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Lagrangian corresponding to some Gup models

    https://doi.org/10.1142/S0219887822502000Cited by:2 (Source: Crossref)

    In this paper, we introduce the generalized Legendre transformation for the GUP Hamiltonian. From this, we define the non-canonical momentum. We interpret the momentum in GUP as the non-canonical momentum. We construct the GUP Lagrangian for some GUP models.

    AMSC: 83C10, 83C20

    References

    • 1. H. S. Snyder, Quantized space-time, Phys. Rev. 71(1) (1947) 38. Crossref, Web of ScienceGoogle Scholar
    • 2. C. N. Yang, On quantized space-time, Phys. Rev. 72(9) (1947) 874. Crossref, Web of ScienceGoogle Scholar
    • 3. C. A. Mead, Possible connection between gravitation and fundamental length, Phys. Rev. B 135(3) (1964) 849. Crossref, Web of ScienceGoogle Scholar
    • 4. F. Karolyhazy, Gravitation and quantum mechanics of macroscopic objects, Il Nuovo Cimento A 42(2) (1966) 390–402. CrossrefGoogle Scholar
    • 5. D. Amati, M. Ciafaloni and G. Veneziano, Superstring collisions at Planckian energies, Phys. Lett. B 197(1–2) (1987) 81–88. Crossref, Web of ScienceGoogle Scholar
    • 6. D. J. Gross and P. F. Mende, The high-energy behavior of string scattering amplitudes, Phys. Lett. B 197(1–2) (1987) 129–134 Crossref, Web of ScienceGoogle Scholar
    • 7. D. Amati, C. Marcello and V. Gabriele, Can spacetime be probed below the string size?, Phys. Lett. B 216(1–2) (1989) 41–47. Crossref, Web of ScienceGoogle Scholar
    • 8. K. Konishi, P. Giampiero and P. Paolo, Minimum physical length and the generalized uncertainty principle in string theory, Phys. Lett. B 234(3) (1990) 276–284. Crossref, Web of ScienceGoogle Scholar
    • 9. J. Polchinski, Quantum gravity at the Planck length, Int. J. Mod. Phys. A 14(17) (1999) 2633–2658. Link, Web of ScienceGoogle Scholar
    • 10. S. Capozziello, G. Lambiase and G. Scarpetta, Generalized uncertainty principle from quantum geometry, preprint (1999), arXiv:gr-qc/9910017. Google Scholar
    • 11. M. Maggiore, A generalized uncertainty principle in quantum gravity, Phys. Lett. B 304(1–2) (1993) 65–69. Crossref, Web of ScienceGoogle Scholar
    • 12. A. Kempf, M. Gianpiero and R. B. Mann, Hilbert space representation of the minimal length uncertainty relation, Phys. Rev. D 52(2) (1995) 1108. Crossref, Web of ScienceGoogle Scholar
    • 13. M. Bojowald and A. Kempf, Generalized uncertainty principles and localization of a particle in discrete space, Phys. Rev. D 86(8) (2012) 085017. Crossref, Web of ScienceGoogle Scholar
    • 14. F. Scardigli, Generalized uncertainty principle in quantum gravity from micro-black hole gedanken experiment, Phys. Lett. B 452(1–2) (1999) 39–44. Crossref, Web of ScienceGoogle Scholar
    • 15. R. J. Adler and D. I. Santiago, On gravity and the uncertainty principle, Mod. Phys. Lett. A 14(20) (1999) 1371–1381. Link, Web of ScienceGoogle Scholar
    • 16. F. Scardigli and R. Casadio, Generalized uncertainty principle, extra dimensions and holography, Class. Quantum Grav. 20(18) (2003) 3915. Crossref, Web of ScienceGoogle Scholar
    • 17. P. Pedram, Pouria, A higher order GUP with minimal length uncertainty and maximal momentum, Phys. Lett. B 714 (2012) 317–323. Crossref, Web of ScienceGoogle Scholar
    • 18. P. Pedram, A higher order GUP with minimal length uncertainty and maximal momentum II: Applications, Phys. Lett. B 718(2) (2012) 638–645. Crossref, Web of ScienceGoogle Scholar
    • 19. J. Vahedi, N. Kourosh and P. Pedram, Generalized uncertainty principle and the Ramsauer–Townsend effect, Gravit. Cosmol. 18(3) (2012) 211–215. Crossref, Web of ScienceGoogle Scholar
    • 20. H. Shababi and W. S. Chung, On the two new types of the higher order GUP with minimal length uncertainty and maximal momentum, Phys. Lett. B 770 (2017) 445–450. Crossref, Web of ScienceGoogle Scholar
    • 21. K. Nouicer, Quantum-corrected black hole thermodynamics to all orders in the Planck length, Phys. Lett. B 646(2–3) (2007) 63–71. Crossref, Web of ScienceGoogle Scholar
    • 22. H. Shababi, P. Pouria and W. S. Chung, On the quantum mechanical solutions with minimal length uncertainty, Int. J. Mod. Phys. A 31(18) (2016) 1650101. Link, Web of ScienceGoogle Scholar
    • 23. P. Jizba, K. Hagen and S. Fabio, Uncertainty relation on a world crystal and its applications to micro black holes, Phys. Rev. D 81(8) (2010) 084030. Crossref, Web of ScienceGoogle Scholar
