ(x⃗,t)$ to n-particle operator tools. You may always rewrite a term $∑_{i≠j}V(|r⃗_i−r⃗_j|)$ of a Hamiltonian describing an n-particle system as $∫∫∫d^3kd^3pd^3q\,V(q⃗ )\,c_{k⃗+q⃗}c_{p⃗−q⃗}c_{p⃗}c_{q⃗}$, where $V(q⃗)$ is the fourier transform of the potential. See e.g. the tight binding model in solid state physics.
Dec
18
revised Can interacting Hamiltonians always be written in second quantized form?
added 8 characters in body
Dec
18
revised Can interacting Hamiltonians always be written in second quantized form?
added 12 characters in body
Dec
18
revised Can interacting Hamiltonians always be written in second quantized form?
added 12 characters in body
Dec
18
answered Can interacting Hamiltonians always be written in second quantized form?
Dec
16
comment Total divergence term and corresponding Feynman Diagram
>Isn't that disturbing...pun intended?
Dec
15
comment Akin to gauge field, why GR's lagrangian is not $R_{abcd}R^{abcd}$? What's the mathematical or physical meaning of $R_{abcd}R^{abcd}$?
There are 50 or so variations in the Wikipedia article Alternatives to GR, maybe you find more information why they are dismissed or set aside. The term pops up e.g. Lovelock and Gauss-Bonnet gravity (which don't seem to live in 3+1 dimensions) and I guess in $f(R)$ variants.
Dec
4
revised The index of a Dirac operator and its physical meaning
computed the index
Dec
4
suggested approved edit on The index of a Dirac operator and its physical meaning
Nov
12
comment Are terms with spinors analogous to $ ( \partial_\mu \Phi )(\partial^\mu \Phi)$ forbidden in the Lagrangian?
@DavidZ: Of course, you make me look it up.
Nov
12
comment How to derive the two-term approximation for the Boltzmann equation?
Thanks, yeah I know the BOLZIG+ reference - everyone cites it when they use the electron collision cross sections that come with it :)
Nov
7
comment What is the difference between $|0\rangle $ and $0$?
Consider the vector $v:=(-5,3,7)$ in ${\mathbb R}^3$. It can be written as $v=-5\,e_1+3\,e_2+7\,e_3$. The object $e_3$ is a vector like $|0\rangle$. The number $3$ is a coefficient, like $0$.
Nov
4
comment Formal definition of an observer?
You say you've seen a few formal definitions. What do you mean by "actual definition", then? Seems like there are several.
Nov
4
comment Are identity types interpreted physically in an infinity-topos formulation of equations of motion?
Or let me say: I get the need for path spaces, but do we need "equality proper" before we define equivalence and by this obtain the desired notion of equality?
Nov
4
comment Are identity types interpreted physically in an infinity-topos formulation of equations of motion?
Why do we need types "$=$" to begin with? After all, weak category theory can do without. Can you point me to why, in HoTT, we start out with an identity type and then impose $(A=B)\simeq(A\simeq B)$? Say we start out with a dependently typed theory (with $\prod, \sum$ in particular) and then define "$\simeq$" as is done in the HoTT book. If the principle of equivalence${}^{TM}$ is to be implemented with this axiom, why do we consider a theory with identity in the first place. It appears all we really want is "just" equivalence anyway. Btw. I lurk the nForum - is there a question section?