Classical string solutions in Non-Relativistic AdS$_5\times$S$^5$: Closed and Twisted sectors

We find classical closed string solutions to the non-relativistic AdS$_5\times$S$^5$ string theory which are the analogue of the BMN and GKP solutions for the relativistic theory. We show that non-relativistic AdS$_5\times$S$^5$ string theory admits a $\mathbb{Z}_2$ orbifold symmetry which allows us to impose twisted boundary conditions. Among the solutions in the twisted sector, we find the one around which the semiclassical expansion in \href{https://arxiv.org/abs/2102.00008}{arXiv:2102.00008} takes place.

Falsification of Einstein’s relativity

In 1915, Einstein published general relativity. In 1916, he published a German language book about relativity, which contained his marble table thought experiment for explaining a continuum. Without realizing it, Einstein introduced a quantized two-dimensional discontinuum geometry and inadvertently falsified the marble table thought experiment continuum, which falsified relativity. The foundations of physics do not now (and never did) include a fundamentally sound relativistic theory to account for macroscopic phenomena. It is well known the success of relativity and its singularity problem indicate general relativity is a first approximation of a more fundamental theory. Combine that indication with the falsification of relativity and it is apparent, without speculation, that relativity is now and always was a first approximation of a more fundamental theory. A possible way forward to the more fundamental theory is developing a discontinuum physics based on the quantized two-dimensional discontinuum geometry or an algebraic version of it. Such discontinuum physics is not presented, because it is beyond the scope of this paper.

A relativistic theory of the field II: Hamilton's principle and Bianchi's identities

As gravitation and electromagnetism are closely analogous long-range interactions, and the current formulation of gravitation is given in terms of geometry. Thence emerges a relativistic theory of the field by generalization of the general relativity. The derivation presented shows how naturally we can extend general relativity theory to a non-symmetric field, and that the field-equations are really the generalizations of the gravitational equations. With curvature tensor and the variational principle, we will deduce the field equations and Bianchi's identities. In consecuense, the field equations will find from Bianchi's identities.

A relativistic theory of the field

As gravitation and electromagnetism are closely analogous long-range interactions, and the current formulation of gravitation is given in terms of geometry, we expect the latter also to appear through the geometry. This unification has however, remained an unfulfilled goal. Thence emerges a relativistic theory of the asymmetric field by generalization of the general relativity. It will demonstrate in a new way that the field-equations chosen for the non-symmetric fields are really the natural ones.

Multimagnetic monopoles

In this work we investigate the presence of magnetic monopoles that engender multimagnetic structures, which arise from an appropriate extension of the $$\mathrm{SU(2)}$$ SU ( 2 ) gauge group. The investigation is based on a modified relativistic theory that contain several gauge and matter fields, leading to a Bogomol’nyi bound and thus to a first order framework, from which stable multimagnetic solutions can be constructed. We illustrate our findings with several examples of stable magnetic monopoles with multimagnetic properties.

Relativistic spin sum rules and the role of the pivot

Spin sum rules depend on the choice of a pivot, i.e. the point about which the angular momentum is defined, usually identified with the center of the nucleon. The latter is however not unique in a relativistic theory and has led to apparently contradictory results in the literature. Using the recently developed phase-space approach, we compute for the first time the contribution associated with the motion of the center of the nucleon, and we derive a general spin sum rule which reduces to established results after appropriate choices for the pivot and the spin component.