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Boundary form factor axioms are derived for the matrix elements of local boundary operators in integrable 1+1 dimensional boundary quantum field theories using the analyticity properties of correlators via the boundary reduction formula. Minimal solutions are determined for the integrable boundary perturbations of the free boson, free fermion (Ising), Lee-Yang and sinh-Gordon models and the two point functions calculated from them are checked against the exact solutions in the free cases and against the conformal data in the ultraviolet limit for the Lee-Yang model. In the case of the free boson/fermion the dimension of the solution space of the boundary form factor equation is shown to match the number of independent local operators. We obtain excellent agreement which proves not only the correctness of the solutions but also confirms the form factor axioms.
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Using the recently introduced boundary form factor bootstrap equations, we map the complete space of their solutions for the boundary version of the scaling Lee-Yang model and sinh-Gordon theory. We show that the complete space of solutions, graded by the ultraviolet behaviour of the form factors can be brought into correspondence with the spectrum of local boundary operators expected from boundary conformal field theory, which is a major evidence for the correctness of the boundary form factor bootstrap framework.
Relativistic spin states are convention dependent. In this work we prove that the zero momentum-transfer limits of the leading two form factors in the decomposition of the energy-momentum tensor matrix elements are independent of this choice. In particular, we demonstrate that these constraints are insensitive to whether the corresponding states are massive or not, and that they arise purely due to the Poincare covariance of the states.
We replace a Hamiltonian by a modular Hamiltonian in the spectral form factor and the level spacing distribution function. This establishes a connection between quantities within quantum entanglement and quantum chaos. To have a universal study for quantum entanglement, we consider the Gaussian random 2-qubit model. For a generic 2-qubit model, a larger value of entanglement entropy gives a larger maximum violation of Bells inequality. We first provide an analytical estimation of the relation between quantum entanglement quantities and the dip when a subregion only has one qubit. Our numerical result confirms the analytical estimation that the occurring time of the first dip in the spectral form factor is further delayed should imply a larger value of entanglement entropy. We observe a classical chaotic behavior that dynamics in a subregion is independent of the choice of the initial state at a late time. The simulation shows that the level spacing distribution is not random matrix theory at a late time. In the end, we develop a technique within QFT to the spectral form factor for its relation to an $n$-sheet manifold. We apply the technology to a single interval in 2d CFT and also the spherical entangling surface in ${cal N}=4$ super Yang-Mills theory. The result is one for both theories, but the Renyi entropy can depend on the Renyi index. It indicates the difference between the continuum and discrete spectrum, and the dependence is then not a suitable criterion for showing whether a state is maximally entangled in QFT. The spectral form factor with a modular Hamiltonian also gives a strong constraint to the entanglement spectrum of QFT, which is useful in the context of AdS/CFT correspondence.
By adopting a local QFT framework one can derive in a non-perturbative manner the constraints imposed by Poincare symmetry on the form factors appearing in the Lorentz covariant decomposition of the energy-momentum tensor matrix elements. In particular, this approach enables one to prove that these constraints are in fact independent of the internal properties of the states appearing in the matrix elements. Here we outline the rationale behind this approach, and report on some of the implications of these findings.
We use recent data on K^+ -> pi^+ e^+ e^-, together with known values for the pion form factor, to derive experimental values for the kaon electromagnetic form factor for 0 < q^2 < 0.125 (GeV/c)^2. The results are then compared with the predictions of the Vector Meson Dominance model, which gives a good fit to the experimental results.
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