It has long been known that photons and gravitons may appear as vector and tensor Goldstone modes caused by spontaneous Lorentz invariance violation (SLIV). Usually this approach is considered for ...photons and gravitons separately. We develop the emergent electrogravity theory consisting of the ordinary QED and the tensor-field gravity model which mimics the linearized general relativity in Minkowski spacetime. In this theory, Lorentz symmetry appears incorporated into higher global symmetries of the length-fixing constraints put on the vector and tensor fields involved,
A
μ
2
=
±
M
A
2
and
H
μ
ν
2
=
±
M
H
2
(
M
A
and
M
H
are the proposed symmetry breaking scales). We show that such a SLIV pattern being related to breaking of global symmetries underlying these constraints induces the massless Goldstone and pseudo-Goldstone modes shared by photon and graviton. While for a vector field case the symmetry of the constraint coincides with Lorentz symmetry
SO
(1, 3) of the electrogravity Lagrangian, the tensor-field constraint itself possesses much higher global symmetry
SO
(7, 3), whose spontaneous violation provides a sufficient number of zero modes collected in a graviton. Accordingly, while the photon may only contain true Goldstone modes, the graviton appears at least partially to be composed of pseudo-Goldstone modes rather than of pure Goldstone ones. When expressed in terms of these modes, the theory looks essentially nonlinear and contains a variety of Lorentz and CPT violating couplings. However, all SLIV effects turn out to be strictly cancelled in the lowest order processes considered in some detail. How this emergent electrogravity theory could be observationally different from conventional QED and GR theories is also briefly discussed.
Celotno besedilo
Dostopno za:
DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, SIK, UILJ, UKNU, UL, UM, UPUK
Spontaneous Lorentz invariance violation (SLIV) realized through a nonlinear tensor field constraint Hμν2=±M2 (M is the proposed scale for Lorentz violation) is considered in tensor field gravity ...theory, which mimics linearized general relativity in Minkowski space–time. We show that such a SLIV pattern, due to which the true vacuum in the theory is chosen, induces massless tensor Goldstone modes some of which can naturally be associated with the physical graviton. When expressed in terms of the pure Goldstone modes, this theory looks essentially nonlinear and contains a variety of Lorentz and CPT violating couplings. Nonetheless, all SLIV effects turn out to be strictly canceled in all the lowest order processes considered, provided that the tensor field gravity theory is properly extended to general relativity (GR). So, as we generally argue, the measurable effects of SLIV, induced by elementary vector or tensor fields, are related to the accompanying gauge symmetry breaking rather than to spontaneous Lorentz violation. The latter appears by itself to be physically unobservable, only resulting in a non-covariant gauge choice in an otherwise gauge invariant and Lorentz invariant theory. However, while Goldstonic vector and tensor field theories with exact local invariance are physically indistinguishable from conventional gauge theories, there might appear some principal distinctions if this local symmetry were slightly broken at very small distances in a way that could eventually allow one to differentiate between them observationally.
We argue that non-Abelian gauge fields can be treated as the pseudo-Goldstone vector bosons caused by spontaneous Lorentz invariance violation (SLIV). To this end, the SLIV which evolves in a general ...Yang–Mills type theory with the nonlinear vector field constraint Tr(AμAμ)=±M2 (M is a proposed SLIV scale) imposed is considered in detail. Specifically, we show that in a theory with an internal symmetry group G having D generators not only the pure Lorentz symmetry SO(1,3), but the larger accidental symmetry SO(D,3D) of the SLIV constraint in itself appears to be spontaneously broken as well. As a result, although the pure Lorentz violation on its own still generates only one genuine Goldstone vector boson, the accompanying pseudo-Goldstone vector bosons related to the SO(D,3D) breaking also come into play properly completing the whole gauge multiplet of the internal symmetry group G taken. Remarkably, they appear to be strictly massless as well, being protected by the starting non-Abelian gauge invariance of the Yang–Mills theory involved. When expressed in terms of the pure Goldstone vector modes, this theory look essentially nonlinear and contains a plethora of Lorentz and CPT violating couplings. However, they do not lead to physical SLIV effects which turn out to be strictly cancelled in all the lowest order processes considered.
Spontaneous Lorentz violation realized through a nonlinear vector field constraint of the type
A
μ
A
μ
=
M
2
(
M is the proposed scale for Lorentz violation) is shown to generate massless vector ...Goldstone bosons, gauging the starting global internal symmetries in arbitrary relativistically invariant theories. The gauge invariance appears in essence as a necessary condition for these bosons not to be superfluously restricted in degrees of freedom, apart from the constraint due to which the true vacuum in a theory is chosen by the Lorentz violation. In the Abelian symmetry case the only possible theory proves to be QED with a massless vector Goldstone boson naturally associated with the photon, while the non-Abelian symmetry case results in a conventional Yang–Mills theory. These theories, both Abelian and non-Abelian, look essentially nonlinear and contain particular Lorentz (and
CPT) violating couplings when expressed in terms of the pure Goldstone vector modes. However, they do not lead to physical Lorentz violation due to the simultaneously generated gauge invariance.
