A Novel Way to Quantize the Harmonic Oscillator and its Connection to Loop Quantum Gravity
Raman Research Institute, Bangalore.
Loop quantum gravity (LQG) is an attempt to quantize Einstein's theory of gravitation while keeping it's general covariance manifest. The quantization techniques used in LQG are quite distinct from the Fock-space methods that we use to quantize non-gravitational interactions. We introduce the basic ideas underlying LQG by applying its methods to quantize a Harmonic oscillator. As we will see, the resulting quantum theory is quite different from the one obtained via Schrodinger quantum mechanics. Nonetheless the well-tested results (e.g. the spectrum of the Harmonic oscillator) can be recovered even in this inequivalent quantization scheme. Only pre-requisite for this talk will be quantum mechanics of Harmonic oscillator.