相关论文: The volume operator for spin networks with planar …

Since the discovery a century ago, spin describing the intrinsic angular momentum of massive elementary particles has exposed its nature and significant roles in wide ranges of (relativistic) quantum phenomena and practical applications for…

Operators that are associated with several important quantities, like angular momentum, play a double role: they are both generators of the symmetry group and ``observables.'' The analysis of different splittings of angular momentum into…

We pursue an analogy of the Schur-Weyl reciprocity for the spinor groups and pick up the irreducible spin representations in the tensor space $\Delta \textstyle{\bigotimes \bigotimes^k V}$. Here $\Delta$ is the fundamental representation of…

We discuss the problem of spin-orbit interaction in a 2D chaotic or diffusive quantum dot in the presence of exchange correlations. Spin-orbit scattering breaks spin rotation invariance, and in the crossover regime between different…

We derive a closed formula for the matrix elements of the volume operator for canonical Lorentzian quantum gravity in four spacetime dimensions in the continuum in a spin-network basis. We also display a new technique of regularization…

We give a formula for the first eigenvalue of the Dirac operator acting on spinor fields of a spin compact irreducible symmetric space $G/K$.

We derive a relativistic-covariant spin operator for massive case directly from space-time symmetry in Minkowski space-time and investigate the physical properties of a derived spin operator. In the derivation we require only two…

Let $V=\bigotimes_{k=1}^{N} V_{k}$ be the $N$ spin-$j$ Hilbert space with $d=2j+1$-dimensional single particle space. We fix an orthonormal basis $\{|m_i\rangle\}$ for each $V_{k}$, with weight $m_i\in \{-j,\ldots j\}$. Let $V_{(w)}$ be the…

The tensorial form of the spin-other-orbit interaction operator in the formalism of second quantization is presented. Such an expression is needed to calculate both diagonal and off-diagonal matrix elements according to an approach, based…

We define supersymmetric spin networks, which provide a complete set of gauge invariant states for supergravity and supersymmetric gauge theories. The particular case of Osp(1/2) is studied in detail and applied to the non-perturbative…

We show how spin networks can be described and evaluated as Feynman integrals over an internal space. This description can, in particular, be applied to the so-called simple SO(D) spin networks that are of importance for higher-dimensional…

A local transformation from fermionic operators to spin matrices is proposed and studied in this work. For this purpose, a system of fermions on a lattice is considered and one applies the scheme to replace the fermionic variables with spin…

We present a symplectic integrator, based on the canonical midpoint rule, for classical spin systems in which each spin is a unit vector in $\mathbb{R}^3$. Unlike splitting methods, it is defined for all Hamiltonians, and is…

We analyze perturbations of the harmonic oscillator type operators in a Hilbert space H, i.e. of the self-adjoint operator with simple positive eigenvalues $\mu_k$ satisfying $\mu_{k+1}-\mu_k \geq \Delta >0$. Perturbations are considered in…

The rotation of the bodies and the eccentricity of the orbit have significant effects on the emitted gravitational radiation of binary systems. This work focuses on the evaluation of the gravitational wave polarization states for spinning…

In this paper the relativistic quantum mechanics is considered in the framework of the nonstandard synchronization scheme for clocks. Such a synchronization preserves Poincar{\'e} covariance but (at least formally) distinguishes an inertial…

By the use of complete orthonormal sets of nonrelativistic scalar orbitals introduced by the author in previous papers the new complete orthonormal basis sets for two-and four-component spinor wave functions, and Slater spinor orbitals…

"The Spin Foams for People Without the 3d/4d Imagination" could be an alternative title of our work. We derive spin foams from operator spin network diagrams} we introduce. Our diagrams are the spin network analogy of the Feynman diagrams.…

Space-time multivectors in Clifford algebra (space-time algebra) and their application to nonlinear electrodynamics are considered. Functional product and infinitesimal operators for translation and rotation groups are introduced, where…

We describe preliminary results of a detailed numerical analysis of the volume operator as formulated by Ashtekar and Lewandowski. Due to a simplified explicit expression for its matrix elements, it is possible for the first time to treat…