The unitary representations of the Poincar\'e group in any spacetime dimension

An extensive group-theoretical treatment of linear relativistic field equations on Minkowski spacetime of arbitrary dimension D\geqslant 3D≥3 is presented. An exhaustive treatment is performed of the two most important classes of unitary irreducible representations of the Poincar'e group, corresponding to massive and massless fundamental particles. Covariant field equations are given for each unitary irreducible representation of the Poincar'e group with non-negative mass-squared.

Relativistic Equations for Arbitrary Spin, Especially for the Spin s = 2

The further approbation of the equation for the particles of arbitrary spin introduced recently in our papers is under consideration. The comparison with the known equations suggested by Bhabha, Pauli–Fierz, Bargmann–Wigner, Rarita–Schwinger (for spin s =3/2) and other authors is discussed. The advantages of the new equations are considered briefly. The advantage of the new equation is the absence of redundant components. The important partial case of spin s =2 is considered in details. The 10-component Dirac-like wave equation for the spin s =(2,2) particle-antiparticle doublet is suggested. The Poincar´e invariance is proved. The three-level consideration (relativistic canonical quantum mechanics, canonical Foldy–Wouthuysen-type field theory, and locally covariant field theory) is presented. The procedure of our synthesis of arbitrary spin covariant particle equations is demonstrated on the example of spin s =(2,2) doublet.

Horizontal spatial correlation of reverberation for rough sea-bottom interface

Correlation sonar, which estimates the velocity of vessel utilizing the principle of waveform invariance, can achieve the sampling of the horizontal spatial correlation of sea-bottom reverberation. The horizontal spatial correlation can be expressed as a correlation function and is affected by sea-bottom characteristics. The expression of the correlation function of the sea-bottom reverberation is derived, which is written as the convolution of the autocorrelation function of transmitted signal, the cross-correlation function of the backscattered impulse response from a plane interface, and the autocorrelation function of the probability density function of the sea-bottom roughness. The isotropic interface roughness of the sea-bottom leads to a circular planform of the correlation function whose width varies with roughness. The anisotropic interface roughness of the sea-bottom leads to an elliptical planform of the correlation function whose major axis is in the direction of weaker roughness. Simulation of submarine reverberation and correlation function verifies this conclusion. The model for the spatially covariant field is used to estimate the backscattering cross section which varies with azimuth angle under the condition of anisotropic seafloor roughness. It should be noted that the horizontal spatial correlation of reverberation is also related to sonar parameters and other sea-bottom characteristics.

Covariant fields on anti-de Sitter spacetimes

The covariant free fields of any spin on anti-de Sitter (AdS) spacetimes are studied, pointing out that these transform under isometries according to covariant representations (CRs) of the AdS isometry group, induced by those of the Lorentz group. Applying the method of ladder operators, it is shown that the CRs with unique spin are equivalent with discrete unitary irreducible representations (UIRs) of positive energy of the universal covering group of the isometry one. The action of the Casimir operators is studied finding how the weights of these representations (reps.) may depend on the mass and spin of the covariant field. The conclusion is that on AdS spacetime, one cannot formulate a universal mass condition as in special relativity.

Polysymplectic formulation for topologically massive Yang–Mills field theory

We analyze the De Donder–Weyl covariant field equations for the topologically massive Yang–Mills theory. These equations are obtained through the Poisson–Gerstenhaber bracket described within the polysymplectic framework. Even though the Lagrangian defining the system of our interest is singular, we show that by appropriately choosing the polymomenta one may obtain an equivalent regular Lagrangian, thus avoiding the standard analysis of constraints. Further, our simple treatment allows us to only consider the privileged [Formula: see text]-forms in order to obtain the correct field equations, in opposition to certain examples found in the literature.