Path integral representations for generalized Schrödinger operators obtained under a class
of Bernstein functions of the Laplacian are established. The one-to-one correspondence of …

This monograph offers a state-of-the-art mathematical account of functional integration
methods in the context of self-adjoint operators and semigroups using the concepts and …

Employing recent results on stochastic differential equations associated with the standard
model of non-relativistic quantum electrodynamics by B. Güneysu, JS Møller, and the …

Quantum statistical mechanics plays a major role in many fields such as thermodynamics,
plasma physics, solid-state physics, and the study of stellar structure. While the theory of …

We give a functional integral representation of the semigroup generated by the spin-boson
Hamiltonian by making use of a Poisson point process and a Euclidean field. We present a …

By means of functional integrations spectral properties of semi-relativistic Pauli–Fierz
Hamiltonians H=(p− α A) 2+ m 2− m+ V+ H rad in quantum electrodynamics are considered …

Absence of Energy Level Crossing for the Ground State Energy of the Rabi Model arXiv:1207.4020v1
[math-ph] 17 Jul 2012 Page 1 Absence of Energy Level Crossing for the Ground State Energy …

We reconstruct and develop the abstract Perron–Frobenius theory studied by Faris. We
apply the results to some models in nonrelativistic quantum field theory and show the …

We provide an explicit combinatorial expansion for the ground state energy of the massless
spin-Boson model as a power series in the coupling parameter. Our method uses the …

We define and prove existence of fractional P (ϕ) 1-processes as random processes
generated by fractional Schrödinger semigroups with Kato-decomposable potentials. Also …