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Hamiltonian BRST-invariant deformations in Abelian gauge theory with higher derivative matter fields

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Abstract

We construct the consistent interactions among the Abelian gauge fields and various higher derivative matter fields within the framework of the Hamiltonian BRST formalism. To achieve this, we mainly investigate a set of iterative equations with respect to the free model under study by using the cohomological technique. Concretely, it is shown that the second-order and the other higher-order deformations of the BRST charge are supposed to be zero. While for the BRST-invariant Hamiltonian, the third-order as well as the corresponding higher-order deformation terms vanish completely for scalar fields. In special, the deformation of BRST-invariant Hamiltonian for the spinor field model terminates at order one as we can imagine. Furthermore, after plugging these deformed quantities into the original Hamiltonian and exploiting the ghost-independent terms, we recover the usual local gauge symmetries of the resulting interacting theory which can be interpreted as the gaugings of the rigid invariance of the uncoupled system.

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References

  1. C. Becchi, A. Rouet, R. Stora, Renormalization of the abelian Higgs–Kibble model. Commun. Math. Phys 42, 127–162 (1975)

    Article  ADS  MathSciNet  Google Scholar 

  2. C. Becchi, A. Rouet, R. Stora, Renormalization of gauge theories. Ann. Phys 98(2), 287–321 (1976)

    Article  ADS  MathSciNet  Google Scholar 

  3. I.V. Tyutin, Gauge Invariance in Field Theory and Statistical Physics in Operator Formalism, P.N. Lebedev Phys. Institute FIAN N. 39 (1975)

  4. J. Zinn-Justin, Renormalization of Gauge theories. Lecture Not. Phys. 37, 1–39 (1975)

    Article  ADS  Google Scholar 

  5. M. Henneaux, Lectures on the antifield-BRST formalism for gauge theories. Nucl. Phys. B 18A, 47–106 (1990)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  6. M. Henneaux, C. Teitelboim, Quantization of Gauge Systems (Princeton University Press, New Jersey, 1992)

    Book  MATH  Google Scholar 

  7. G. Barnich, F. Brandt, M. Henneaux, Local BRST cohomology in the antifield formalism: I–general theorems. Commun. Math. Phys. 174, 57–92 (1995)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  8. G. Barnich, F. Brandt, M. Henneaux, Local BRST cohomology in the antifield formalism: II–application to Yang–Mills theory. Commun. Math. Phys. 174, 93–116 (1995)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  9. F. Brandt, Local BRST cohomology and covariance. Commun. Math. Phys. 190(2), 459–489 (1997)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  10. G. Barnich, F. Brandt, M. Henneaux, Local BRST cohomology in gauge theories. Phys. Rep. 338, 439–569 (2000)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  11. A. Fuster, M. Henneaux, A. Maas, BRST-antifield quantization: a short review. Int. J. Geom. Methods Mod. Phys. 2, 939–964 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  12. E.S. Fradkin, G.A. Vilkovisky, Quantization of relativistic systems with constraints. Phys. Lett. B 55, 224 (1975)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  13. I.A. Batalin, G.A. Vilkovisky, Relativistic S-matrix of dynamical systems with boson and fermion constraints. Phys. Lett. B 69, 309 (1977)

    Article  ADS  Google Scholar 

  14. I.A. Batalin, E.S. Fradkin, Operator quantization of relativistic dynamical systems subject to first class constraints. Phys. Lett. B 128, 303 (1983)

    Article  ADS  Google Scholar 

  15. M. Henneaux, Hamiltonian form of the path integral for theories with a gauge freedom. Phys. Rep. 126, 1 (1985)

    Article  ADS  MathSciNet  Google Scholar 

  16. R.E. Damgaard, F. De Jonghe, K. Bering, Sp(2)-symmetric Langrangian BRST quantization. Nucl. Phys. B 455(1–2), 440–460 (1995)

    Article  ADS  MATH  Google Scholar 

  17. R. Ferraro, D.M. Sforza, BRST operator quantization of generally covariant gauge systems. Phys. Rev. D 55, 4785–4790 (1997)

    Article  ADS  MathSciNet  Google Scholar 

  18. C. Bizdadea, S.O. Saliu, On the BRST quantization of massive Abelian gauge fields. Rom. Rep. Phys. 50, 225–231 (1998)

    MathSciNet  Google Scholar 

  19. R. Marnelius, On the quantum BRST structure of classical mechanics. Mod. Phys. Lett. A 15, 1665–1678 (2000)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  20. A.A. Varshovi, Gauge fixing invariance and anti-BRST symmetry. Int. J. Geom. Methods Mod. Phys. 14(11), 1750168 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  21. J.W. Holten, Aspects of BRST quantization, in Topology and Geometry in Physics. Lecture Notes in Physics, vol. 659 (Springer, Berlin, 2005), pp. 99–166

  22. P.M. Lavrov, P.Y. Moshin, A.A. Reshetnyak, Superfield formulation of the Lagrangian BRST quantization method. Mod. Phys. Lett. A 10, 2687–2694 (1995)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  23. D.M. Gitman, P.Y. Moshin, A.A. Reshetnyak, Local superfield Lagrangian BRST quantization. J. Math. Phys. 46, 072302 (2005)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  24. D.M. Gitman, P.Y. Moshin, A.A. Reshetnyak, An embedding of the BV quantization into an \(N=1\) local superfield formalism. Phys. Lett. B 621, 295–308 (2005)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  25. R.P. Malik, Nilpotent (anti-)BRST symmetry transformations for dynamical non-Abelian 2-form gauge theory: superfield formalism. EPL 91(5), 51003 (2010)