Spontaneous Lorentz invariance violation (SLIV) realized through a nonlinear tensor field constraint H_{}^2=\pm M^2 (M is the proposed scale for Lorentz violation) is considered in tensor field ...gravity theory, which mimics linearized general relativity in Minkowski space-time. We show that such a SLIV pattern, due to which the true vacuum in the theory is chosen, induces massless tensor Goldstone modes some of which can naturally be associated with the physical graviton. When expressed in terms of the pure Goldstone modes, this theory looks essentially nonlinear and contains a variety of Lorentz and CPT violating couplings. Nonetheless, all SLIV effects turn out to be strictly cancelled in all the lowest order processes considered, provided that the tensor field gravity theory is properly extended to general relativity (GR). So, as we generally argue, the measurable effects of SLIV, induced by elementary vector or tensor fields, are related to the accompanying gauge symmetry breaking rather than to spontaneous Lorentz violation. The latter appears by itself to be physically unobservable, only resulting in a non-covariant gauge choice in an otherwise gauge invariant and Lorentz invariant theory. However, while Goldstonic vector and tensor field theories with exact local invariance are physically indistinguishable from conventional gauge theories, there might appear some principal distinctions if this local symmetry were slightly broken at very small distances controlled by quantum gravity in an explicit, rather than spontaneous, way that could eventually allow one to differentiate between them observationally.
Emergent photons and gravitons Chkareuli, J. L; Jejelava, J; Kepuladze, Z
arXiv (Cornell University),
11/2018
Journal Article
Odprti dostop
Now, it is already not a big surprise that due to the spontaneous Lorentz
invariance violation (SLIV) there may emerge massless vector and tensor
Goldstone modes identified particularly with photon ...and graviton. Point is,
however, that this mechanism is usually considered separately for photon and
graviton, though in reality they appear in fact together. In this connection,
we recently develop the common emergent electrogravity model which would like
to present here. This model incorporates the ordinary QED and tensor field
gravity mimicking linearized general relativity. The SLIV is induced by
length-fixing constraints put on the vector and tensor fields, $A_{\mu
}^{2}=\pm M_{A}^{2}$ and $H_{\mu \nu }^{2}=\pm M_{H}^{2}$ ($M_{A}$ and $M_{H}$
are the proposed symmetry breaking scales) which possess the much higher
symmetry then the model Lagrangian itself. As a result, the twelve Goldstone
modes are produced in total and they are collected into the vector and tensor
field multiplets. While photon is always the true vector Goldstone boson,
graviton contain pseudo-Goldstone modes as well. In terms of the appearing zero
modes, theory becomes essentially nonlinear and contains many Lorentz and CPT
violating interaction. However, as argued, they do not contribute in processes
which might lead to the physical Lorentz violation. Nonetheless, how the
emergent electrogravity theory could be observationally differed from
conventional QED and GR theories is also briefly discussed.
We argue that non-Abelian gauge fields can be treated as the pseudo-Goldstone vector bosons caused by spontaneous Lorentz invariance violation (SLIV). To this end, the SLIV which evolves in a general ...Yang-Mills type theory with the nonlinear vector field constraint \(Tr(% \boldsymbol{A}_{\mu }\boldsymbol{A}^{\mu})=\pm M^{2}\) (\(M\) is a proposed SLIV scale) imposed is considered in detail. With an internal symmetry group \(G\) having \(D\) generators not only the pure Lorentz symmetry SO(1,3), but the larger accidental symmetry \(SO(D,3D)\) of the SLIV constraint in itself appears to be spontaneously broken as well. As a result, while the pure Lorentz violation still generates only one genuine Goldstone vector boson, the accompanying pseudo-Goldstone vector bosons related to the \(SO(D,3D)\) breaking also come into play in the final arrangement of the entire Goldstone vector field multiplet. Remarkably, they remain strictly massless, being protected by gauge invariance of the Yang-Mills theory involved. We show that, although this theory contains a plethora of Lorentz and \(CPT\) violating couplings, they do not lead to physical SLIV effects which turn out to be strictly cancelled in all the lowest order processes considered. However, the physical Lorentz violation could appear if the internal gauge invariance were slightly broken at very small distances influenced by gravity. For the SLIV scale comparable with the Planck one the Lorentz violation could become directly observable at low energies.
