## Angular Momentum Rule and Scalar Photons

[1] Tian Ma and Shouhong Wang, Quantum Rule of Angular Momentum, AIMS Mathematics, 1:2(2016), 137-143.

[2] Tian Ma and Shouhong Wang, Mathematical Principles of Theoretical Physics, Science Press, 2015

## 1. Angular Momentum Rule of Quantum Systems

Quantum physics is the study of the behavior of matter and energy at molecular, atomic, nuclear, and sub-atomic levels. Two most distinct features of quantum mechanics, drastically different from classical mechanics, are the Heisenberg uncertainty relation and the Pauli exclusion principle.

We present a new feature, the angular momentum rule, discovered recently by the authors [1, 2], This new angular momentum rule can be considered as an addition to the Heisenberg uncertainty relation and the Pauli exclusion principle in quantum mechanics.

Quantum Rule of Angular Momentum [1, 2]. Only fermions with spin ${J=\frac{1}{2}}$ and bosons with ${J=0}$ can rotate around a center with zero moment of force, and particles with ${J\neq 0,\frac{1}{2}}$ will move on a straight line unless there is a nonzero moment of force present.

This quantum mechanical rule is important for the structure of atomic and sub-atomic particles. In fact, the rule gives the very reason why the basic constituents of atomic and sub-atomic particles are all spin-${\frac{1}{2}}$ fermions.

The angular momentum rule provides the theoretical evidence and support of scalar photons, a recent prediction from our unified field theory and the weakton model of elementary particles.

## 2. Prediction of Scalar Photons

First, we recall that the photon, denoted by ${\gamma}$, is the mediator of the electromagnetic force. The photon is a massless spin-1 particle, described by a vector field ${A_\mu}$ defined on the space-time manifold, which obeys the Maxwell equations:

$\displaystyle \partial^\mu F_{\mu\nu}=0, \qquad F_{\mu\nu} = \partial_\mu A_\nu - \partial_\nu A_\mu.$

Second, the scalar photon, denoted by ${\gamma_0}$, was first introduced as a natural byproduct of our unified field theory based on the principle interaction dynamics (PID), which we have discussed in the previous posts. The scalar photon ${\gamma_0}$ is a massless, spin-0 particle, described by a scalar field ${\phi_0}$, satisfying the following Klein-Gordon equation:

$\displaystyle \Box \phi_0=0.$

Third, the puzzling decay and reaction behavior of subatomic particles suggest that there must be interior structure of charged leptons, quarks and mediators. Careful examinations of subatomic decays/reactions lead us to propose six elementary particles, which we call weaktons, and their anti-particles:

$\displaystyle w^*, \quad w_1, \quad w_2, \quad \nu_e, \quad \nu_{\mu}, \quad \nu_{\tau},$

$\displaystyle \bar{w}^*, \quad \bar{w}_1, \quad \bar{w}_2, \quad \bar{\nu}_e, \quad \bar{\nu}_{\mu}, \quad \bar{\nu}_{\tau},$

where ${\nu_e,\nu_{\mu},\nu_{\tau}}$ are the three generation neutrinos, and ${w^*,w_1,w_2}$ are three new particles, which we call ${w}$-weaktons.

Remarkably, the weakton model offers a perfect explanation for all sub-atomic decays. In particular, all decays are achieved by 1) exchanging weaktons and consequently exchanging newly formed quarks, producing new composite particles, and 2) separating the new composite particles by weak and/or strong forces.

In the weakton model, the constituents of the photon ${\gamma}$ is given as follows:

$\displaystyle \gamma =\cos\theta_ww_1\bar{w}_1-\sin\theta_ww_2\bar{w}_2\ (\uparrow \uparrow,\downarrow \downarrow),$

and different spin arrangements of the weaktons give rise naturally to the scalar photon ${\gamma_0}$ with the following constituents:

$\displaystyle \gamma_0=\cos\theta_ww_1\bar{w}_1-\sin\theta_ww_2\bar{w}_2\ (\downarrow \uparrow,\uparrow \downarrow).$

## 3. Bremsstrahlung as an Experimental Evidence for Scalar Photons

It is known that an electron emits photons as its velocity changes, which is called the bremsstrahlung. The reasons why bremsstrahlung can occur is unknown in classical theories.

In fact, our viewpoint is that the bremsstrahlung suggest that a mediator cloud is present near a naked electron, and the mediator cloud contains photons. The angular momentum rule demonstrates that the photons circling the naked electron must be scalar photons, as free vector photons can only take straight line motion. We refer the interested readers to Section 5.4 of [2] for more detailed discussions.

In summary, bremsstrahlung, together with the angular momentum rule, offers an experimental evidence for scalar photons. Of course, further direct experimental verification and discovery of scalar photons are certainly important feasible.