    Article  ADS  Google Scholar 

  26. A.V. Bratchikov, Classical BRST charge and observables in reducible gauge theories. Acta Phys. Polon. B 48, 1335 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  27. G. Barnich, M. Henneaux, Consistent couplings between fields with a gauge freedom and deformations of the master equation. Phys. Lett. B 311, 123–129 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  28. C. Bizdadea, M.T. Miauta, S.O. Saliu, Hamiltonian BRST interactions in Abelian theories. Eur. Phys. J. C 19, 191–200 (2001)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  29. C. Bizdadea, M.T. Miauta, S.O. Saliu, Nonabelian interactions from Hamiltonian BRST cohomology. Eur. Phys. J. C 21, 577–585 (2001)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  30. C. Bizdadea, E.M. Cioroianu, I. Negru, S.O. Saliu, Cohomological derivation of the couplings between an abelian gauge field and matter fields. Ann. Phys. 10, 415–427 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  31. C. Bizdadea, E.M. Cioroianu, M.T. Miauta, I. Negru, S.O. Saliu, Lagrangian cohomological couplings among vector fields and matter fields. Ann. Phys. 10, 921–934 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  32. M.C. Bertin, B.M. Pimentel, G.E.R. Zambrano, The canonical structure of Podolsky’s generalized electrodynamics on the null-plane. J. Math. Phys. 52, 10 (2009)

    MathSciNet  MATH  Google Scholar 

  33. A.A. Nogueira, C. Palechor, A.F. Ferrari, Reduction of order and Fadeev–Jackiw formalism in generalized electrodynamics. Nucl. Phys. B 939, 372–390 (2019)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  34. D.A. Eliezer, R.P. Woodard, The problem of nonlocality in string theory. Nucl. Phys. B 325(2), 389–469 (1989)

    Article  ADS  MathSciNet  Google Scholar 

  35. A. Anisimov, E. Babichev, A. Vikman, B-inflation. JCAP 0506, 006 (2005)

    Article  ADS  Google Scholar 

  36. R. Myrzakulov, S. Odintsov, L. Sebastiani, Inflationary universe from higher derivative quantum gravity coupled with scalar electrodynamics. Nucl. Phys. B 907, (2016)

  37. R.P. Woodard, Avoiding dark energy with \(1/R\) modifications of gravity. Lect. Notes. Phys. 720, 403 (2007)

    Article  ADS  Google Scholar 

  38. M. Ostrogradsky, Mem. Ac. St. Petersbourg VI 4, 385 (1850)

  39. F.J. Urries, J. Julve, Ostrogradski formalism for higher-derivative scalar field theories. J. Phys. A 31, 6949–6964 (1998)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  40. L. Faddeev, R. Jackiw, Hamiltonian reduction of unconstrained and constrained systems. Phys. Rev. Lett. 60, 1692 (1988)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  41. L. Liao, Y.C. Huang, Non-equivalence of Faddeev–Jackiw method and Dirac-Bergmann algorithm and the modification of Faddeev–Jackiw method for keeping the equivalence. Ann. Phys. 322, 2469 (2007)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  42. D.J. Toms, Faddeev–Jackiw quantization and the path integral. Phys. Rev. D 92, 105026 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  43. J.L. Dai, Stability and consistent interactions in higher derivative matter field theories. Eur. Phys. J. Plus 135, 555 (2020)

    Article  Google Scholar 

  44. G. Barnich, N. Boulanger, M. Henneaux, B. Julia, V. Lekeu, A. Ranjbar, Deformations of vector-scalar models. JHEP 2, 064 (2018)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  45. D.S. Kaparulin, I.Y. Karataeva, S.L. Lyakhovich, Higher derivative extensions of 3d Chern–Simons models: conservation laws and stability. Eur. Phys. J. C 75, 552 (2015)

    Article  ADS  Google Scholar 

  46. P. Mukherjee, B. Pau, Gauge invariances of higher derivative Maxwell–Chern–Simons field theory: a new Hamiltonian approach. Phys. Rev. D 85, 045028 (2012)

    Article  ADS  Google Scholar 

  47. S.C. Sararu, A first-class approach of higher derivative Maxwell–Chern–Simons–Proca model. Eur. Phys. J. C 75, 11 (2014)

    Google Scholar 

  48. H.J. Rothe, K.D. Rothe, From the BRST invariant Hamiltonian to the field–antifield formalism. Ann. Phys 323, 1384–1396 (2008)

    Article  ADS  MathSciNet  MATH  Google Scholar 

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Acknowledgements

The author would like to thank the G.W.Wan for long time encouragements and is grateful to S.M.Zhu for useful support.

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  1. Department of Mathematical Sciences, Zhejiang Sci-Tech University, Hangzhou, 310018, P. R. China

    Jialiang Dai

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  1. Jialiang Dai
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Dai, J. Hamiltonian BRST-invariant deformations in Abelian gauge theory with higher derivative matter fields. Eur. Phys. J. Plus 136, 135 (2021). https://doi.org/10.1140/epjp/s13360-021-01148-x

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