LOG#243. Elliptic trigonometry.

Jacobi elliptic functions allow to solve many physical problems. Today I will review briefly some features. Let me first highlight that the simple pendulum, Euler asymmetric top, the heavy top, the Duffing oscillator, the Seiffert spiral motion, and the Ginzburg-Landau … Continue reading

LOG#186. Polylogarithmic condensates.

Today, I return to my best friends. The polylogs! Are you ready for polylog wars? The polylogarithm can be represented by the next integral: (1)   As you know, if you follow my blog, you have         … Continue reading

LOG#148. Path integral (III).

Round 3! Fight… with path integrals! XD Introduction: generic aspects Consider a particle moving in one dimension (the extension to ND is trivial), the hamiltonian being of the usual form: The fundamental question and problem in the path integral (PI) … Continue reading

LOG#096. Group theory(XVI).

Given any physical system, we can perform certain “operations” or “transformations” with it. Some examples are well known: rotations, traslations, scale transformations, conformal transformations, Lorentz transformations,… The ultimate quest of physics is to find the most general “symmetry group” leaving … Continue reading

LOG#036. Action and relativity.

The hamiltonian formalism and the hamiltonian H in special relativity has some issues with the definition. In the case of the free particle one possible definition, not completely covariant, is the relativistic energy     There are two others interesting … Continue reading