Relativistic Quantum Mechanics Lecture 2 Books Recommended: Lectures on Quantum Field Theory by Ashok Das Advanced Quantum Mechanics by Schwabl Relativistic Quantum Mechanics by Greiner Quantum Field Theory by Mark Srednicki http://www.physicspages.com/2015/11/12/klein-gordon-equation/ http://www.quantumfieldtheory.info/

Lorentz Transformations (along x-axis) Postulates of special theory of relativity: All the physical laws are same in all inertial frames of reference which are moving with constant velocity relative to each other. There is no absolute or universal frame of reference. (2) The speed of light in vacuum is the same in every inertial frame Lorentz Transformations (along x-axis)

Lorentz Transformations Under Lorentz boost, coordinates transform from one Inertial frame to other as Such that -----(1) --------(2)

Above eq is written as ------(3) In above ω is known as rapidity.

In last eq. ------(4) Such that As Thus

Thus, we write the Lorentz transformation as -------(5) Where, Lorentz transformation matrix ----(6)

We write ---(7) Covariant co-ordinate will transform as

Matrix representing Lorentz transformation are orthogonal

Lorenz transformations leave the length of vector invariant