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Einstein's dream of describing elementary particles as solutions of a classical field theory is severely limited by our current understanding of Nature. Quantum theory is inconsistent with any local realistic theory such as evolving…
The acceleration of the cosmic expansion is a fundamental challenge to standard models of particle physics and cosmology. The new physics of dark energy may lie in the nature of gravity, the quantum vacuum, or extra dimensions. I give a…
Relative motion of particles is examined in the context of relational space-time. It is shown that de Broglie waves may be derived as a representation of the coordinate maps between the rest-frames of these particles. Energy and momentum…
The so-called Einstein-Aether theory is General Relativity coupled (at second derivative order) to a dynamical unit time-like vector field (the aether). It is a Lorentz-violating theory, and gained much attention in the recent years. In the…
A new derivation is given of the known generalized position-momentum uncertainty relation, which takes into account gravity. The problem of two massive particles, the relative motion of which is described by the Schroedinger equation, is…
Special theory of relativity has been formulated in a vacuum momentum-energy representation which is equivalent to Einstein special relativity and predicts just the same results as it. Although in this sense such a formulation would be at…
While the standard model accurately describes data at the electroweak scale without inclusion of gravity, beyond the standard model physics is increasingly intertwined with gravitational phenomena and cosmology. Thus gravity mediated…
The presence of a non-zero cosmological term in Einstein field equations can be interpreted as the physical possibility for preferred reference frames without breaking of general covariance. This possibility is used in the process of…
To describe dark energy we introduce a fluid model with no free parameter on the microscopic level. The constituents of this fluid are massless particles which are a dynamical realisation of the unextended $D=(3+1)$ Galilei algebra. These…
We argue that discreteness at the Planck scale (naturally expected to arise from quantum gravity) might manifest in the form of minute violations of energy-momentum conservation of the matter degrees of freedom when described in terms of…
In the framework of the Einstein-aether theory we consider a cosmological model, which describes the evolution of the unit dynamic vector field with activated rotational degree of freedom. We discuss exact solutions of the Einstein-aether…
The motion of spinning relativistic particles in external electromagnetic and gravitational fields is considered. Covariant equations for this motion are demonstrated to possess pathological solutions, when treated nonperturbatively in…
The Standard Model of particle physics is a $SU(3)_c\times SU(2)_L\times U(1)_Y$ gauge theory that can explain the strong, weak, and electromagnetic interactions between the particles. The gravitational interaction is described by…
In this paper we review some aspects of relativistic particles' mechanics in the case of a non-trivial geometry of momentum space. We start with showing how the curved momentum space arises in the theory of gravity in 2+1 dimensions coupled…
In this introductory review article, we explore the special relativistic equations of particle motions and the consequent derivation of Einstein's famous formula $E=mc^2$. Next, we study the special relativistic electromagnetic field…
We revisit the theory of background fields constructed on the BRST-algebra of a spinning particle with $\mathcal{N}=4$ worldline supersymmetry, whose spectrum contains the graviton but no other fields. On a generic background, the closure…
The Standard Model (SM) ascribes the observed mass of elementary particles to an effective interaction between basis states defined without mass terms and a scalar potential associated with the Higgs boson. In the relativistic field theory…
The dynamics of "dipolar particles", i.e. particles endowed with a four-vector mass dipole moment, is investigated using an action principle in general relativity. The action is a specific functional of the particle's world line, and of the…
We propose a new scenario where dark matter belongs to a secluded sector coupled to the Standard Model through energy--momentum tensors. Our model is motivated by constructions where gravity {\it emerges} from a hidden sector, the graviton…
The Einstein$-$Cartan$-$Sciama$-$Kibble theory of gravity naturally extends general relativity to include quantum-mechanical, intrinsic angular momentum of matter by equipping spacetime with torsion. Using the Einstein energy$-$momentum…