Ghost-free scalar-fermion interactions

Abstract

We discuss a covariant extension of interactions between scalar fields and fermions in a flat spacetime. We show, in a covariant theory, how to evade fermionic ghosts appearing because of the extra degrees of freedom behind a fermionic nature even in the Lagrangian with first derivatives. We will give a concrete example of a quadratic theory with up to the first derivative of multiple scalar fields and a Weyl fermion. We examine not only the maximally degenerate condition, which makes the number of degrees of freedom correct, but also a supplementary condition guaranteeing that the time evolution takes place properly. We also show that proposed derivative interaction terms between scalar fields and a Weyl fermion cannot be removed by field redefinitions. * K =   A ab B aβ,J B aβ,J C αb,I D αβ,IJ D αβ,IJ Cα b,I Dα β,IJ Dαβ ,IJ   =    Lφ aφb −Lφ aψ β J −Lφ aψβ J Lψα Iφ b Lψ α Iψ β J Lψ α Iψβ J Lψα Iφ b Lψα Iψ β J    Lφ a φ b −Lφ a ψ β J −Lφ aψβ J Lψα I φ b Lψα I ψ β J Lψ α Iψβ J Lψα I φ b Lψα I ψ β J Lψα Iψβ J      δφ b δψ β J δψβ J   . (5)From the definition of the canonical momenta of fermions, we generally haveafter we locally solve the canonical momenta of the scalar fields forφ a , which can be justified by our assumption that ∂π a /∂φ b = A ab has an inverse. Taking the derivative of (B1) with respect toψ β J andψβ J , we have Lψ α Iψ β J = Lφ aψ β J ∂F α,I ∂π φ a + ∂F α,I ∂ψ β J ⇔ ∂F α,I ∂ψ β J

Black Holes in an Effective Field Theory Extension of General Relativity

“…Thus, following the argument in Ref. [56], mathematically this system is mode-stable for any coupling (within the small coupling regime of the effective field theory).…”

Stability analysis of black holes by the S -deformation method for coupled systems

“…Also, we applied our formalism to the case of the Schwarzschild black hole in dynamical Chern-Simons gravity and a charged Kaluza-Klein black hole [22,30], and we showed the stability of the spacetime by finding a regular S-deformation function numerically. While the dynamical Chern-Simons gravity case is a test problem because the stability was already shown in [26], our study of charged Kaluza-Klein black hole case gives a first numerical proof 9 In Fig. 1 in the erratum for [32], the curves for ρ 0 /ρ + = 30, 50, 100 apparently looks regular, but in fact they are divergent near the horizon.…”

“…If there exists a continuous S which gives V = K † K, since Φ †Ṽ Φ = |KΦ| 2 ≥ 0, we can say the non-existence of the negative energy bound state, i.e., the non-existence of the exponentially growing mode in time. In [25,26], this method was used for stability analysis.…”

“…where κ is the gravitational constant, and β is the coupling constant [21,26]. 5 The relation among Φ 1 , Φ 2 and perturbed quantities can be seen in [21,26].…”

“…We note that the β → ∞ limit corresponds to the general relativity case. Recently, the stability of this system was proven analytically for β ≥ 0 [26]. We apply our formalism to this system as a test problem.…”