Geometry of physical dispersion relations

Raetzel, Dennis; Rivera, Sergio; Schüller, F.

doi:10.1103/physrevd.83.044047

Cited by 74 publications

(143 citation statements)

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“…Requiring that matter equations of the form (1) are predictive, interpretable and quantizable imposes necessary conditions on the underlying geometry G. These conditions have been derived and explained in detail in [6]. Here we present a practical summary of these conditions and their implications as far as they are directly relevant for the present article.…”

Section: A Primer On Tensorial Spacetime Geometriesmentioning

confidence: 99%

“…which by virtue of the energy-orientability of P possesses a unique inverse L −1 x on its domain, one finds [6] that the worldlines of free massless and massive particles are stationary curves of the reparametrization-invariant Lagrangian actions…”

Section: A Primer On Tensorial Spacetime Geometriesmentioning

confidence: 99%

“…The technical proofs underlying this summary are presented in detail in [6] and rather pedagogical fashion in the lecture notes [9]. To aid the reader's intuition, we illustrate each abstract construction in this section immediately for the familiar example of a standard metric geometry, before moving on to the next construction.…”

Section: A Primer On Tensorial Spacetime Geometriesmentioning

confidence: 99%

“…Fortunately, these rather fundamental physical conditions translate into three simple algebraic conditions [6] that an otherwise arbitrary tensor field must satisfy in order to provide a valid spacetime geometry: it must be hyperbolic, time-orientable and energy-distinguishing, as we will explain in the first technical section below. Thus the spectrum of tensor fields that can serve as a spacetime structure in the presence of specific matter field dynamics [25] is greatly restricted.…”

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confidence: 99%

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Gravitational dynamics for all tensorial spacetimes carrying predictive, interpretable, and quantizable matter

et al. 2012

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Only a severely restricted class of tensor fields can provide classical spacetime geometries, namely those that can carry matter field equations that are predictive, interpretable and quantizable. These three conditions on matter translate into three corresponding algebraic conditions on the underlying tensorial geometry, namely to be hyperbolic, time-orientable and energy-distinguishing. Lorentzian metrics, on which general relativity and the standard model of particle physics are built, present just the simplest tensorial spacetime geometry satisfying these conditions. The problem of finding gravitational dynamics-for the general tensorial spacetime geometries satisfying the above minimum requirements-is reformulated in this paper as a system of linear partial differential equations, in the sense that their solutions yield the actions governing the corresponding spacetime geometry. Thus the search for modified gravitational dynamics is reduced to a clear mathematical task.

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Section: A Primer On Tensorial Spacetime Geometriesmentioning

confidence: 99%

Section: A Primer On Tensorial Spacetime Geometriesmentioning

confidence: 99%

Section: A Primer On Tensorial Spacetime Geometriesmentioning

confidence: 99%

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confidence: 99%

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Gravitational dynamics for all tensorial spacetimes carrying predictive, interpretable, and quantizable matter

et al. 2012

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“…* * * We are indebted to F.P. Schuller for bringing to our notice [50] which gives a mathematical characterisation of a dispersion relation in any background geometry in terms of functions on the cotangent bundle based on the fundamental physical assumptions of predictivity and an observer independent notion of positive energy. We also thank the referees for suggesting improvements to the manuscript.…”

Section: Spinor Fieldmentioning

confidence: 99%

Lorentz-preserving fields in Lorentz-violating theories

Ganguly

Gangopadhyay

Majumdar

2011

EPL

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Abstract. -We identify a fairly general class of field configurations (of spins 0, 1 2 and 1) which preserve Lorentz invariance in effective field theories of Lorentz violation characterized by a constant timelike vector. These fields concomitantly satisfy the equations of motion yielding cubic dispersion relations similar to those found earlier. They appear to have prospective applications in inflationary scenarios.Introduction. -Invariance under Lorentz transformation is known till date to be a global symmetry of the standard theory of elementary particles when gravitation is ignored. However, questions have been raised regarding the validity of this symmetry at small length scales owing to probable quantum gravity effects . The natural mass scale of quantum gravity is the Planck mass M P l . Departures, suppressed by the Planck mass, from the standard special relativistic dispersion relation of free particles of mass m at large energies have been accepted as a signature of Lorentz invariance violation and has been the principal objet de l'attention of experimental and theoretical probes of Lorentz violation. These hypothesised ad hoc corrections due to Lorentz non-invariance must have their origin in new terms in the action of the system. Myers and Pospelov [38] have studied this issue within the framework of effective field theory involving fields of spins 0, 1/2 and 1, by incorporating into the action dimension five operators containing a constant timelike 4-vector n which ostensibly breaks Lorentz invariance. Choosing a Lorentz frame where n µ = (1, 0), corrections of O(p 3 ) to the dispersion relation of each of the three fields have been obtained in [38] in the limit of relatively high energies E (M P l >> E >> m).

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The non‐birefringent limit of all linear, skewonless media and its unique light‐cone structure

Favaro

Bergamin

2011

Annalen der Physik

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Based on a recent work by Schuller et al., a geometric representation of all skewonless, nonbirefringent linear media is obtained. The derived constitutive law is based on a "core", encoding the optical metric up to a constant. All further corrections are provided by two (anti-)selfdual bivectors, and an "axion". The bivectors are found to vanish if the optical metric has signature (3,1) -that is, if the Fresnel equation is hyperbolic. We propose applications of this result in the context of transformation optics and premetric electrodynamics.

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Geometry of physical dispersion relations

Cited by 74 publications

References 63 publications

Gravitational dynamics for all tensorial spacetimes carrying predictive, interpretable, and quantizable matter

Gravitational dynamics for all tensorial spacetimes carrying predictive, interpretable, and quantizable matter

Lorentz-preserving fields in Lorentz-violating theories

The non‐birefringent limit of all linear, skewonless media and its unique light‐cone structure

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