Exact Solutions of Einstein's Field Equations: Notation

Clifford Algebras and the Classical Groups: The classical groups

An alternative approach to Einstein's theory of General Relativity (GR) is reviewed, which is motivated by a range of serious theoretical issues inflicting the theory, such as the cosmological constant problem, presence of non-Machian solutions, problems related with the energy-stress tensor $T^{ik}$ and unphysical solutions. 
The new approach emanates from a critical analysis of these problems, providing a novel insight that the matter fields, together with the ensuing gravitational field, are already present inherently in the spacetime without taking recourse to $T^{ik}$. Supported by numerous evidences, the new insight revolutionizes our views on the representation of the source of gravitation and establishes the spacetime itself as the source, which becomes crucial for understanding the unresolved issues in a unified manner. This leads to a new paradigm in GR by establishing equation $R^{ik}=0$ as the field equation of gravitation plus inertia in the very presence of matter.

Einstein and Beyond: A Critical Perspective on General Relativity

Quaternionic quantum mechanics in real Hilbert space

(2 < p < 4) [200]. (Uq(∫u(1, 1)), oq1/2(2n)) [92]. 1 [273, 79, 304, 119]. 1 + 1 [252]. 2 [352, 318, 226, 40, 233, 157, 299, 60]. 2× 2 [185]. 3 [456, 363, 58, 18, 351]. ∗ [238]. 2 [277]. 3 [350]. p [282]. B−L [427]. α [216, 483]. α− z [322]. N = 2 [507]. D [222]. ẍ+ f(x)ẋ + g(x) = 0 [112, 111, 8, 5, 6]. Eτ,ηgl3 [148]. g [300]. κ [244]. L [205, 117]. L [164]. L∞ [368]. M [539]. P [27]. R [147]. Z2 [565]. Z n 2 [131]. Z2 × Z2 [25]. D(X) [166]. S(N) [110]. ∫l2 [154]. SU(2) [210]. N [196, 242]. O [386]. osp(1|2) [565]. p [113, 468]. p(x) [17]. q [437, 220, 92, 183]. R, d = 1, 2, 3 [279]. SDiff(S) [32]. σ [526]. SLq(2) [185]. SU(N) [490]. τ [440]. U(1) N [507]. Uq(sl 2) [185]. φ 2k [283]. φ [553]. φ4 [365]. ∨ [466]. VOA[M4] [33]. Z [550].

/pdf/a-complete-bibliography-of-publications-in-the-journal-of-3brkwhz8a7.pdf

A Complete Bibliography of Publications in the Journal of Mathematical Physics: 2005{2009

In this paper, rotating strings in three directions of $AdS_4 \times \mathbb{CP}^3$ geometry are studied; its divergent energy limit, and conserved charges are also determined. An interpretation of these configurations as either giant magnons or spiky strings are discussed.

Classical strings in $AdS_4\times\mathbb{CP}^3$ with three angular momenta

If Ψ is a quaternionic wave function, then iΨ ≠ Ψi Thus, there are two versions of the quaternionic Schrodinger equation (QSE) In this article, we present the second possibility for solving the Q

/pdf/quaternionic-quantum-particles-new-solutions-e9x3jcx500.pdf

Quaternionic Quantum Particles: New Solutions

The one-dimensional infinite square well is the simplest solution of quantum mechanics, and consequently one of the most important. In this article, we provide this solution using the real Hilbert space approach to quaternic quantum mechanics ($\mathbbm{H}$QM). We further provide the one-dimensional finite as well and a method to generate quaternic solutions from non-degenerate complex solutions.

Square-well potential in quaternic quantum mechanics

This paper describes general relativity at the gravito-electromagnetic precision level as a constrained field theory. In this novel formulation, the gravity field comprises two auxiliary fields, a static matter field and a moving matter field. Equations of motion, continuity equation, energy conservation, field tensor, energy-momentum tensor, constraints and Lagrangian formulation are presented as a simple and unified formulation that can be useful for future research.

A novel covariant approach to gravito-electromagnetism

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Papers

Classical strings in $AdS_4\times\mathbb{CP}^3$ with three angular momenta

Quaternionic Quantum Particles: New Solutions

Square-well potential in quaternic quantum mechanics

A novel covariant approach to gravito-electromagnetism