Conjugate spinor field equation for massless spin-3/2 field in de Sitter ambient space

S. Falahi, S. Parsamehr


The quantum field theory in de Sitter ambient space provide us with a comprehensive description of massless gravitational field. Using the gauge-covariant derivative in the de Sitter ambient space, the gauge invariant Lagrangian density has been found.
In this paper, the equation of the conjugate spinor for massless spin-$\frac{3}{2}$ field is obtained by Euler-Lagrange equation. Then the field equation is written in terms of the Casimir operator of the de Sitter group. Finally, the gauge invariant field equation is presented.

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S. Perlmutter et al., Measurement of and Ω from 42 highredshift supernovae, Astrophys. J. 517 (1999) 565.

A.G. Riess et al., Observational evidence from supernovae for an accelerating universe and a cosmological constant, Astron. J. 116 (1998) 1009.

J. P. Henry, U. G. Briel, and H. Bohringer,The evolution of galaxy clusters, Scientific American 279 (1998) 52.

J. P. Henry,Measuring cosmological parameters from the evolution of cluster X-ray temperatures, Astrophys. J. 534 (2000) 565 .

P. de Bernardis, et al., A flat universe from high-resolution maps of the cosmic microwave background radiation, Nature 404 (2000) 955.

P. A. R. Ade, et al.,Detection of B-Mode polarization at degree angular scales by BICEP2, Phys. Rev. Lett. 112, (2014) 241101. 112.241101

T.S. Bunch, P.C.W. Davies,Quantum field theory in de sitter space: renormalization by point-splitting, Proc. R. Soc. Lond. A., 360 (1978) 117.

B. Allen,Vacuum states in de Sitter space, Phys. Rev. D 32 (1985) 3136.

J. Bros, U. Moschella,Two-point functions and quantum field in the de Sitter Universe, Rev. Math. Phys. 8 (1996) 327.

N.A. Chernikov, E. A. Tagirov,Quantum theory of scalar field in de Sitter space-time, Ann. Inst. Henri Poincare´ IX, A9 (1968) 109.

M.V. Takook,Entropy of quantum fields in de sitter space-time, Annals of Physics 367 (2016) 6.

M.V. Takook, Quantum field theory in de Sitter universe: ambient space formalism (2016) arXiv:1403.1204v2.

S. Parsamehr, M.Enayati, M.V.Takook,Super-gauge field in de Sitter universe, Eur. Phys. J. C 76 (2016) 260.

M.V. Takook,Theorie quantique des champs pour des syst ´ emes `el´ ementaires “massifs” et de “masse nulle” sur l’espace- temps ´ de de Sitter, These de l’universit ` e Paris VI (1997). ´

P. Bartesaghi, J.P. Gazeau, U. Moschella, M.V. Takook, Dirac fields and thermal effects in the de Sitter universe, Class.

Quant. Grav. 18 (2001) 4373.


E. Yusofi, M. Mohsenzadeh,Scale-dependent power spectrum

from initial excited-de Sitter modes, JHEP, 09 (2014) 020.

P. Nath and R. Arnowitt,Generalized Supergauge Symmetry as a New Framework for Unified Gauge Theories, Phys. Lett. B 56 (1975) 177.

D. Z. Freedman, P. van Nieuwenhuizen, and S. Ferrara,Progress toward a theory of supergravity, Phys. Rev. D 13 (1976) 3214.3218. 19. W. Rarita, J. Schwinger,On a Theory of Particles with HalfIntegral Spin Phys. Rev. 60(1941) 61.

B. Binegar,C. Fronsdal,W. Heidenreich,Conformal QED, J. Math. Phys. 24 (1983) 2828.

F. Strocchi,Spontaneous symmetry breaking in local gauge quantum field theory; the Higgs mechanism, Commun. Math. Phys. 56 (1977) 57.

T. Garidi, J.P. Gazeau, S. Rouhani, M.V. Takook,Massless vector field in de Sitter universe, J. Math. Phys. 49 (2008) 032501.

S. Parsamehr,Lagrangian for massless gravitational field in de Sitter space, Eur. Phys. J. Plus 132 (2017) 291.



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