2134/24097
Fumio Hiroshima
Fumio
Hiroshima
Jozsef Lorinczi
Jozsef
Lorinczi
Functional integral representations of the Pauli-Fierz model with spin 1/2
Loughborough University
2017
Functional integration
Jump processes
Quantum field theory
Mathematical Sciences not elsewhere classified
2017-02-13 15:57:27
Journal contribution
https://repository.lboro.ac.uk/articles/journal_contribution/Functional_integral_representations_of_the_Pauli-Fierz_model_with_spin_1_2/9386057
A Feynman–Kac-type formula for a Lévy and an infinite-dimensional Gaussian random process associated with a quantized radiation field is derived. In particular, a functional integral representation of e−tHPF generated by the Pauli–Fierz Hamiltonian with spin 1/2 in non-relativistic quantum electrodynamics is constructed. When no external potential is applied HPF turns translation-invariant and it is decomposed as a direct integral HPF=∫R3⊕HPF(P)dP. The functional integral representation of e−tHPF(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.