Perturbative approach to higher derivative and nonlocal theories

Cheng, Tai-Chung; Ho, Pei-Ming; Yeh, Mao-Chuang

doi:10.1016/s0550-3213(02)00020-2

Cited by 57 publications

(65 citation statements)

References 40 publications

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“…The most immediate possibility to proceed along the lines of maintaining the original number of degrees of freedom x,ẋ, is to simply neglect the acceleration term and compute the corrections to ω to first order in g. Nevertheless, this result does not coincide with the first order expansion of the exact frequency ω to that order. On the other hand, the application of the modified perturbative method proposed in [8] does indeed leads to the correct expression to that order. Moreover, in this simple case, the corrections can be calculated to all orders in g and the sum of this perturbation series can also be performed, leading to the exact expression for ω.…”

Section: Pos(qg-ph)040mentioning

confidence: 88%

“…A proof of self-consistency to all orders, in a mechanical setting 2 , is provided in Ref. [8]. It consists in showing that to each order in the expansion parameter, the Lagrangian constructed according to the summary described in the above paragraph reproduces exactly the corresponding equations obtained by the iteration procedure stating from the exact HOTD ones.…”

Section: Pos(qg-ph)040mentioning

confidence: 93%

“…[8]. The authors consider a system of two one-dimensional oscillators coupled in the presence of a constant gravitational field.…”

Section: Pos(qg-ph)040mentioning

confidence: 99%

“…[8], which allowed us to successfully deal with two of the general problems originating from the HOTD character of the terms describing the Lorentz violations in the model: (i) the increase in the number of degrees of freedom, which we must not allow in a perturbative modification of standard QED, and (ii) the appearance of Hamiltonians which are not bounded from below, which do not provide a good starting point for quantization. The calculation of interacting processes is deferred for a future publication.…”

Section: Final Commentsmentioning

confidence: 99%

“…In fact, a perturbation of electrodynamics should not introduce additional degrees of freedom, so that a careful strategy is required to define an adequate perturbative procedure in the LIV parameters. Fortunately, a systematic approach to carry out this task, which also provides a positive definite zeroth order Hamiltonian, already exists in the literature [7,8] and here we adhere to it.…”

Section: Introductionmentioning

confidence: 99%

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Quantum corrections in the Myers-Pospelov model: a progress report

Urrutia¹

2008

Proceedings of From Quantum to Emergent Gravity: Theory and Phenomenology — PoS(QG-Ph)

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The Myers-Pospelov (MP) model is an effective field theory (EFT), including dimension five operators, which describes the phenomenology of active Lorentz invariance violation produced by a preferred reference frame. We concentrate here in the case of the modified electrodynamics. The point of view taken in this work is that the Lorentz violating part of the action in the MP model, which includes higher order time derivative (HOTD) operators, is to be considered as a perturbation over the dynamics described by standard Electrodynamics, particularly in the quantum case. HOTD theories, besides incorporating additional degrees of freedom, suffer from well known difficulties in their quantization, among which one finds Hamiltonians which are not bounded from below. Thus, in order to cope with these challenges it will be necessary to deal with a modified perturbation theory which is well described in the literature. We apply such methods to this specific model providing a quantization of the free sector of the theory by identifying the modified normal mode expansions of the fields together with the modified propagators and the interaction terms. The calculation of interacting processes, together with radiative corrections, is beyond the scope of the present article and will be deferred for future publications. From Quantum to Emergent Gravity: Theory and Phenomenology

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Section: Pos(qg-ph)040mentioning

confidence: 88%

Section: Pos(qg-ph)040mentioning

confidence: 93%

“…[8]. The authors consider a system of two one-dimensional oscillators coupled in the presence of a constant gravitational field.…”

Section: Pos(qg-ph)040mentioning

confidence: 99%

Section: Final Commentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Quantum corrections in the Myers-Pospelov model: a progress report

Urrutia¹

2008

Proceedings of From Quantum to Emergent Gravity: Theory and Phenomenology — PoS(QG-Ph)

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Avoiding Dark Energy with 1/R Modifications of Gravity

Woodard

2007

Lecture Notes in Physics

682

837

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Scalar quintessence seems epicyclic because one can choose the potential to reproduce any cosmology (I review the construction) and because the properties of this scalar seem to raise more questions than they answer. This is why there has been so much recent interest in modified gravity. I review the powerful theorem of Ostrogradski which demonstrates that the only potentially stable, local modification of general relativity is to make the Lagrangian an arbitrary function of the Ricci scalar. Such a theory can certainly reproduce the current phase of cosmic acceleration without Dark Energy. However, this explanation again seems epicyclic in that one can construct a function of the Ricci scalar to support any cosmology (I give the technique). Models of this form are also liable to problems in the way they couple to matter, both in terms of matter's impact upon them and in terms of the long range gravitational force they predict. Because of these problems my own preference for avoiding Dark Energy is to bypass Ostrogradski's theorem by considering the fully nonlocal effective action built up by quantum gravitational processes during the epoch of primordial inflation.Comment: 30 pages, no figures, conference proceedings for the 3rd Aegean Summer School, Chios, 26 September - 1 October, 2005. Replaced version corrects some typoes and adds reference

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String theory as a diffusing system

Calcagni

Nardelli

2010

J. High Energ. Phys.

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Recent results on the effective non-local dynamics of the tachyon mode of open string field theory (OSFT) show that approximate solutions can be constructed which obey the diffusion equation. We argue that this structure is inherited from the full theory, where it admits a universal formulation. In fact, all known exact OSFT solutions are superpositions of diffusing surface states. In particular, the diffusion equation is a spacetime manifestation of OSFT gauge symmetries.

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Perturbative approach to higher derivative and nonlocal theories

Cited by 57 publications

References 40 publications

Quantum corrections in the Myers-Pospelov model: a progress report

Quantum corrections in the Myers-Pospelov model: a progress report

Avoiding Dark Energy with 1/R Modifications of Gravity

String theory as a diffusing system

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