It has long been known that photons and gravitons may appear as vector and tensor Goldstone modes caused \ by spontaneous Lorentz invariance violation (SLIV). Usually this approach is considered for ...photons and gravitons separately. We develop the emergent electrogravity theory consisting of the ordinary QED and the tensor field gravity model which mimics the linearized general relativity in Minkowski spacetime. In this theory, Lorentz symmetry appears incorporated into higher global symmetries of the length-fixing constraints put on the vector and tensor fields involved, \(A_{\mu }^{2}=\pm M_{A}^{2}\) and \(H_{\mu \nu }^{2}=\pm M_{H}^{2}\) (\(M_{A}\) and \(M_{H}\) are the proposed symmetry breaking scales). We show that such a SLIV pattern being related to breaking of global symmetries underlying these constraints induces the massless Goldstone and pseudo-Goldstone modes shared among photon and graviton. While for a vector field case the symmetry of the constraint coincides with Lorentz symmetry \(SO(1,3)\) of the electrogravity Lagrangian, the tensor field constraint itself possesses much higher global symmetry \(SO(7,3)\), whose spontaneous violation provides a sufficient number of zero modes collected in a graviton. Accordingly, while photon may only contain true Goldstone modes, graviton appears at least partially composed from pseudo-Goldstone modes rather than from pure Goldstone ones. When expressed in terms of these modes, the theory looks essentially nonlinear and contains a variety of Lorentz and \(CPT\) violating couplings. However, all SLIV effects turn out to be strictly cancelled in the lowest order processes that is considered in some detail. How this emergent electrogravity theory could be observationally differed from conventional QED and GR theories is also briefly discussed.
Spontaneous Lorentz violation realized through a nonlinear vector field constraint of the type \(A_{\mu}A^{\mu}=M^{2}\) (\(M\) is the proposed scale for Lorentz violation) is shown to generate ...massless vector Goldstone bosons, gauging the starting global internal symmetries in arbitrary relativistically invariant theories. The gauge invariance appears in essence as a necessary condition for these bosons not to be superfluously restricted in degrees of freedom, apart from the constraint due to which the true vacuum in a theory is chosen by the Lorentz violation. In the Abelian symmetry case the only possible theory proves to be QED with a massless vector Goldstone boson naturally associated with the photon, while the non-Abelian symmetry case results in a conventional Yang-Mills theory. These theories, both Abelian and non-Abelian, look essentially nonlinear and contain particular Lorentz (and \(CPT\)) violating couplings when expressed in terms of the pure Goldstone vector modes. However, they do not lead to physical Lorentz violation due to the simultaneously generated gauge invariance.
Category:
Ankle; Basic Sciences/Biologics
Introduction/Purpose:
Extracorporeal shockwave therapy (ESWT) is a non-invasive treatment modality that is utilized in the treatment of chronic Achilles ...tendinopathy (AT).
The purpose of this study was to retrospectively assess outcomes following ESWT for both NAT and IAT at greater than 1-year follow-up, and to identify potential predictors of outcomes.
Methods:
Chart review was conducted to identify patients who underwent ESWT for AT with a minimum of 1-year follow-up. Data collected and assessed included: patient demographics, pathological characteristics, treatment characteristics, Victorian Institute of Sports Assessment-Achilles (VISA-A) and visual analog scale (VAS) scores and failures. Linear regression was performed to identify potential predictors of outcomes. Survival analysis was conducted using Kaplan Meier curves.
Fifty-two cases of IAT and 34 cases of NAT were included. The mean follow-up in the NAT cohort was 22.3±10.2 months and the mean follow-up time in the IAT cohort was 26.8±15.8 months.
Results:
Improvements in VISA-A and VAS scores were observed in the NAT cohort at 6 months follow-up and at final follow-up (p < 0.01). Improvements in VISA-A scores and VAS scores were recorded in the IAT cohort at 6 months follow-up which subsequently deteriorated at final follow-up. In the NAT cohort, the failure rate at 6 months follow-up was 11.8% which increased to 29.4% at final follow-up. In the IAT cohort, the failure rate at 6 months follow-up was 32.7% which increased to 59.6% at final follow-up. Predictors of poor outcomes in the NAT cohort included pre-ESWT subjective clinical score, male, presence of cardiovascular risk factor, and increasing MRI severity. Predictors of poor outcomes in the IAT cohort included pre-ESWT subjective clinical score and increasing MRI severity.
Conclusion:
This study found that superior subjective clinical outcomes together with a lower failure rate maintained over 1 year in the NAT cohort compared to the IAT cohort. This may implicate ESWT as a temporising treatment in IAT and a longer term solution in patients with NAT.
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