Related papers: Boosting Wigner's nj-symbols
After a summary of a recently proposed new type of instant form of dynamics (the Wigner-covariant rest-frame instant form), the reduced Hamilton equations in the covariant rest-frame Coulomb gauge for the isolated system of N scalar…
The quantization of the reduced phase-space of the Einstein-Hilbert action for gravity in $2+1D$ has been shown to bring about the emergence, at the quantum level, of a topological quantum field theory endowed with an $SU_q(2)$ quantum…
Nonperturbative model of glueball is studied. The model is based on the nonperturbative quantization technique suggested by Heisenberg. 2- and 4-point Green functions for a gauge potential are expressed in terms of two scalar fields. The…
We address effects of spin-orbit coupling (SOC), phenomenologically added to a two-component Bose-Einstein condensate composed of particles moving by Levy flights, in one- and two-dimensional (1D and 2D) settings. The corresponding system…
The Volume Operator plays a crucial role in the definition of the quantum dynamics of Loop Quantum Gravity (LQG). Efficient calculations for dynamical problems of LQG can therefore be performed only if one has sufficient control over the…
We consider the effective model of $H=-J_{1}\sum_{<i,j>}\mathbf{S}_{i}\cdot \mathbf{S}_{j}-J_{2}\sum_{<i,j>}(\mathbf{S}_{i}\cdot \mathbf{S}_{j}) ^{2}$, describing the Mott insulating phase with odd number of spin-1 bosons in optical…
We define an effective action for spin foam models of quantum gravity by adapting the background field method from quantum field theory. We show that the Regge action is the leading term in the semi-classical expansion of the spin foam…
A theory of Clebsch-Gordan coefficients for $SL(2, C)$ is given using only rational numbers. Features include orthogonality relations, recurrence relations, and Regge's symmetry group. Results follow from elementary representation theory…
Fast, accurate, and stable computation of the Clebsch-Gordan (C-G) coefficients is always desirable, for example, in light scattering simulations, the translation of the multipole fields, quantum physics and chemistry. Current recursive…
We present a study of the excitations of the edge of a two-dimensional electron droplet in a magnetic field in terms of a contour dynamics formalism. We find that, beyond the usual linear approximation, the non-linear analysis yields…
Wave functions and energy eigenvalues of the path integral Hamiltonian are studied in Lorentz frame moving with velocity $v$. The instantaneous interaction produced by the Wilson loop is shown to be reduced by an overall factor…
The model which generalizes Ponzano and Regge $3D$ and Carfora-Martellini-Marzuoli $4D$ euclidean quantum gravity is considered. The euclidean Einstein-Regge action for a $D$-simplex is given in the semiclassical limit by a gaussian…
It has long been argued that higher categories provide the proper algebraic structure underlying state sum invariants of 4-manifolds. This idea has been refined recently, by proposing to use 2-groups and their representations as specific…
The perspective that gravity may govern the unification of all elementary forces calls for extending the gauge-gravity symmetry $SL(2,C)$ to the broader local symmetry $SL(2N,C)$, where $N$ reflects the internal $SU(N)$ subgroup. This…
The decomposition of tensor products of representations into irreducibles is studied for a continuous family of integrable operator representations of $U_q(sl(2,R)$. It is described by an explicit integral transformation involving a…
We present parametrizations of the $\gamma^\ast N \to N(1535)1/2^-$, $\gamma^\ast N \to N(1520)3/2^-$ and $\gamma^\ast N \to \Delta(1232)3/2^+$ transition amplitudes that are compatible with the analytic constraints at the pseudothreshold…
We present a spin foam model in which the fundamental ``bubble amplitudes'' (the analog of the one-loop corrections in quantum field theory) are finite as the cutoff is removed. The model is a natural variant of the field theoretical…
We describe the unitarity approach for the numerical computation of two-loop integral coefficients of scattering amplitudes. It is well known that the leading propagator singularities of an amplitude's integrand are related to products of…
We prove that the asymptotic behavior of the recoupling coefficients of the symmetric group is characterized by a quantum marginal problem -- namely, by the existence of quantum states of three particles with given eigenvalues for their…
We present a systematic technique for constructing Lorentz covariant orbital-spin ($LS$) bases for matrix elements of local operators and the associated form factors, thereby extending the traditional multipole expansion to a Lorentz…