We describe an algebra G of diagrams that faithfully gives a diagrammatic representation of the structures of both the Heisenberg–Weyl algebra H – the associative algebra of the creation and annihilation operators of quantum mechanics – and U(LH), the enveloping algebra of the Heisenberg Lie algebra LH. We show explicitly how G may be endowed with the structure of a Hopf algebra, which is also ...

The SO(32) theory, in the limit where it is an open superstring theory, is completely specified in the light–cone gauge as a second–quantized string theory in terms of a “matrix string” model. The theory is defined by the neighbourhood of a 1+1 dimensional fixed point theory, characterized by an Abelian gauge theory with type IB Green–Schwarz form. Non–orientability and SO(32) gauge symmetry ar...

We describe methods for simulating general second-quantized Hamiltonians using the compact encoding, in which qubit states encode only occupied modes physical occupation number basis states. These apply to composed of a constant interactions, i.e., linear combinations ladder operator monomials fixed form. Compact encoding leads requirements that are optimal up logarithmic factors. show how use ...

We consider an approach in which the usual wave function quadrature representation of mode j electromagnetic field is further quantized to produce a operator. Since already second quantized, this corresponds additional or third quantization. The third-quantization can be used perform certain quantum optics calculations Heisenberg picture that could only performed Schrodinger when using conventi...