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According to the Goldstone theorem a scalar theory with a spontaneously broken global symmetry contains strictly massless states. In this letter we identify a loophole in the current-algebra proof of the theorem. Therefore, the question whether in models with Mexican hat potential the tangential excitations are strictly massless or are just almost massless as compared to the radial ones remains open. We also argue that mass of the tangential excitations approaches zero even if the symmetry is not spontaneously broken but a combination of the field components invariant under the symmetry transformations acquires a large vacuum expectation value.
The clockwork mechanism has recently been proposed as a natural way to generate hierarchies among parameters in quantum field theories. The mechanism is characterized by a very specific pattern of spontaneous and explicit symmetry breaking, and the p
The transition between the broken and unbroken phases of massive gauge theories, namely the rearrangement of longitudinal and Goldstone degrees of freedom that occurs at high energy, is not manifestly smooth in the standard formalism. The lack of smo
Historically, Ehrenfests theorem (1927) is the first one which shows that classical physics can emerge from quantum physics as a kind of approximation. We recall the theorem in its original form. Next, we highlight its generalizations to the relativi
Steve Gull, in unpublished work available on his Cambridge University homepage, has outlined a proof of Bells theorem using Fourier theory. Gulls philosophy is that Bells theorem can be seen as a no-go theorem for a project in distributed computing (
Having so far only indirect evidence for the existence of Dark Matter a plethora of experiments aims at direct detection of Dark Matter through the scattering of Dark Matter particles off atomic nuclei. For the correct interpretation and identificati