General Quartic Interactions Research Articles

Long-range multi-scalar models at three loops

We compute the three-loop beta functions of long-range multi-scalar models with general quartic interactions. The long-range nature of the models is encoded in a kinetic term with a Laplacian to the power 0 < ζ < 1, rendering the computation of Feynman diagrams much harder than in the usual short-range case (ζ = 1). As a consequence, previous results stopped at two loops, while seven-loop results are available for short-range models. We push the renormalization group analysis to three loops, in an ϵ = 4ζ − d expansion at fixed dimension d < 4, extensively using the Mellin–Barnes representation of Feynman amplitudes in the Schwinger parametrization. We then specialize the beta functions to various models with different symmetry groups: O(N), , and O(N) × O(M). For such models, we compute the fixed points and critical exponents.

Enhancement and state tomography of a squeezed vacuum with circuit quantum electrodynamics

We study the dynamics of a general quartic interaction Hamiltonian under the influence of dissipation and nonclassical driving. We show that this scenario could be realized with a cascaded superconducting cavity-qubit system in the strong dispersive regime in a setup similar to recent experiments. In the presence of dissipation, we find that an effective Hartree-type decoupling with a Fokker-Planck equation yields a good approximation. We find that the stationary state is approximately a squeezed vacuum, which is enhanced by the $Q$ factor of the cavity but conserved by the interaction. The qubit nonlinearity, therefore, does not significantly influence the highly squeezed intracavity microwave field but, for a range of realistic parameters, enables characterization of itinerant squeezed fields.

The S-matrix of the Faddeev-Reshetikhin model, diagonalizability andPTsymmetry

We study the question of diagonalizability of the Hamiltonian for the Faddeev-Reshetikhin (FR) model in the two particle sector. Although the two particle S-matrix element for the FR model, which may be relevant for the quantization of strings on $AdS_{5}\times S^{5}$, has been calculated recently using field theoretic methods, we find that the Hamiltonian for the system in this sector is not diagonalizable. We trace the difficulty to the fact that the interaction term in the Hamiltonian violating Lorentz invariance leads to discontinuity conditions (matching conditions) that cannot be satisfied. We determine the most general quartic interaction Hamiltonian that can be diagonalized. This includes the bosonic Thirring model as well as the bosonic chiral Gross-Neveu model which we find share the same S-matrix. We explain this by showing, through a Fierz transformation, that these two models are in fact equivalent. In addition, we find a general quartic interaction Hamiltonian, violating Lorentz invariance, that can be diagonalized with the same two particle S-matrix element as calculated by Klose and Zarembo for the FR model. This family of generalized interaction Hamiltonians is not Hermitian, but is $PT$ symmetric. We show that the wave functions for this system are also $PT$ symmetric. Thus, the theory is in a $PT$ unbroken phase which guarantees the reality of the energy spectrum as well as the unitarity of the S-matrix.

Instability of stationary states for nonlinear spinor models with quartic self-interaction

The stability of lumps generated by stationary state solutions belonging to a general quartic interaction is investigated. It is shown that all these solutions are unstable in the sense that the second variation of the energy is not positive.