We obtain a canonical form of a quadratic Hamiltonian for linear waves in a weakly inhomogeneous medium. This is achieved by using the WKB representation of wave packets. The canonical form of the Hamiltonian is obtained via the series of canonical Bogolyubov-type and near-identical transformations. Various examples of the application illustrating the main features of our approach are presented...

The Hartree-Fock-Bogoliubov equation for the ground states of even-even atomic nuclei is solved using the canonical representation in the coordinate space for zero range interactions like the Skyrme force. The gradient method is improved for faster convergence to the solutions under constraint of orthogonality between canonical orbitals. Necessity of the cut-off of the pairing interaction is sh...

Let V be the representation of the quantized enveloping algebra of gl(n) which is the q-analogue of the vector representation and let V ∗ be the dual representation. We construct a basis for ⊗r (V ⊕ V ∗) with favorable properties similar to those of Lusztig’s dual canonical basis. In particular our basis is invariant under the bar involution and contains a basis for the subspace of invariant te...

We consider Gaussian processes that are equivalent in law to the fractional Brownian motion and their canonical representations. We prove a Hitsuda type representation theorem for the fractional Brownian motion with Hurst index H [ 2 . For the case H> 2 we show that such a representation cannot hold. We also consider briefly the connection between Hitsuda and Girsanov representations. Using the...

Abstract. We develop an algorithm for the canonical computation of general Fourier integral operators whose canonical relations are graphs. The algorithm is based on dyadic parabolic decomposition using wave packets and enables the discrete approximate evaluation of the action of such operators on data in the presence of caustics. The procedure consists in the construction of a universal operat...

The Rabi Hamiltonian, describing the coupling of a two-level system to a single quantized boson mode, is studied in the BargmannFock representation. The corresponding system of differential equations is transformed into a canonical form in which all regular singularities between zero and infinity have been removed. The canonical or Birkhoff-transformed equations give rise to a two-dimensional e...

We present a versatile quantitative framework for comparing representations in deep neural networks, based on Canonical Correlation Analysis, and use it to analyze the dynamics of representation learning during the training process of deep networks. We find that layers converge to their final representation from the bottom-up, but that the representations themselves migrate downwards in the net...

Motivated by the fact that in computer vision data samples are matrices, in this paper, we propose a matrix-variate probabilistic model for canonical correlation analysis (CCA). Unlike probabilistic CCA which converts the image samples into the vectors, our method uses the original image matrices for data representation. We show that the maximum likelihood parameter estimation of the model lead...

A covariant spinor representation of iosp(d, 2/2) is constructed for the quantization of the spinning relativistic particle. It is found that, with appropriately defined wavefunctions, this representation can be identified with the state space arising from the canonical extended BFV-BRST quantization of the spinning particle with admissible gauge fixing conditions after a contraction procedure....

A general pedagogical survey of the basics of the Bethe-Salpeter equation and in particular Wick-Cutkosky model is given in great technical details. The Bethe-Salpeter approach to the relativistic two-body bound state problem assumes that all needed information about a bound state |B > is contained in the B-S amplitude Φ(x 1 , x 2 ; P B) =< 0|T φ 1 (x 1)φ 2 (x 2)|B > (1) and in its conjugate ¯ ...