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We treat the problem of normally ordering expressions involving the standard boson operators a, a* where [a,a*]=1. We show that a simple product formula for formal power series - essentially an extension of the Taylor expansion - leads to a double exponential formula which enables a powerful graphical description of the generating functions of the combinatorial sequences associated with such functions - in essence, a combinatorial field theory. We apply these techniques to some examples related to specific physical Hamiltonians.
The derivation of the Feynman path integral based on the Trotter product formula is extended to the case where the system is in a magnetic field.
Although symmetry methods and analysis are a necessary ingredient in every physicists toolkit, rather less use has been made of combinatorial methods. One exception is in the realm of Statistical Physics, where the calculation of the partition functi
A conventional context for supersymmetric problems arises when we consider systems containing both boson and fermion operators. In this note we consider the normal ordering problem for a string of such operators. In the general case, upon which we to
The general normal ordering problem for boson strings is a combinatorial problem. In this note we restrict ourselves to single-mode boson monomials. This problem leads to elegant generalisations of well-known combinatorial numbers, such as Bell and S
Various Hamiltonian simulation algorithms have been proposed to efficiently study the dynamics of quantum systems using a universal quantum computer. However, existing algorithms generally approximate the entire time evolution operators, which may ne