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21h
comment Noncommutative Field Quantization
Just google search "Quantum Field Theory Noncommutative space arxiv" and/or "Quantum Field Theory Noncommutative space connes" for the approach by Alain Connes
1d
comment Relation between component and algebraic definition of covariant vectors
Stricly speaking, the isomorphism is valid only for finite dimensional (vector) spaces. The dual vector space is a more general formalism, and it is ofen used in differential geometry, too. So try to use it and become familiar with it, because it will be useful to you in the future.
2d
answered The DLCZ Protocol
2d
comment Is topology of universe observable?
See this paper. The consequences of the topology (Circle searching...) have not been observed, so the model is not correct, but it is interesting.
2d
comment Relation between component and algebraic definition of covariant vectors
As I said before, there is an isomorphism. Isomorphism means that the two points of view are equivalent. So you may adopt the "reciprocal basis" point of view : $\vec f^j.\vec e_i= \delta^j_i$, or the dual vector space point of view : $ f^j(\vec e_i)= \delta^j_i$.
Jul
21
answered In what sense is a quantum field an infinite set of harmonic oscillators?
Jul
21
comment Is the potential in Schrödinger equation an operator?
Designing by $\hat V$ the operator, you have : $\hat V \Psi(x,t) = V(x,t)\Psi(x,t)$, where $V(x,t)$ is a scalar quantity.
Jul
21
answered Is thermodynamic free energy and potential energy the same thing?
Jul
21
comment What is “Energy” of a vacuum in the context of quantum theory?
Have a look at Wikipedia quantum harmonic oscillator. You will see that, because the position and the momentum operator do not commute, the lower energy is not zero. In quantum field theory, the behaviour of relativistic bosonic fields is just the same (a relativistic bosonic field is just a sum of independent quantum harmonic oscillators labelled by momentum and eventually spin)
Jul
21
comment Relation between component and algebraic definition of covariant vectors
"Reciprocal basis" and "Basis from the dual of the vector" space are the "same thing". More precisely, there is an isomorphism. See my UPDATE 2 in the answer.
Jul
21
revised Relation between component and algebraic definition of covariant vectors
Precision
Jul
20
awarded  Notable Question
Jul
19
comment Relation between component and algebraic definition of covariant vectors
I update my answer
Jul
19
revised Relation between component and algebraic definition of covariant vectors
added 277 characters in body
Jul
18
answered Relation between component and algebraic definition of covariant vectors
Jul
18
comment What is the basis of gauge theory?
+1 for the clear explanation. However, one has to notice that gauge symmetries are more the expression of mathematical redundancies (describing the same physical reality) than real symmetries. For instance, describing spin $1$ particles by a covariant vector $A_\mu$ is not "economic". And you have to eliminate spurious degrees of freedom by some technic : choice of gauge, Fadeev-Popop trick, etc...
Jul
18
comment Values of Spacetime Dimension and Virasoro Generator Ambiguity in Bosonic String Theory
I did not say that. I don't know if there are physical spurious states in non-critical bosonic string theories, but probably the identification of the spurious and physical states is different (you would have consider the dilation field, etc..)
Jul
17
awarded  Pundit
Jul
17
comment Values of Spacetime Dimension and Virasoro Generator Ambiguity in Bosonic String Theory
I think that the constants $a$ and $D$ are parameters of your model, so IMHO, they are the same for the whole Hilbert space. After, it is up to you to describe what are the physical states in your model.
Jul
17
comment Does time move slower at the equator?
In this paper, chapter "Relativity on the Earth’s surface", there is an interesting discussion, where it seems that the gravitationnal effect (+ $108$ ns by $24$ h) compensates the special relativity effect (- $104$ ns by $24$ h).