A symmetric zero mass tensor of rank two is constructed using the superstring modes of excitation which satisfies the physical state constraints of a superstring. These states have one to one correspondence with the quantised operators and are shown to be the absorption and emission quanta of the Minkowski space Lorentz tensor, using the Gupta-Bleuler method of quantisation. The principle of eq...

We study the role of bosonic zero modes in light-cone quantisation on the invariant mass spectrum for the simplified setting of two-dimensional SU(2) Yang-Mills theory coupled to massive scalar adjoint matter. Specifically, we use discretised light-cone quantisation where the momentum modes become discrete. Two types of zero momentum mode appear – constrained and dynamical zero modes. In fact o...

We determine coherent states peaked at classical space-time of the Schwarzschild black hole in the frame-work of canonical quantisation of general relativity. The information about the horizon is naturally encoded in the phase space variables, and the perturbative quantum fluctuations around the classical geometry depend on the distance from the horizon. For small black holes, space near the vi...

I aim to discuss a reasonably wide range of quantum-mechanical phenomena from condensed matter physics, with an emphasis mainly on physical ideas rather than mathematical formalism. The most important prerequisite is some understanding of second quantisation for fermions and bosons. There will be two problems classes in addition to the lectures. Michaelmas Term 2013: Lectures in the Fisher Room...

The Spinning Particle Model for anyon is analysed in the Batalin-Tyutin scheme of quantisation in extended phase space. Here additional degrees of freedom are introduced in the phase space such that all the constraints in the theory are rendered First Class that is commuting in the sense of Poisson Brackets. Thus the theory can be studied without introducing the Dirac Brackets which appear in t...

An orthodox formulation of quantum mechanics relies on a set postulates in Hilbert space supplemented with rules to connect it classical such as quantisation techniques, correspondence principle, etc. Here we deduce qubit and its dynamics straightforwardly from discrete deterministic conservation the collision entropy. No is required although can be inferred this approach if necessary.

I shall focus, in this presentation of Deformation Quantization, to some mathematical aspects of the theory of star products. The first lectures will be about the general concept of Deformation Quantisation, with examples, with Fedosov’s construction of a star product on a symplectic manifold and with the classification of star products on a symplectic manifold. We will then introduce the notio...