Electromagnetic fields are quantized in a manifestly covariant way by means of a class of reducible "center-of-mass N -representations" of the algebra of canonical commutation relations (CCR). The four-potential A a (x) transforms in these representations as a Hermitian four-vector field in Minkowski four-position space (without change of gauge), but in momentum space it splits into spin-1 massless photons and two massless scalars. What we call quantum optics is the spin-1 sector of the theory. The scalar fields have physical status similar to that of dark matter (spin-1 and spin-0 particle numbers are separately conserved). There are no negative-norm or zero-norm states. Unitary dynamics is given by the point-form interaction picture, with minimal-coupling Hamiltonian constructed from fields that are free on the null-cone boundary of the Milne universe. SL(2,C) transformations as well as the dynamics are represented unitarily in the Hilbert space corresponding to N fourdimensional oscillators. Vacuum is a Bose-Einstein condensate of the N -oscillator gas and is given by any N -oscillator product state annihilated by all annihilation operators. The form of A a (x) is determined by an analogue of the twistor equation. The same equation guarantees that the set of vacuum states is Poincaré invariant. The formalism is tested on quantum fields produced by pointlike classical sources. Photon statistics is well defined even for pointlike charges, with ultraviolet and infrared regularizations occurring automatically as a consequence of the formalism. The probabilities are not Poissonian but of a Rényi type with α = 1 − 1/N ; the Shannon limit N → ∞ is an ultraviolet/infrared-regularized Poisson distribution. The average number of photons occurring in Bremsstrahlung splits into two parts: The one due to acceleration, and the one that remains nonvanishing even for inertially moving charges. Classical Maxwell electrodynamics is reconstructed from coherent-state averaged solutions of Heisenberg equations. We show in particular that static pointlike charges polarize vacuum and produce effective charge densities and fields whose form is sensitive to both the choice of representation of CCR and the corresponding vacuum state.M. Czachor ( ) · K. Wrzask Katedra Fizyki Teoretycznej i Informatyki Kwantowej,

Relativistic EPR-type experiments for photons in the background of reducible representation algebras are discussed. A model for the four Bell states, such that maintains maximally correlated in two bases: linear and circular in all reference frames is developed. Relativistic correlation functions are derived for two cases: when the detectors are transformed under Lorentz transformation in such a way that they still remain in the same reference frame and when just one of the detectors is transformed.

No abstract

One of the most crucial tasks for naval architects is computing the energy required to meet the ship’s operational needs. When predicting a ship’s energy requirements, a series of hull resistance tests on a scale model vessel is carried out in constant speed stages, while the acceleration stage measurements are ignored. Another important factor in seakeeping analysis is the ship’s hydrodynamic added mass. The second law of dynamics states that all this valuable information, that is, the dependence of the hull resistance on the vessel’s speed and the added mass, is accessible from just one acceleration stage towing test done up to the maximum speed. Therefore, the acceleration stage, often overlooked in traditional towing experiments, can be a valuable source of information. For this reason, this work aims to generalise Froude’s scaling procedure to full-scale vessels for the accelerated stage towing tests.