Landau & Lifschitz's fluid mechanics book proposes the following statement for an isentropic proccess:
$$dH=vdp \Rightarrow \nabla H=v\nabla p$$
What's the rigorous way to get this result (converting differentials to gradients)? Thanks in advance.
I found something that I'm confused with when calculating the propagator of harmonic oscillator.
Using the energy representation, the propagator of a quantum harmonic oscillator can be expressed as :
$$
K(x_f,t_f;x_i,t_i)=\sum_ne^{-i\omega T(n+\frac{1}{2})}\psi_n(x_f)\psi_n^*(x_i)\tag{1}
$$
where...
My understanding of fermions, bosons, and anyons is that anyons are disallowed in 3+1 dimensions (or $n+1 | n\geq3$) because of the topology of spacetime. The paths of swapping two particles twice is contractible in 3+1. In 2+1, this isn't the case and so anyons can exist.
However, what is the ca...