The resonance frequency of an atom in an ensemble is shifted from that for an isolated atom due to the net polarization of the ensemble. This shift, ∆ω L , was first derived by Lorentz [1] and Lorenz [2] independently, thus it is known as the Lorentz–Lorenz shift and is given by where N is the number density and µ is the dipole moment. The corresponding modification to the dielec-tric constant ...

The aim of this note is to relate the classical Schwarzian derivative and the geometry of Lorentz surfaces of constant curvature. 1. The starting point of our investigations lies in the following remark (joint work with L. Guieu). Consider a curve y = f(x) in the Lorentz plane with metric g = dxdy. If f (x) > 0, then its Lorentz curvature can be computed : ̺(x) = f (x) (f (x)) and enjoys the qui...

Canonical quantisation of rigid particles is considered paying special attention to the restriction on phase space due to causal propagation. A mixed Lorentz-gravitational anomaly is found in the commutator of Lorentz boosts with world-line reparametrisations. The subspace of gauge invariant physical states is therefore not invariant under Lorentz transformations. The analysis applies for an ar...

We give an overview on the problem of finding isometry as Lorentz transformation between given vectors of 4-velocity and its solutions. These Lorentz transformations are usually referenced as Lorentz links. We show that the links by boost, obtained independently by different authors in different forms, are identical. Finally, we discuss briefly some implications of the non-uniqueness of boost l...

The standard forms of supersymmetry and supergravity are inextricably wedded to Lorentz invariance. Here a Lorentz-violating form of supergravity is proposed. The superpartners have exotic properties that are not possible in a theory with exact Lorentz symmetry and microcausality. For example, the bosonic sfermions have spin 1/2 and the fermionic gauginos have spin 1. The theory is based on a p...

Relating the effective Lorentz violation coefficients for composite particles to the coefficients for their constituent fields is a challenging problem. We calculate the Lorentz violation coefficients relevant to the dynamics of an α-particle in terms of proton and neutron coefficients. The α-particle coefficients would lead to anisotropies in the α-decays of nuclei, and because the decay proce...

The three-dimensional Heisenberg group H3 has three left-invariant Lorentz metrics g1 , g2 and g3 as in [R92] . They are not isometric each other. In this paper, we characterize the left-invariant Lorentzian metric g1 as a Lorentz Ricci soliton. This Ricci soliton g1 is a shrinking non-gradient Ricci soliton. Likewise we prove that the isometry group of flat Euclid plane E(2) has Lorentz Ricci ...

We consider how Lorentz-violating interactions in the Faddeev-Popov ghost sector will affect scalar QED. The behavior depends sensitively on whether the gauge symmetry is spontaneously broken. If the symmetry is not broken, Lorentz violations in the ghost sector are unphysical, but if there is spontaneous breaking, radiative corrections will induce Lorentz-violating and gauge-dependent terms in...