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Comment: 6 pages

Functional Integral Representation of the Pauli-Fierz Model with Spin 1/2

A Feynman-Kac-type formula for a L\'evy and an infinite dimensional Gaussian random process associated with a quantized radiation field is derived. In particular, a functional integral representation of $e^{-t\PF}$ generated by the Pauli-Fierz Hamiltonian with spin $\han$ in non-relativistic quantum electrodynamics is constructed. When no external potential is applied $\PF$ turns translation invariant and it is decomposed as a direct integral $\PF = \int_\BR^\oplus \PF(P) dP$. The functional integral representation of $e^{-t\PF(P)}$ is also given. Although all these Hamiltonians include spin, nevertheless the kernels obtained for the path measures are scalar rather than matrix expressions. As an application of the functional integral representations energy comparison inequalities are derived.

Multiscale expansion of the lattice potential KdV equation on functions of infinite slow-varyness order

Comment: 9 pages, submitted to Journ. Phys. A

Symmetry of Planar Four-Body Convex Central Configurations

Comment: 12 pages

On Minkowskian Branching Structures

Comment: 16 pages

Exact treatment of linear difference equations with noncommutative coefficients

Comment: 7 pages, 0 figures

Riccati equation-based generalization of Dawson's integral function

Comment: 11 pages. Accepted on Mathematical Methods in the Applied Sciences

Materials with a desired refraction coefficient can be made by embedding small particles

Comment: 35J05, 35J10, 70F10, 74J25, 81U40, 81V05

Constructive $\phi^4$ field theory without tears

Comment: 22 pages, 10 figures

On the relation between states and maps in infinite dimensions

Comment: 19 pages
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