## Tags » Mathematical Physics

#### Evidence of the square root of Brownian motion

A mathematical proof of existence of a stochastic process involving fractional exponents seemed out of question after some mathematicians claimed this cannot not exist. This observation is strongly linked to the current definition and may undergo revision if nature does not agree with it. 376 more words

Physics

#### Recursive structure in the definitions of gauge-invariant variables for any order perturbations [CL]

http://arxiv.org/abs/1403.1004

The construction of gauge-invariant variables for any order perturbations is discussed. Explicit constructions of the gauge-invariant variables for perturbations to 4th order are shown. From these explicit construction, the recursive structure in the definitions of gauge-invariant variables for any order perturbations is found. 24 more words

Cosmology And Extragalactic Astrophysics

#### Vector (Linear) Spaces - Part 1

Please read the first chapter of Geometric Algebra for Physicists, up to section 1.1  (it’s short, and to the point).

Geometric Algebra

#### Nailing down the Yang-Mills problem

Millennium problems represent a major challenge for physicists and mathematicians. So far, the only one that has been solved was the Poincaré conjecture (now a theorem) by… 889 more words

Physics

#### fundamental physical constants

(the following is a little wordy, but hopefully sets out why numbers might be human inventions, but the physical constants of quantity they describe and the numerical relationships between quantities are *not* human inventions… they are human *descriptions*.) 138 more words

Mathematical Universe Hypothesis

#### number theory and physics

there is a growing body of evidence that number theory and physics are connected

a playfully serious theory of everything offers an explanation for how and why these connections exist, and predicts (confidently) that many more connections will be discovered in the coming years

Mathematical Universe Hypothesis

#### A Riccati equation based approach to isotropic scalar field cosmologies with arbitrary self-interaction potentials [CL]

http://arxiv.org/abs/1402.4363

Gravitationally coupled scalar fields $\phi$, distinguished by the choice of an effective self-interaction potential $V(\phi )$, simulating a temporarily non-vanishing cosmological term, can generate both inflation and late time acceleration. 91 more words

Cosmology And Extragalactic Astrophysics