相关论文: A Note on $3 + 1$ Dimensionality
We survey some known facts and open questions concerning the global properties of 3+1 dimensional spacetimes containing a compact Cauchy surface. We consider spacetimes with an $\ell$-dimensional Lie algebra of space-like Killing fields.…
A physical theory of the world is presented under the unifying principle that all of nature is laid out before us and experienced through the passage of time. The one-dimensional progression in time is opened out into a multi-dimensional…
We describe the twisted space-time symmetries which imply the quantum Poincar\'{e} covariance of noncommutative Minkowski spaces, with constant, Lie algebraic and quadratic commutators. Further we present the relativistic and…
The logical line is traced of formulation of theory of mechanics founded on the basic correlations of mathematics of hypercomplex numbers and associated geometric images. Namely, it is shown that the physical equations of quantum, classical…
A solution to the cosmological constant problem has been proposed in which our universe is a 3-brane in a 5-dimensional spacetime. With a bulk scalar, the field equations admit a Poincare invariant brane solution regardless of the value of…
Several approaches to the quantum-gravity problem predict that spacetime should be "fuzzy", but have been so far unable to provide a crisp physical characterization of this notion. An intuitive picture of spacetime fuzziness has been…
We assume that our universe originated from highly excited and interacting strings with coupling constant g_s = {\cal O} (1). Fluctuations of spacetime geometry are large in such strings and the physics dictating the emergence of a final…
Fractal sets, by definition, are non-differentiable, however their dimension can be continuous, differentiable, and arithmetically manipulable as function of their construction parameters. A new arithmetic for fractal dimension of polyadic…
A non-commutative multi-dimensional cosmological model is introduced and used to address the issues of compactification and stabilization of extra dimensions and the cosmological constant problem. We show that in such a scenario these…
A physical interpretation of axioms of the differential structure of space-time is presented. Consequences of such interpretation for cosmic string's space-time with a scalar field are studied. It is shown that the assumption of smoothness…
Why does the physical 4-dimensional space have a 3 + 1 signature rather than a 4 + 0 or a 2 + 2 for its metric? We give a simple explanation based largely on a group-theoretic argument a la Wigner. Applied to flat spaces of higher…
The contemporary physics has revealed growing evidences that the emergence can be applied to not only biology and condensed matter systems but also gravity and spacetime. We observe that noncommutative spacetime necessarily implies emergent…
For over a century Minkowskian spacetime has dominated discussions of space contraction and time dilation within special relativity. Brown and Pooley have called into question both the assumptions of Minkowski and the effects his presumed…
As an example of a noncommutative space we discuss the quantum 3-dimensional Euclidean space $R^3_q$ together with its symmetry structure in great detail. The algebraic structure and the representation theory are clarified and discrete…
We briefly review ideas about ``noncommutativity of space-time'' and approaches toward a corresponding theory of gravity.
First, we briefly review the Coset Space Dimensional Reduction scheme and the results of the best model so far. Then, we present the introduction of fuzzy coset spaces used as extra dimensions and perform a dimensional reduction. In turn,…
The ${\overline{\mathbb Q}}$-algebra of periods was introduced by Kontsevich and Zagier as complex numbers whose real and imaginary parts are values of absolutely convergent integrals of ${\mathbb Q}$-rational functions over ${\mathbb…
We review the origin of the physical consistency of the Lorentz- Poincar\'e symmetry. We outline seemingly catastrophic physical inconsistencies recently identified for noncanonical-nonunitary generalized theories defined on conventional…
The theory of noncommutative geometry provides an interesting mathematical background for developing new physical models. In particular, it allows one to describe the classical Standard Model coupled to Euclidean gravity. However,…
I review the basis and limitations of plausible inference in cosmology, in particular the limitation that it can only provide fundamentally true inferences when the hypotheses under consideration form a set that is exhaustive. They never…