Abstract
We discuss, in the relativistic limits, Heisenberg's uncertainty principle for the electromagnetic orbital angular momentum (OAM) of monochromatic fields. The Landau and Peierls relativistic approa ...
Highlights
The classical electromagnetic (EM) field transports energy E and momentum P as well as angular momentum J
In gravitational fields generated by a rotating mass such as the Kerr [17,38,39,40], or the Gödel solutions [41], one instead finds that photon orbital angular momentum (OAM) interacts with that of the rotating body: Both solutions belong to the class of Petrov type-D geometries, where the mixing of space and time coordinates actively imprint OAM or even to subtract OAM from light or modify the properties of the beam with an additional rotation [17,40,42]
We show that there are finite limits for the determination of OAM states of light dictated by the Hubble horizon of the Universe and by the finiteness of Planck units, below which space and time are not defined
Summary
The classical electromagnetic (EM) field transports energy E and momentum P as well as angular momentum J. This is the case at the quantum level, where it finds a precise and comprehensive description through the second-quantization formalism of quantum electrodynamics (QED) [1] or in the first quantization language via the photon wave function by using the Majorana-Wigner approach to quantum electrodynamics, based on the Riemann-Silberstein formalism in a direct correspondence to QED [2]. In a fully covariant approach, the photon wave function has a total spinorial representation of rank 6, equivalent to a spinor of rank 2 for each coordinate, i.e., a vector giving photons an intrinsic spin s = 1 with associated helicity quantum numbers, λ = ±1.
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