abstract

The term \(\theta {\epsilon ^{\mu \nu \rho \sigma }}F_{\mu \nu }F_{\rho \sigma }\), when added to the electromagnetic Lagrangian \(-{1\over 16\pi }F^{\mu \nu }F_{\mu \nu }\), does not change the signature of the Lagrangian. Actually, it increases the part with negative kinetic energy term at the spatial infinity. For this reason’ it does not change the conclusion that at the spatial infinity the magnetic part of the electromagnetic field should be absent.

abstract

Motivated by the growing interest in the existence of new massive gauge bosons, we suggest that massive dark photons \(A^{\prime }\) can be a consequence of a broken new Abelian symmetry U\((1)_{X}^{\prime }\). Such a dark symmetry U\((1)_{D}^{\prime }\) is afterwards supposed to be associated with the conservation of the weak number \(W\) belonging to the weakly interacting slim particles U\((1)_{W}^{\prime }\), being a strong candidate for hot dark matter. The latters correspond then to light dark photons \(m_{A}^{\prime } \lesssim \) keV from a weak symmetry breaking scale \(\gtrsim 10\) keV.

abstract

Recently proposed Future Circular Collider-based muon–proton colliders will allow for investigating lepton–hadron interactions at the highest center-of-mass energy. In this study, we investigate the potential of these colliders for a four-fermion contact interactions search. Regarding the constructive and destructive interferences of contact interactions, we estimated discovery, observation, and exclusion limits on the compositeness scale for the left–left, right–right, left–right, and right–left helicity structures. In this regard, we obtained compositeness scales for the left–left helicity structure at \(\sqrt {s} = 63.2\) TeV FCC-based \(\mu p\) collider with the 100 fb\(^{-1}\) integrated luminosity as \(225.7\pm 1.9\)% TeV (discovery), \(269.0\pm 2.0\)% TeV (observation), and \(311.3\pm 2.1\)% TeV (exclusion). This study’s findings show that the FCC-based \(\mu p\) colliders have great potential for investigating four-fermion contact interactions.

abstract

An unstable field theory is what we obtain when we linearise the equations of an interacting field theory near an unstable state. Theories of this kind are adopted to model the onset of spontaneous symmetry breakings, when the fields are sitting on the top of the Mexican hat, and they start to “roll down” to the bottom. At present, there exists no rigorous proof that unstable quantum field theories are Lorentz-invariant (in the sense of Wigner’s theorem). Here, we show that they should not be. In fact, unstable theories always have a limited regime of applicability, and they are valid only for a very short time. As a consequence, there is a preferred simultaneity hyperplane, along which the unstable theory is everywhere applicable, while a generic observer (whose four-velocity is not orthogonal to such hyperplane) must use the full non-linear theory. In summary: the current quantization schemes are “ok”, independently of whether they lead to a Lorentz-invariant theory.