Some fundamental mottos: Fundamental spacetime: no more? Fundamental spacetime falls: no more? Fundamentalness vs emergence(ness) is an old fight in Physics. Another typical mantra is not Shamballa but the old endless debate between what theory is fundamental (or basic) … Continue reading

# Category Archives: Calculus

I am going to review the powerful Cartan calculus of differential forms applied to differential geometry. In particular, I will derive the structure equations and the Bianchi identities. Yes! Firstly, in a 2-dim manifold, we and introduce the Cartan 1-forms … Continue reading

Hi, everyone. The saddest thing about job (working with teenagers and other people) is that it delays other stuff, like blogging! So, you should be patient about getting more of “my stuff”. What is going on today? Hyperballs. Or hyperspheres … Continue reading

Hi, there! Today some Kepler third law stuff plus cosmic speed calculations and formulae. Cosmic speed sounds cool…But first… From High School, you surely calculated how fast is A PLANET moving around the sun (or any star, indeed). To simplify … Continue reading

There are some cool identities, very well known to mathematicians and some theoretical physicists or chemists, related with Ramanujan. They are commonly referred as Rogers-Ramanujan identities (Rogers, 1894; Ramanujan 1913,1917 and Rogers and Ramanujan, 1919). They are related to some … Continue reading

In this blog post I am going to define and talk about some interesting objects. They are commonly referred as q-objects in general. The q-Pochhammer symbol is the next product: (1) with . The infinite product extension is also … Continue reading

The year 2013 is coming to its end…And I have a final gift for you. An impossible post! This year was the Bohr model 100th anniversary. I have talked about this subject already, here, here and here. The hydrogen spectrum is very important in … Continue reading

Position or displacement and its various derivatives define an ordered hierarchy of meaningful concepts. There are special names for the derivatives of position (first derivative is called velocity, second derivative is called acceleration, and some other derivatives with proper name), … Continue reading