Related papers: Reflection positivity and quantum Griffiths' inequ…
We present here a relation of different types of Friedrichs models and their use in the description and comprehension of resonance phenomena. We first discuss the basic Friedrichs model and obtain its resonance in the case that this is…
The concept of reflection positivity has its origins in the work of Osterwalder--Schrader on constructive quantum field theory. It is a fundamental tool to construct a relativistic quantum field theory as a unitary representation of the…
We scatter a meson off of a scalar kink in quantum field theory, at leading order in perturbation theory. We calculate the full quantum state, at leading order, at all times and also check that the reflection and transmission coefficients…
We employ the Schwinger-Keldysh formalism to study the nonequilibrium dynamics of the mirror with perfect reflection moving in a quantum field. Within the regime of linear response in terms of a first order expansion of the mirror's…
In this paper I discuss a formulation of relativistic few-particle scattering theory where the dynamical input is a collection of reflection-positive Euclidean covariant Green functions. This formulation of relativistic quantum mechanics…
In this note we continue our investigations of the representation theoretic aspects of reflection positivity, also called Osterwalder--Schrader positivity. We explain how this concept relates to affine isometric actions on real Hilbert…
Using equivalencies between different models we reduce the model of two spin-1/2 Heisenberg chains crossed at one point to the model of free fermions. The spin-spin correlation function is calculated by summing the perturbation series in…
Using the Quantum Inverse Scattering Method we construct an integrable Heisenberg-XXZ-model, or equivalently a model for spinless fermions with nearest-neighbour interaction, with defects. Each defect involves three sites with a fine tuning…
The Griffiths inequalities for Ising spin-glass models with Gaussian randomness of non-vanishing mean are proved using properties of the Gaussian distribution and gauge symmetry of the system. These inequalities imply that correlation…
We prove strictly that one dimension spin 1/2 Heisenberg model has a symmetry of energy spectrum between its subspace $n$ and the subspace $L-n$ of the Fock space. Our proof is completed by introducing two general quantum operations. One is…
We consider reflection-positivity (Osterwalder-Schrader positivity, O.S.-p.) as it is used in the study of renormalization questions in physics. In concrete cases, this refers to specific Hilbert spaces that arise before and after the…
The relevance that the property of complete positivity has had in the determination of quantum structures is briefly reviewed, together with recent applications to neutron optics and quantum Brownian motion. A possible useful application…
In quantum systems with many degrees of freedom the replica method is a useful tool to study the entanglement of arbitrary spatial regions. We apply it in a way which allows them to back-react. As a consequence, they become dynamical…
On the base of a 1D Shr\"{o}dinger equation the non-linear first-order differential equation (Ricatti type) for a quantum wave impedance function was derived. The advantages of this approach were discussed and demonstrated for a case of a…
The reflection positivity property has played a central role in both mathematics and physics, as well as providing a crucial link between the two subjects. In a previous paper we gave a new geometric approach to understanding reflection…
We prove Griffiths inequalities for spins in n>1 dimensions with no interaction.
This work is divided into two parts. The first examines recent proposals for "witnessing" quantum gravity via entanglement from the point of view of Bronstein's original objection to a quantization of gravity. Using techniques from open…
The Griffiths first and second inequalities have played an important role in the analysis of ferromagnetic models. In spin-glass models, although the counterpart of the Griffiths first inequality has been obtained, the counterpart of the…
The off-diagonal Bethe Ansatz method [1] is used to revisit the periodic XXX Heisenberg spin-1/2 chain. It is found that the spectrum of the transfer matrix can be characterized by an inhomogeneous T-Q relation, a natural but nontrivial…
We present a relativistic generalization of the Wigner inequality for the scalar and pseudoscalar particles decaying to two particles with spin (fermions and photons.) We consider Wigner's inequality with the full spin anticorrelation (with…