Ambidextrous light transforms for celestial amplitudes

Low multiplicity celestial amplitudes of gluons and gravitons tend to be distributional in the celestial coordinates z,$$ \overline{z} $$ z ¯ . We provide a new systematic remedy to this situation by studying celestial amplitudes in a basis of light transformed boost eigenstates. Motivated by a novel equivalence between light transforms and Witten’s half-Fourier transforms to twistor space, we light transform every positive helicity state in the coordinate z and every negative helicity state in $$ \overline{z} $$ z ¯ . With examples, we show that this “ambidextrous” prescription beautifully recasts two- and three-point celestial amplitudes in terms of standard conformally covariant structures. These are used to extract examples of celestial OPE for light transformed operators. We also study such amplitudes at higher multiplicity by constructing the Grassmannian representation of tree-level gluon celestial amplitudes as well as their light transforms. The formulae for n-point Nk−2MHV amplitudes take the form of Euler-type integrals over regions in Gr(k, n) cut out by positive energy constraints.

Quantum field theory of space-like neutrino

We performed a Lorentz covariant quantization of the spin-1/2 fermion field assuming the space-like energy-momentum dispersion relation. We achieved the task in the following steps: (i) determining the unitary realizations of the inhomogenous Lorentz group in the preferred frame scenario by means of the Wigner–Mackey induction procedure and constructing the Fock space; (ii) formulating the theory in a manifestly covariant way by constructing the field amplitudes according to the Weinberg method; (iii) obtaining the final constraints on the amplitudes by postulating a Dirac-like free field equation. Our theory allows to predict all chiral properties of the neutrinos, preserving the Standard Model dynamics. We discussed the form of the fundamental observables, energy and helicity, and show that non-observation of the $$+\tfrac{1}{2}$$ + 1 2 helicity state of the neutrino and the $$-\tfrac{1}{2}$$ - 1 2 helicity state of the antineutrino could be a direct consequence of the “tachyoneity” of neutrinos at the free level. We found that the free field theory of the space-like neutrino is not invariant under the C and P transformations separately but is CP-invariant. We calculated and analyzed the electron energy spectrum in tritium decay within the framework of our theory and found an excellent agreement with the recent measurement of KATRIN. In our formalism the questions of negative/imaginary energies and the causality problem does not appear.

FIRST-ORDER DISTRIBUTED FERMI ACCELERATION OF COSMIC RAY HADRONS IN NON-UNIFORM MAGNETIC FIELDS

Large-scale spatial variations of the guide magnetic field of interplanetary and interstellar plasmas give rise to the adiabatic focusing term in the Fokker–Planck transport equation of cosmic rays. As a consequence of the adiabatic focusing term, the diffusion approximation to cosmic ray transport in the weak focusing limit gives rise to first-order Fermi acceleration of energetic particles if the product HL of the cross helicity state of Alfvenic turbulence H and the focusing length L is negative. The basic physical mechanisms for this new acceleration process are clarified and the astrophysical conditions for efficient acceleration are investigated. It is shown that in the interstellar medium this mechanism preferentially accelerates cosmic ray hadrons over 10 orders of magnitude in momentum. Due to heavy Coulomb and ionization losses at low momenta, injection or preacceleration of particles above the threshold momentum pc≃0.17Z2/3 GeV /c is required.

ENTANGLEMENT ENTROPY: HELICITY VERSUS SPIN

For a massive spin 1/2 field, we present the reduced spin and helicity density matrix, respectively, for the same pure one particle state. Their relation has also been developed. Furthermore, we calculate and compare the corresponding entanglement entropy for spin and helicity within the same inertial reference frame. Due to the distinct dependence on momentum degree of freedom between spin and helicity states, the resultant helicity entropy is different from that of spin in general. In particular, we find that both helicity entanglement for a spin eigenstate and spin entanglement for a right handed or left handed helicity state do not vanish, and their Von Neumann entropy has no dependence on the specific form of momentum distribution, as long as it is isotropic.