Charged and spinning test-body quantities

Use the smooth, time-oriented Lorentzian background $(M,g,N)$, signature $(-,+,+,+)$, and the distinct chart, observer, congruence, tetrad and worldline meanings of Particle spacetime, observers and worldlines. The metric and time orientation are prescribed data, not dynamical variables. A charged spinning test body in this definition consists of the following model quantities along a massive worldline $z:I\to M$:

• $I\subseteq \mathbb{R}$ is an open interval whose parameter is proper time $\tau$ in seconds; $z$ is $C^2$, future-directed and timelike, and $U:=dz\mathrm{/}d\tau$ obeys $g(U,U)=-c^2$. The SI conversion constant is $c>0$ metres per second; in a flat specialization use the affine Minkowski model and the proper-time decomposition of Oriented time-oriented affine Minkowski space (the spacetime primitives) and Norms of four-velocity and four-acceleration, and the observer rest-space decomposition.
• The constant rest-mass parameter $m>0$ has unit kilogram, and the constant charge parameter $q\in \mathbb{R}$ has unit coulomb. They are primitive model parameters; this definition does not derive them from the background field or from another framework.
• The kinetic four-momentum is the derived vector $P:=mU$ along $z$, with unit kilogram metre per second. It is distinct from the potential-dependent covector defined in Gauge boundary term and kinetic/canonical momentum.
• The spin or polarization vector is a $C^1$ tangent vector field $s(\tau )\in T_{z(\tau )}M$ constrained by $g(s,U)=0$, so it lies in the positive-definite instantaneous rest space $U^{\perp }$. Its unit is angular momentum, kilogram metre squared per second. This is a classical model vector; no quantization or quantum spin state is defined here.
• The gyromagnetic ratio $g_s\in \mathbb{R}$ is a dimensionless primitive species parameter. In the instantaneous rest space the model defines the magnetic-moment vector by $\mu =(g_{s}q\mathrm{/}2m)s$, with unit ampere metre squared. No value $g_s=2$ is assumed, and this constitutive relation is not deduced from Lorentz covariance or classical electromagnetism.
• The prescribed external electromagnetic field is a $C^1$ alternating covariant two-tensor $F$ on an open region of $M$, independent of the unknown curve. Define $F^{\mathrm{♯}}:TM\to TM$ by $g(F^{\mathrm{♯}}(v),w)=F(w,v)$. In the flat specialization, a named inertial chart with $x^0=ct$ and $x^i$ in metres uses $F_{0i}=-E_i\mathrm{/}c$ and $F_{ij}={ϵ}_{ijk}{B}_k$, matching The electromagnetic two-form, its observer decomposition and the four-current. On the curved background, $F$ is only a two-form; at an event its components in a chosen orthonormal tetrad use the same algebraic convention. Such a tetrad is a basis field, not a coordinate chart or an observer congruence, as distinguished in Particle spacetime, observers and worldlines. The components in an orthonormal tetrad have tesla units. This is an explicit curved-background model input. The cited EM supplier is a flat Minkowski definition and does not derive a curved field or curved Maxwell system.
• On any open potential domain where a $C^2$ covector field $A$ exists, $F=dA$ with components $F_{ab}={\mathrm{\partial }}_a{A}_b-{\mathrm{\partial }}_b{A}_a$ and $A$ has tesla metre components in the stated coordinates. No global potential is assumed, and no Maxwell equation or constitutive law is imposed here.

This is a test-body model on a fixed background: self-gravity, gravitational backreaction, self-field evaluation, radiation reaction, collisions, electric dipole moments, field-gradient translational forces and higher multipoles are outside this definition. Units follow the framework-local SI conventions of Framework-local SI units, the vacuum constants and the exact/measured status of their values and do not identify quantities across frameworks.