Given a signal $f(t)$ defined on $t\in(-\infty,\infty),$ what is the precise definition of the power spectrum of $f$, i.e., what is the mathematical operation that takes $f$ to the output of an ideal spectrometer applied to $f$? Wikipedia defines the energy spectral density as $$S(\omega)=|\hat{f...

I was wondering if these two theorems do not conflict with one another in some sense. It sees as if one allow us to move from the free to the interacting theory, while the other forbids it.

I just saw in the dynamic periodic table that He is liquid at $-273^\circ \rm C$ is that true? How is that even possible can someone explain?

Let's say we build a train track around the earth running from the Arctic to the Antarctic and back again. A train is going to run on this track at a speed of almost the speed of light lets say $299,792,457 \;\text{m/s}$ ($1 \;\text{m/s}$ less than the speed of light). We have observers on the gr...