We speculate on Dyson series for the $S$-matrix when the interaction depends on derivatives of the fields. We stick on two particular examples: the scalar electrodynamics and the renormalised $phi ^4$ theory. We eventually give evidence that Lorentz invariance is satisfied and that usual Feynman rules can be applied to the interaction Lagrangian.
In this paper, we discuss the chiral anomaly in a Lorentz-breaking extension of QED which, besides the common terms that are present in the Standard Model Extension, includes some dimension-five nonminimal couplings. We find, using the Fujikawa forma
lism, that these nonminimal couplings induce new terms in the anomaly which depend on the Lorentz-violating parameters. Perturbative calculations are also carried out in order to investigate whether or not new ambiguous Carroll-Field-Jackiw terms are induced in the effective action.
We consider a topological coupling between a pseudo-scalar field and a 3-form gauge field in ${cal N}=1$ supersymmetric higher derivative 3-form gauge theories in four spacetime dimensions. We show that ghost/tachyon-free higher derivative Lagrangian
s with the topological coupling can generate various potentials for the pseudo-scalar field by solving the equation of motion for the 3-form gauge field. We give two examples of higher derivative Lagrangians and the corresponding potentials: one is a quartic order term of the field strength and the other is the term which can generate a cosine-type potential of the pseudo-scalar field.
In this paper, we generalize the duality between self-dual and Maxwell-Chern-Simons theories for the case of a CPT-even Lorentz-breaking extension of these theories. The duality is demonstrated with use of the gauge embedding procedure, both in free
and coupled cases, and with the master action approach. The physical spectra of both Lorentz-breaking theories are studied. The massive poles are shown to coincide and to respect the requirements for unitarity and causality at tree level. The extra massless poles which are present in the dualized model are shown to be nondynamical.
Twisted quantum field theories on the Groenewold-Moyal plane are known to be non-local. Despite this non-locality, it is possible to define a generalized notion of causality. We show that interacting quantum field theories that involve only couplings
between matter fields, or between matter fields and minimally coupled U(1) gauge fields are causal in this sense. On the other hand, interactions between matter fields and non-abelian gauge fields violate this generalized causality. We derive the modified Feynman rules emergent from these features. They imply that interactions of matter with non-abelian gauge fields are not Lorentz- and CPT-invariant.
We propose a way to recover Lorentz invariance of the perturbative S matrix in the Discrete Light-Cone Quantization (DLCQ) in the continuum limit without spoiling the trivial vacuum.
Vincenzo Denisi
,Alessandro Papa
,Marco Rossi
.
(2020)
.
"On the Lorentz-invariance of the Dyson series in theories with derivative couplings"
.
Alessandro Papa
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