Alina E. Sagaydak, Zurab K. Silagadze
We demonstrate that Robb-Geroch's definition of a relativistic interval admits a simple and fairly natural generalization leading to a Finsler extension of special relativity. Another justification for such an extension goes back to the works of Lalan and Alway and, finally, was put on a solid basis and systematically investigated by Bogoslovsky under the name "Special-relativistic theory of locally anisotropic space-time". The isometry group of this space-time, DISIMb(2), is a deformation of the Cohen and Glashow's very special relativity symmetry group ISIM(2). Thus, the deformation parameter b can be regarded as an analog of the cosmological constant characterizing the deformation of the Poincare group into the de Sitter (anti-de Sitter) group. The simplicity and naturalness of Finslerian extension in the context of this article adds weight to the argument that the possibility of a nonzero value of b should be carefully considered.
Comments: 8 pages, 3 figures
Generator of spatial evolution of the electromagnetic field: https://arxiv.org/abs/2201.12138
Dmitri B. Horoshko
Starting with Maxwell's equations and defining normal variables in the Fourier space, we write the equations of temporal evolution of the electromagnetic field with sources in the Hamiltonian and Lagrangian forms, making explicit all intermediate steps often omitted in standard textbooks. Then, we follow the same steps to write the equations of evolution of this field along a spatial dimension in the Hamiltonian and Lagrangian forms. In this way, we arrive at the explicit form of the generator of spatial evolution of the electromagnetic field with sources and show that it has a physical meaning of the modulus of momentum transferred through a given plane orthogonal to the direction of propagation. In a particular case of free field this generator coincides with the projection of the full momentum of the field on the propagation direction, taken with a negative sign. The Hamiltonian and Lagrangian formulations of the spatial evolution are indispensable for a correct quantization of the field when considering its spatial rather than temporal evolution, in particular, for a correct definition of the equal-space commutation relations.
Comments: 17 pages, 2 figures, final accepted version
Subjects: Classical Physics (physics.class-ph); Quantum Physics (quant-ph)
Journal reference: Phys. Rev. A 105, 013708 (2022)