相关论文: The Representation Transformation of Multiquark Wa…
The block-diagonalization of the Hamiltonian is not sufficient for the transformation to the Foldy-Wouthuysen (FW) representation. The conditions enabling the transition from the Dirac representation to the FW one are formulated and proved.…
The gauge variance of wave functionals for a gauge theory quantized in the momentum (curvature) representation is described. It is shown that a gauge transformation gives rise to a cocycle, which for theories in two space-time dimensions is…
Further results for conformal partial waves for four point functions for conformal primary scalar fields in conformally invariant theories are obtained. They are defined as eigenfunctions of the differential Casimir operators for the…
We develop graphical calculation methods. Jones-Wenzl projectors for U_q(sl(2,C)) are very powerful tools to find not only invariants of links but also invariants of 3-manifolds. We find single clasp expansions of generalized Jones-Wenzl…
We study the computational complexity of converting one representation of real numbers into another representation. Typical examples of representations are Cauchy sequences, base-10 expansions, Dedekind cuts and continued fractions.
Motivated by the multivariate wavelet theory, and by the spectral theory of transfer operators, we construct an abstract affine structure and a multiresolution associated to a matrix-valued weight. We describe the one-to-one correspondence…
The purported observation of a state $\Theta^+$ with strangeness S = +1 led to its quark model interpretation in terms of a pentaquark combination involving a triquark-diquark structure -- the Karliner-Lipkin model. In this work, the proper…
Relativistic particles with spins $J>0$ are described by means of multicomponent wave functions which transform covariantly according to Lorentz-group representations that contain at rest the spin of interest. The symmetry group of…
We study multifractal properties of wave functions for a one-parameter family of quantum maps displaying the whole range of spectral statistics intermediate between integrable and chaotic statistics. We perform extensive numerical…
In this paper, we find the number of representations of the quadratic form $x_1^2+ x_1x_2 + x_2^2 + \ldots + x_{2k-1}^2 + x_{2k-1}x_{2k} + x_{2k}^2,$ for $k=7,9,11,12,14$ using the theory of modular forms. By comparing our formulas with the…
Multiple-integral representations of the (skew-)Macdonald symmetric functions are obtained. Some bosonization schemes for the integral representations are also constructed.
For a rational function of several variables with nonnegative imaginary part on the upper poly-half-plane, the matrix representations are obtained.
The polarization transfer coefficients of a relativistic magnetized plasma are derived. These results apply to any momentum distribution function of the particles, isotropic or anisotropic. Particles interact with the radiation either in a…
The covariance between real finite variance random variables can be expressed as the commutator of taking expectations and multiplying, both viewed as operators extended to act jointly on pairs of functions. The efficient influence curve of…
There are given conditions for represention of a function of many arguments as the difference of convex functions.
A set of gauge transformations of a relativistic field of quantum harmonic oscillators is studied in a mathematically rigorous manner. Each wave function in the domain of the number operator of a single oscillator generates a…
A study of fundamental geometrical interactions shows that the Dirac electron can be represented as a conformal wave. A Riemannian space is used, having coordinates that transform locally as spinors. The wave function becomes a gradient.…
Electron Paramagnetic Resonance experiments show that the decay of Rabi oscillations of ensembles of spin qubits depends noticeably on the microwave power and more precisely on the Rabi frequency, an effect recently called "driven…
In this work, we review formulations of wave equations for spin-3/2 fields constructed from different Lorentz group representations. We analyze the Joss-Weinberg single-spin chiral representation and the double-spin chiral representation,…
This paper which is part of a series, is devoted to several technical issues. In the first part of the paper, we discuss the usual wavefunctions in the CM frame for baryons, by clarifying the representations of the three-quark permutation…