Quantum field formalism for the higher-derivative nonrelativistic electrodynamics in 1+1 dimensions

Manavella, E. C.

doi:10.1142/s0217751x19500507

Cited by 7 publications

(9 citation statements)

References 63 publications

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“…where H denotes the Hamiltonian (33). In the case β 2 = 0 , β 1 = 1, equation ( 43) reproduces the Ostrogradski action for the variational model (17),…”

Section: Hamiltonian Formalismmentioning

confidence: 92%

“…The Lagrangian interaction vertex (17) does not meet stability requirements. This confirms the instability of the variational coupling proposed in [42].…”

Section: Stable Interactionsmentioning

confidence: 99%

“…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.…”

Section: Introductionmentioning

confidence: 99%

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Extended Chern-Simons model for a vector multiplet

Kaparulin

Lyakhovich

Nosyrev

2021

Preprint

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We consider a gauge theory of vector fields in 3d Minkowski space. At the free level, the dynamical variables are subjected to the extended Chern-Simons (ECS) equations with higher derivatives. If the color index takes n values, the third-order model admits a 2n-parameter series of second-rank conserved tensors, which includes the canonical energy-momentum. Even though the canonical energy is unbounded, the other representatives in the series can have bounded from below 00-component. The theory admits consistent self-interactions with the Yang-Mills gauge symmetry. The Lagrangian couplings preserve the unbounded from below energy-momentum tensor, and they do not lead to a stable non-linear theory. The non-Lagrangian couplings are consistent with the existence of conserved tensor with a bounded from below 00-component. These models are stable at the non-linear level. The dynamics of interacting theory admits a constraint Hamiltonian form. The Hamiltonian density is given by the 00-component of the conserved tensor. In the case of stable interactions, the Poisson bracket and Hamiltonian do not follow from the canonical Ostrogradski construction. The particular attention is paid to the "triply massless" ECS theory, which demonstrates instability already at the free level. It is shown that the introduction of extra scalar field, serving as Higgs, can stabilize dynamics in the vicinity of the local minimum of energy. The equations of motion of stable model are non-Lagrangian, but they admit the Hamiltonian form of dynamics with a bounded from below Hamiltonian.

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“…where H denotes the Hamiltonian (33). In the case β 2 = 0 , β 1 = 1, equation ( 43) reproduces the Ostrogradski action for the variational model (17),…”

Section: Hamiltonian Formalismmentioning

confidence: 92%

“…The Lagrangian interaction vertex (17) does not meet stability requirements. This confirms the instability of the variational coupling proposed in [42].…”

Section: Stable Interactionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Extended Chern-Simons model for a vector multiplet

Kaparulin

Lyakhovich

Nosyrev

2021

Preprint

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“…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].…”

Section: Introductionmentioning

confidence: 99%

Natural Higher-Derivatives Generalization for the Klein-Gordon Equation

Thibes

2020

Preprint

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We propose a natural family of higher-order partial differential equations generalizing the second-order Klein-Gordon equation. We characterize the associated model by means of a generalized action for a scalar field, containing higher-derivative terms. The limit obtained by considering arbitrarily higher-order powers of the d'Alembertian operator leading to a formal infinite-order partial differential equation is discussed. The general model is constructed using the exponential of the d'Alembertian differential operator. The canonical energymomentum tensor densities and field propagators are explicitly computed. We consider both homogeneous and non-homogeneous situations. The classical solutions are obtained for all cases.

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“…The gauge-fixing condition for this extension can be adapted to be compatible with the 2 degrees of freedom of the photon and the 3 additional ones connected to the massive mode [25]. Further developments [26,27] in Podolsky's theory deserve to be mentioned including investigations of a dimension-six quantum electrodynamics in (1+1) spacetime dimensions [28].Another relevant extension of Maxwell theory with higher derivatives is Lee-Wick electrodynamics, described by the dimension-6 term F µν ∂ α ∂ α F µν [29]. This theory also implies a finite self-energy for a pointlike charge in (1 + 3) spacetime dimensions.…”

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confidence: 99%

Maxwell electrodynamics modified by a CPT -odd dimension-five higher-derivative term

et al. 2019

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In this paper, we consider an electrodynamics of higher derivatives coupled to a Lorentz-violating background tensor. Specifically, we are interested in a dimension-five term of the CPT -odd sector of the nonminimal Standard-Model Extension. By a particular choice of the operatorkAF , we obtain a higher-derivative version of the Carroll-Field-Jackiw (CFJ) term, 1 2 κλµν A λ Dκ Fµν , with a Lorentz-violating background vector Dκ. This modification is subject to being investigated. We calculate the propagator of the theory and from its poles, we analyze the dispersion relations of the isotropic and anisotropic sectors. We verify that classical causality is valid for all parameter choices, but that unitarity of the theory is generally not assured. The latter is found to break down for certain configurations of the background field and momentum. In an analog way, we also study a dimension-five anisotropic higher-derivative CFJ term, which is written as κλµν A λ Tκ(T ·∂) 2 Fµν and is directly linked to the photon sector of Myers-Pospelov theory. Within the second model, purely timelike and spacelike Tκ are considered. For the timelike choice, one mode is causal, whereas the other is noncausal. Unitarity is conserved, in general, as long as the energy stays real -even for the noncausal mode. For the spacelike scenario, causality is violated when the propagation direction lies within certain regimes. However, there are particular configurations preserving unitarity and strong numerical indications exist that unitarity is guaranteed for all purely spacelike configurations. The results improve our understanding of nonminimal CPT-odd extensions of the electromagnetic sector.Here, we also stated the general structure of individual terms. A generic dimensionless background tensor with a set X of Lorentz indices is indicated by n X whereÔ X is a field operator with the same set of Lorentz indices. The mass dimension of the background has been extracted explicitly to show the dependence on the scales M QG and M . The remaining Lagrange density δL other contains all additional contributions that have not been taken into account previously. These could be nonperturbative in nature. According to the perturbative series of Eq. (1), the nonminimal SME is a natural extension of the higher-derivative Lorentz-invariant contributions in the same sense as the minimal SME is an extension of the SM. Searching for physics beyond the SM via an effective theory, there is a priori no reason why such nonminimal terms should be discarded. Interpreting these terms as theories that are valid within a certain energy range only, power-counting nonrenormalizability is not considered to be a problem.Due to the arguments explained above, individual terms have an energy dependence of the form (E/M QG ) d−4 and (E/M ) d−4 , respectively. Nonminimal contributions grow with energy, i.e., after a certain point they dominate the minimal ones. Therefore, they might be essential in experiments involving particles of high energies, e.g., cosmic rays. From the ...

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Quantum field formalism for the higher-derivative nonrelativistic electrodynamics in 1+1 dimensions

Cited by 7 publications

References 63 publications

Extended Chern-Simons model for a vector multiplet

Extended Chern-Simons model for a vector multiplet

Natural Higher-Derivatives Generalization for the Klein-Gordon Equation

Maxwell electrodynamics modified by a CPT -odd dimension-five higher-derivative term

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