Treating Ostrogradski instability for Galilean invariant Chern-Simon’s model via 
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 symmetry

Paul, Biswajit; Dhar, Himangshu; Chowdhury, Mangobinda; Saha, Biswajit

doi:10.1103/physrevd.99.065018

Cited by 6 publications

(7 citation statements)

References 48 publications

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“…The problem of ghosts starts back at the beginning of the quantum field theories where unwanted degrees of freedom contribute divergences and leads to instability in the theory. There have been many attempts to remove these ghost fields with different approaches while a common way is still a topic of research [5,37,42]. Keeping this in mind, we have considered the use of PT −symmetries as in [5] where ghosts were successfully removed from the Pias-Ulhenback oscillator.…”

Section: Discussionmentioning

confidence: 99%

“…In [36] the author has removed the ghost from the degenerate gravity theories, with a surface term making it HD model, by solving the second class constraints. While in the case of the Gallilean invariant Chern-Simon's model, the constraint structure was not much helpful [37]. The second class constraints can be useful only if the ghost field is contained in it and is solvable.…”

Section: Introductionmentioning

confidence: 99%

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Ghosts in higher derivative Maxwell-Chern-Simon's theory and $\mathcal{PT}-$symmetry

Paul,

Dhar,

Saha

2020

Preprint

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Ghost fields in quantum field theory have been a long standing problem. Specifically, theories with higher derivatives involve ghosts that appear in the Hamiltonian in the form of linear momenta term, which is commonly known as the Ostrogradski ghost. Higher derivative theories may involve both types of constraints i.e. first class and second class. Interestingly, these higher derivative theories may have non-Hermitian Hamiltonian respecting PT −symmetries. In this paper, we have considered the PT −symmetric nature of the extended Maxwell-Chern-Simon's theory and employed the second class constraints to remove the linear momenta terms causing the instabilities. We found that the removal is not complete rather conditions arise among the coefficients of the operator Q.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Ghosts in higher derivative Maxwell-Chern-Simon's theory and $\mathcal{PT}-$symmetry

Paul,

Dhar,

Saha

2020

Preprint

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“…Being a non-Hermitian Hamiltonian, it does not necessarily has complex energy eigenvalues . As discussed in (33), owing to the PT symmetric nature, the model has real energy eigenvalues. The existence of antilinearity in the model is confirmed since the Hamiltonian obeys…”

Section: The Galilean Invariant Chern-simons Modelmentioning

confidence: 99%

“…In PT symmetries, the theory may not be invariant under individual transformations of P (which works as x → −x, p → − p ) and T (which works as x → x, p → − p, i → −i), but, under the collective effect of PT , the theory should remain invariant. Apart from the PT operator, Bender et al also pointed out another operator, called the C operator [31], which can be used to remove the ghost states as shown in [32,33]. The existence and completeness of the theory demand that the C-operator should be governed by the three conditions…”

Section: Antilinearity In General Quantum Theoriesmentioning

confidence: 99%

Removal of instabilities of the higher derivative theories in the light of antilinearity

2021

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Theories with higher derivatives involve linear instabilities in the Hamiltonian commonly known as Ostrogradski ghosts and can be viewed as a very serious problem during quantization. To cure this, we have considered the properties of antilinearity that can be found inherently in the non-Hermitian Hamiltonians. Owing to the existence of antilinearity, we can construct an operator, called the V-operator, which acts as an intertwining operator between the Hamiltonian and its Hermitian conjugate. We have used this V-operator to remove the linear momentum term from the higher derivative Hamiltonian by making it non-Hermitian in the first place via an isospectral similarity transformation. The final form of the Hamiltonian is free from the Ostrogradski ghosts under some restriction on the mass term.

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“…al. pointed out another operator called the C operator [26] that can serve to remove the ghost fields as shown in [27,28]. The existence and completeness of the theory demands that the C−operator should be governed by the three conditions that…”

Section: Antilinearity In General Quantum Theoriesmentioning

confidence: 99%

Groundwater quality assessment in Jirania Block, west district of Tripura, India, using hydrogeochemical fingerprints

et al. 2019

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A hydrogeochemical assessment was carried out in Jirania Block of west district of Tripura, India, to evaluate the geochemical processes and groundwater suitability for drinking and irrigation purposes. Twenty-two groundwater samples were collected at different lithologies in the study area during post-monsoon period. The collected samples were analyzed for major ions and heavy metals using the standard protocols. The analyzed parameters were used for various geochemical plots and indices to classify the groundwater quality. The order of dominance of cations is Ca 2+ > Mg 2+ > Na + > K + and HCO 3 − > Cl − > SO 4 2− > NO 3 − for anions. Higher concentration of Fe and Mn was observed in most of the samples, which are above the acceptable limit of BIS standard. Correlation analysis and factor analysis were applied to unravel the relationship between ions and to identify the possible geochemical processes in groundwater. The interpretation of analytical data, plots and indices reveals that the weathering, mineral dissolution and ion exchange reactions are the major controlling factors for the groundwater geochemistry. The quality of the groundwater is suitable for drinking and irrigation purposes to the local community in this assessment period.

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Treating Ostrogradski instability for Galilean invariant Chern-Simon’s model via PT symmetry

Cited by 6 publications

References 48 publications

Ghosts in higher derivative Maxwell-Chern-Simon's theory and $\mathcal{PT}-$symmetry

Ghosts in higher derivative Maxwell-Chern-Simon's theory and $\mathcal{PT}-$symmetry

Removal of instabilities of the higher derivative theories in the light of antilinearity

Groundwater quality assessment in Jirania Block, west district of Tripura, India, using hydrogeochemical fingerprints

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