O'Reilly logo

Foundations of Quantum Gravity by James Lindesay

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

4 Group theory in quantum mechanics

Quantum states are best represented as vectors in a complex space. Matrix elements of operations that act on those states mimic relationships familiar to linear algebra, which can be completely described in terms of group theory. The generators for infinitesimal space-time translations have classical correspondence with the momentum-energy of the system. These observations demonstrate the potential usefulness of formal group theory in describing quantum dynamics. This chapter will briefly discuss useful aspects of group theory in formulating quantum mechanics.

4.1 Quantum mechanics and the Galilean group

4.1.1 Vector and ray representations

The Poincaré group structure relates the generators describing boosts, ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required