[5] **viXra:1905.0616 [pdf]**
*submitted on 2019-05-31 05:50:12*

**Authors:** Vu B Ho

**Comments:** 9 Pages.

In this work we discuss a geometric and topological quantisation of mass by extending our work on the principle of least action in which the quantisation of both the angular momentum of a Bohr hydrogen atom and the charge of an elementary particle can be shown to be quantised from the continuous deformation of a differentiable manifold. Similar to the case of the quantisation of charge using the two-dimensional Ricci scalar curvature, we show that in the case of three-dimensional differentiable manifolds we can apply the Yamabe problem, which states that any Riemannian metric on a compact smooth manifold of dimension greater or equal to three is conformal to a metric with constant scalar curvature, to show that mass can also be quantised by the deformation of differentiable manifolds. The Yamabe problem is a generalisation of the uniformisation theorem for two-dimensional differentiable manifolds. We also discuss whether quantum particles can be expressed as direct sums of quantum masses when they possess mathematical structures of differentiable manifolds, with the quantum masses are considered as prime manifolds. This may be regarded as a physical manifestation of an established mathematical proposition in differential geometry and topology that states that any compact, connected, and orientable differentiable manifold M can be decomposed into prime manifolds and the decomposition is unique up to an absorption or emission of 3-spheres S^3. This process of decomposition of differentiable manifolds into prime manifolds and the radiation of 3-spheres is similar to the radiation of the quanta of physical fields from a quantum system, such as the radiation of photons from a hydrogen atom. Even though our work is highly speculative and suggestive, we hope that it may pay way for further rigorous mathematical investigations into whether mass is also quantised like charge and other fundamental entities in physics.

**Category:** Mathematical Physics

[4] **viXra:1905.0587 [pdf]**
*submitted on 2019-05-29 07:46:52*

**Authors:** Michele Nardelli, Antonio Nardelli

**Comments:** 186 Pages.

In the present research thesis, we have obtained various and interesting mathematical connections with the Ramanujan’s numbers 1728, 1729, 728, 729 and some sectors of Particle Physics and Supersymmetry

**Category:** Mathematical Physics

[3] **viXra:1905.0268 [pdf]**
*submitted on 2019-05-17 17:43:20*

**Authors:** Abdelmajid Ben Hadj Salem

**Comments:** 22 Pages. In French.

In this note, we study Einstein equations (EE) of general relativity considering a manifold M with a diagonal metric g_{ij}. We calculate the expression of the components of Ricci and Riemann tensors and the value of the scalar curvature R. Then we give the expression of the (EE) :
-a- for the case where g_{ii}=g_i=g_i(x_i);
-b- for the case where g_1=g_1(x_1=t) and g_i=g_i(t,x_i) for i=2,3,4$;
-c- for the case (b) with x_4=z_0=constant.

**Category:** Mathematical Physics

[2] **viXra:1905.0142 [pdf]**
*submitted on 2019-05-09 19:53:08*

**Authors:** Andrei Lucian Dragoi

**Comments:** 7 Pages.

This paper proposes a new definition of life forms in relation to a new type of “hybrid” causality, gravity and the possible existence of hierarchical parallel universes.
Keywords: life forms, gravity, hierarchical parallel universes;

**Category:** Mathematical Physics

[1] **viXra:1905.0012 [pdf]**
*replaced on 2019-09-14 23:48:35*

**Authors:** Dang Dang

**Comments:** 29 Pages.

The idea of energy, matter, and motion has perplexed many philosophers and physicists from antiquity to modern physics, from Plato to Einstein. New and developing physical theories raise different interpretations of energy and matter but no complete theory of everything exists at present. However, there is a law we can almost take for granted: the law of conservation of energy, which states that energy cannot be created nor destroyed although it can be transformed from one form to another. After establishing the foundational theory and history of conservation of energy, this literature review aims to provide an overview of the concept of mass and energy conservation in two of the most fundamental physical theories - quantum mechanics and general relativity. Consequences and challenges of mass-energy conservation and equivalence - dark energy - is studied in an introductory manner.

**Category:** Mathematical Physics