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2 votes
Accepted

Do different bases of Fock space commute?

For a given decomposition of the Fock space into $n$-particle subspaces, creation operator commute. For a $1$ particle state $|\psi\rangle$, there is an associated annihilation operator $a(\psi)$. If $...
SolubleFish's user avatar
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2 votes

Causality for gauge dependent operators in quantum field theories

Correct. As an example of how causality cannot be imposed on the electromagnetic potentials, consider the Coulomb gauge. In this gauge the propagation is instantaneous.
my2cts's user avatar
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1 vote
Accepted

Conjugate observables - can the commutation relations be generalised?

The notion of conjugate variables comes all the way from classical mechanics. There one defined a "conjugate momentum" from the derivative of the Lagrangian. Enter quantum physics and we get ...
flippiefanus's user avatar
1 vote

Conjugate observables - can the commutation relations be generalised?

I am not sure to understand well the issue. Conjugate variables are defined in the usual way and this is nothing but a definition, useful for many proposals and arising from classical Hamiltonian ...
Valter Moretti's user avatar
1 vote

Do different bases of Fock space commute?

It is evident linear algebra. Intuition? Try a space of just two bosonic oscillators, i=1,2, $$ [a_i,a^\dagger_j]=\delta_{ij}, \qquad [a_i,a_j]=0, $$ and ditto for the conjugates. Rotate them to $$ \...
Cosmas Zachos's user avatar
1 vote

Does the creation operators for photons with different polarization commute?

Boson creation operators always commute, i.e. $[a_\alpha^\dagger, a_\beta^\dagger]=0$ for all $\alpha,\beta$. In fact, $[a_\alpha^\dagger,a_\beta]=0$ if $\alpha\ne \beta$ as well provided that $\...
ZeroTheHero's user avatar
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1 vote
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Definition of the Conformal algebra generators

It is an error currently not listed in the errata. The sentence above eq. (2.9) should read: One can then verify that $J_{m,n}$ with $m, n = −1, 0, 1, \dots , \color{red}{d}$ satisfy the following ...
1 vote

Is it possible to derive Schrödinger's equation from Hamilton's equations?

First of all, it should be stressed that the TDSE (1) cannot be derived from classical physics alone, cf. e.g. this Phys.SE post. However, assuming that the classical system at hand can be quantized, ...
Qmechanic's user avatar
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1 vote

Relationship between normal-ordered vacuum state and parity operator

Another possible approach is to leverage the identity: $$F(\lambda)\equiv\lambda^{a^\dagger a} = N(e^{(\lambda-1)a^\dagger a}),$$ which is found for example in [CG1969] (see Eqs. 4.31 and 4.35). The ...
glS's user avatar
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