Related papers: Irreducible tensor form of three-particle operator…
This work establishes a systematic framework for operator construction in the non-relativistic effective field theory, incorporating both the three dimensional Euclidean symmetry and the internal symmetries. By employing double cover of the…
We construct a second-quantized representation with a structure of balanced ternary formalism, which involves three substances in organic molecular materials, namely electron, hole and charge-transfer exciton, into a uniform framework. The…
We develop a new formalism to treat nuclear many-body systems using bare nucleon-nucleon interaction. It has become evident that the tensor interaction plays important role in nuclear many-body systems due to the role of the pion in…
Following Brown[1], we construct composite operators for the scalar $\phi^3$ theory in six dimensions using renormalisation group methods with dimensional regularisation. We express bare scalar operators in terms of renormalised composite…
Whether for fundamental studies or nuclear data evaluations, first-principle calculations of atomic nuclei constitute the path forward. Today, performing \textit{ab initio} calculations (a) of heavy nuclei, (b) of doubly open-shell nuclei…
In the paper, analysis of a quantum optical system--three-level atom in a quantum electromagnetic field is given. Evolution operators are constructed in closed form.
This is the fourth part of a series of papers developing a tensor product theory of modules for a vertex operator algebra. In this paper, We establish the associativity of $P(z)$-tensor products for nonzero complex numbers $z$ constructed…
The transformation properties of irreducible tensor operators and the applicability of the Wigner-Eckart theorem to finite magnetic groups have been studied.
We consider $u_t=u^{\alpha} u_{xxx}+n(u)u_xu_{xx}+m(u)u_x^3+ r(u)u_{xx} +p(u)u_x^2 + q(u)u_x+s(u)$ with $\alpha=0$ and $\alpha=3$, for those functional forms of $m, n, p, q, r, s$ for which the equation is integrable in the sense of an…
We formulate a general framework for the study of operator systems arising from discrete groups. We study in detail the operator system of the free group on $n$ generators, as well as the operator systems of the free products of finitely…
We examine mathematical questions around angle (or phase) operator associated with a number operator through a short list of basic requirements. We implement three methods of construction of quantum angle. The first one is based on operator…
We resolve a number of questions related to an analytic description of electromagnetic form factors of non-Dirac particles with the rest spin 1/2. We find the general structure of a matrix antisymmetric tensor operator. We obtain two…
We discuss characterizations of the decoupleability, partial and full, of trilinear or completely symmetric real $n\times n\times n$ tensors, which inform on the structure of certain coupled KPZ equations. Informally, when the tensor is…
Analytical formulas for some useful three-particles integrals are derived. Many of these integrals include Bessel and/or trigonometric functions of one and two interparticle (relative) coordinates $r_{32}, r_{31}$ and $r_{21}$. The formulas…
Irreducible modules of the 3-permutation orbifold of a rank one lattice vertex operator algebra are listed explicitly. Fusion rules are determined by using the quantum dimensions. The $S$-matrix is also given.
It is shown that the mixed states of a closed dynamics support a reduplicated symmetry, which is reduced back to the subgroup of the original symmetry group when the dynamics is open. The elementary components of the open dynamics are…
Crystal tensor operators, which tranform under U_q->0(sl(2)), in analogous way as the vectors of the crystal basis, are introduced. The Wigner-Eckart theorem for the crystal tensor is defined: the selection rules depend on the initial state…
We address the general question of how to reconstruct the field content of a quantum field theory from a given scattering theory in the context of the form factor program. For the $SU(3)_2$-homogeneous Sine-Gordon model we construct…
We use Faddeev's decomposition to solve the shell-model problem for three nucleons. The dependence on harmonic-oscillator excitations allowed in the model space, up to $32 \hbar\Omega$ in the present calculations, and on the…
We explicitly establish a unitary correspondence between spherical irreducible tensor operators and cartesian tensor operators of any rank. That unitary relation is implemented by means of a basis of integer-spin wave functions that…