Stability and consistent interactions in higher derivative matter field theories

Extended Chern-Simons model for a vector multiplet

“…As it is required, the gauge symmetry (18) is given by the deformation of the gradient gauge symmetry of free model. The important difference is that the gauge symmetry ( 18) is non-abelian.…”

“…The interaction, being defined by equations ( 48), is consistent. The equations are preserved by the standard Yang-Mills gauge symmetry (18). The scalar field is preserved by the gauge transformation.…”

“…We note that the gauge generator involves the scalar field explicitly. The model has the same number of physical degrees of freedom as the free theory because the orders of equations of motion (48), gauge identities (51), and gauge symmetries (18) are preserved by coupling. Equations (48) do not follow from the least action principle from the least action principle for a functional with higher derivatives unless β 2 = 0.…”

“…The Pais-Uhlenbeck oscillator [9], Podolsky [10] and Lee-Wick [11,12] electrodynamics, ECS theory [13], and conformal gravity [14] are examples. For the current studies we mention [15][16][17][18] and references therein. In all these models the quantum theory is expected to be well-defined [2,19], but the application of the canonical quantization procedure based on the Ostrogradski procedure 1 leads to the model with an unbounded from below spectrum of energy.…”

Natural Higher-Derivatives Generalization for the Klein-Gordon Equation

“…Another interesting path for obtaining higher-derivative models can be seen in [25], where it is shown that nonlocality in space-time via the introduction of forward and back-ward fields can lead to higher-order derivatives with a particular example of a fourth-order generalization of the KG equation given. In this day and age, the study of higher-derivative theories continues to be an active lively field, still containing various chalenging problems and being the main subject of a significative number of works in the most recent literature [26,27,28,29,30,31,32,33,34]. Besides their own mathematical interest, the address of important issues and open questions in physics such as the quantization of gravity and its alternative modified theories, the construction of effective low energy field theories, the dark energy and matter problems and the possibility of Lorentz symmetry breaking at a fundamental level in cosmological models has granted higher-derivative models an important role in the current contemporary physics scenario [35,36,37,38,39].…”