Related papers: Vectors and Operators For Spin 1 Derived From Firs…
This article develops a variational formulation for the relativistic Klein-Gordon equation. The main results are obtained through an extension of the classical mechanics approach to a more general context, which in some sense, includes the…
We present a streamlined axiom system of special relativity in first-order logic. From this axiom system we "derive" an axiom system of general relativity in two natural steps. We will also see how the axioms of special relativity transform…
We develop a general formalism for computing classical observables for relativistic scattering of spinning particles, directly from on-shell amplitudes. We then apply this formalism to minimally coupled Einstein-gravity amplitudes for the…
We generalize first-species counterpoint theory to arbitrary rings and obtain some new counting and maximization results that enrich the theory of admitted successors, pointing to a structural approach, beyond computations. The…
An analytical formula is obtained to describe the evolution of the average populations of spin components of spin-1 atomic gases. The formula is derived from the exact time-dependent solution of the Hamiltonian $H_{S}=c mathbf{S}^{2}$…
We present a rigorous explicit expression for an extensive number of local conserved quantities in the XYZ spin-1/2 chain with general coupling constants. All the coefficients of operators in each local conserved quantity are calculated. We…
We consider the spin-$J$ XXZ-Hamiltonian on general graphs $\mathcal{G}$ and show its equivalence to a direct sum of discrete many-particle Schr\"odinger type operators on what we call "$N$-particle graphs with maximal local occupation…
We develop a new setting for the exponential principle in the context of multisort species, where indecomposable objects are generated intrinsically instead of being given in advance. Our approach uses the language of functors and natural…
Assume that A is a bounded selfadjoint operator in a Hilbert space H. Then, the variational principle is obtained for some functional. As an application of this principle, a variational principle for the electrical capacitance of a…
Lagrangian and Hamiltonian formulations of a free spinning particle in 2+1-dimensions or {\it anyon} are established, following closely the analysis of Hanson and Regge. Two viable (and inequivalent) Lagrangians are derived. It is also…
We revisit the construction of higher spin representations by Kleinschmidt and Nicolai for E10, generalize it to arbitrary simply laced types, and provide a coordinate-free approach to the 3/2-spin and 5/2-spin representations. Moreover, we…
We develop a first-order approximation method for the influence of spin on the motion of extended spinning test masses in a gravitational field. This approach is illustrated for approximately circular equatorial motion in the exterior Kerr…
We define a generalization of the winding number of a piecewise $C^1$ cycle in the complex plane which has a geometric meaning also for points which lie on the cycle. The computation of this winding number relies on the Cauchy principal…
A general concept for the derivation of symmetry-based pseudo spin Hamiltonians is described. It systematically bridges the gap between the atomistic basis and various pseudo spin models presented in literature. It thus allows the…
A method is presented, and used, for determining any heat-kernel coefficient for the form-valued Laplacian on the $D$-ball as an explicit function of dimension and form order. The calculation is offerred as a particular application of a…
A method of calculation for the variational derivatives for gravitational actions in the pseudo-Riemannian case is proposed as a practical variant of the first order formalism with constraints. The method is then used to derive the metric…
The 2(2s+1)-component relativistic basis spinors for the arbitrary spin particles are established in position, momentum and four-dimensional spaces, where s=0,1 / 2,1, 3 / 2, 2, ... . These spinors for integral- and half-integral spins are…
One of the theoretical pillars that sustain certain machine learning models are universal approximation theorems, which prove that they can approximate all functions from a function class to arbitrary precision. Independently, classical…
We investigate certain classes of integrable classical or quantum spin systems. The first class is characterized by the recursively defined property $P$ saying that the spin system consists of a single spin or can be decomposed into two…
Rotational invariance of physical laws is a generally accepted principle. We show that it leads to an additional external constraint on local realistic models of physical phenomena involving measurements of multiparticle spin 1/2…