    • 24. W. S. Chung and H. Hassanabadi, On the position representation of Pedrams higher order GUP, Int. J. Theor. Phys. 58(6) (2019) 1791–1802. Crossref, Web of ScienceGoogle Scholar
    • 25. H. Shababi and W. S. Chung, Some applications of the most general form of the higher-order GUP with minimal length uncertainty and maximal momentum, Mod. Phys. Lett. A 33(12) (2018) 1850068. Link, Web of ScienceGoogle Scholar
    • 26. W. S. Chung and H. Hassanabadi, New generalized uncertainty principle from the doubly special relativity, Phys. Lett. B 785 (2018) 127–131. Crossref, Web of ScienceGoogle Scholar
    • 27. W. S. Chung and H. Hassanabadi, A new higher order GUP: one dimensional quantum system, Eur. Phys. J. C 79(3) (2019) 1–7. Crossref, Web of ScienceGoogle Scholar
    • 28. O. I. Chashchina, S. Abhijit and Z. K. Silagadze, On deformations of classical mechanics due to Planck-scale physics, Int. J. Mod. Phys. D 29(10) (2020) 2050070. Link, Web of ScienceGoogle Scholar
    • 29. S. Mignemi, Classical and quantum mechanics of the nonrelativistic Snyder model, Phys. Rev. D 84(2) (2011) 025021. Crossref, Web of ScienceGoogle Scholar
    • 30. R. Casadio and S. Fabio, Generalized uncertainty principle, classical mechanics, and general relativity, Phys. Lett. B 807 (2020) 135558. Crossref, Web of ScienceGoogle Scholar
    • 31. S. Das and E. C. Vagenas, Phenomenological implications of the generalized uncertainty principle, Can. J. Phys. 87(3) (2009) 233–240. Crossref, Web of ScienceGoogle Scholar
    • 32. B. Bagchi and F. Andreas, Minimal length in quantum mechanics and non-Hermitian Hamiltonian systems, Phys. Lett. A 373(47) (2009) 4307–4310. Crossref, Web of ScienceGoogle Scholar
    • 33. A. Paliathanasis, P. Supriya and P. Souvik, Scalar field cosmology modified by the generalized uncertainty principle, Class. Quantum Grav. 32(24) (2015) 245006. Crossref, Web of ScienceGoogle Scholar
    • 34. S. Benczik, L. N. Chang, D. Minic, N. Okamura, S. Rayyan and T. Takeuchi, Short distance versus long distance physics: The classical limit of the minimal length uncertainty relation, Phys. Rev. D 66(2) (2002) 026003. Crossref, Web of ScienceGoogle Scholar
    • 35. K. Nozari and S. Akhshabi, Noncommutative geometry and the stability of circular orbits in a central force potential, Chaos, Solitons Fractals 37(2) (2008) 324–331. Crossref, Web of ScienceGoogle Scholar
    • 36. A. F. Ali, Minimal length in quantum gravity, equivalence principle and holographic entropy bound, Class. Quantum Grav. 28(6) (2011) 065013. Crossref, Web of ScienceGoogle Scholar
    • 37. V. M. Tkachuk, Deformed Heisenberg algebra with minimal length and the equivalence principle, Phys. Rev. A 86(6) (2012) 062112. Crossref, Web of ScienceGoogle Scholar
    • 38. X. Guo, W. Peng and H. Yang, The classical limit of minimal length uncertainty relation: revisit with the Hamilton-Jacobi method, J. Cosmol. Astropart. Phys. 2016(5) (2016) 062. Crossref, Web of ScienceGoogle Scholar
    • 39. S. Ghosh, Quantum gravity effects in geodesic motion and predictions of equivalence principle violation, Class. Quantum Grav. 31(2) (2013) 025025. Crossref, Web of ScienceGoogle Scholar
    • 40. S. Mignemi and R. Trajn, Snyder dynamics in a Schwarzschild spacetime, Phys. Rev. D 90(4) (2014) 044019. Crossref, Web of ScienceGoogle Scholar
    • 41. F. Scardigli and C. Roberto, Gravitational tests of the generalized uncertainty principle, Eur. Phys. J. C 75(9) (2015) 1–12. Crossref, Web of ScienceGoogle Scholar
    • 42. L. Faddeev and R. Jackiw, Hamiltonian reduction of unconstrained and constrained systems, Phys. Rev. Lett. 60(17) (1988) 1692. Crossref, Web of ScienceGoogle Scholar
    • 43. S. Ghosh and P. Pal, Deformed special relativity and deformed symmetries in a canonical framework, Phys. Rev. D 75(10) (2007) 105021. Crossref, Web of ScienceGoogle Scholar
    • 44. S. Ghosh, Lagrangian for doubly special relativity particle and the role of noncommutativity, Phys. Rev. D 74(8) (2006) 084019. Crossref, Web of ScienceGoogle Scholar
    • 45. A. Kempf and G. Mangano, Minimal length uncertainty relation and ultraviolet regularization, Phys. Rev. D 55(12) (1997) 7909. Crossref, Web of ScienceGoogle Scholar
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