Skip to main content
SpringerLink
Log in

Enhancing Gauge Symmetries Via the Symplectic Embedding Approach

  • Chapter
  • First Online:
Distance, Symmetry, and Topology in Carbon Nanomaterials

Part of the book series: Carbon Materials: Chemistry and Physics ((CMCP,volume 9))

  • 537 Accesses

Abstract

One of the best ways to increase the fundamental symmetries of the physical systems with singular Lagrangian is the gauging of those models with the help of symplectic formalism of constrained systems. The main idea of this approach is based on the embedding of the model in an extended phase-space. After the gauging process had done, we can obtain generators of gauge transformations of the model.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Abarghouei Nejad S, Dehghani M, Monemzadeh M (2014) Gauging the relativistic particle model on the noncommutative plane. arXiv:hep-th/1507.02329

    Google Scholar 

  • Abreu EMC, Neto JA, Mendes ACR, Neves C, Oliveira W (2012) Obtaining gauge invariant actions via symplectic embedding formalism. Ann Phys 524(8):434–455

    Article  Google Scholar 

  • Abreu EMC, Mendes ACR, Neves C, Oliveira W, Silva RCN (2013) QCD gauge symmetries through Faddeev–Jackiw symplectic method. JHEP 6:093, front matter + 10 pp

    Google Scholar 

  • Batalin IA, Fradkin ES (1987) Operational quantization of dynamical systems subject to second class constraints. Nucl Phys B 279:514–528

    Article  Google Scholar 

  • Batalin IA, Tyutin IV (1991) Existence theorem for the effective gauge algebra in the generalized canonical formalism with abelian conversion of second-class constraints. Inter J Mod Phys A 6(18):3255–3282

    Article  Google Scholar 

  • Batalin IA, Vilkovisky GA (1981) Gauge algebra and quantization. Phys Lett B 102(1):27–31

    Article  Google Scholar 

  • Batalin IA, Fradkin ES, Fradkina TE (1989) Another version for operatorial quantization of dynamical systems with irreducible constraints. Nucl Phys B 314(1):158–174

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Bergmann PG, Goldberg I (1955) Dirac bracket transformations in phase space. Phys Rev 98(2):531–538

    Article  Google Scholar 

  • Dirac PAM (1950) Generalized Hamiltonian dynamics. Can J Math 2:129–148

    Article  Google Scholar 

  • Dirac PAM (1967) Lectures on quantum mechanics. Second printing of the 1964 original. Belfer Graduate School of Science monographs series, 2. Belfer Graduate School of Science, New York; produced and distributed by Academic Press, Inc, New York

    Google Scholar 

  • Ebrahimi AS, Monemzadeh M (2014) Mathematical feature of gauge theory. Inter J Theor Phys 53(12):4121–4131

    Article  Google Scholar 

  • Faddeev L, Jackiw R (1988) Hamiltonian reduction of unconstrained and constrained systems. Phys Rev Lett 60(17):1692–1694

    Article  Google Scholar 

  • Govaerts J (1990) Hamiltonian reduction of first-order actions. Inter J Mod Phys A 5(18):3625–3640

    Article  Google Scholar 

  • Henneaux M, Teiltelboim C (1992) Quantization of gauge system. Princeton University Press, Princeton

    Google Scholar 

  • Henneaux M, Teitelboim C, Zanelli J (1990) Gauge invariance and degree of freedom count. Nucl Phys B 332(1):169–188

    Article  Google Scholar 

  • Jackiw R (1994) (Constrained) Quantization without tears. Constraint theory and quantization methods (Montepulciano, 1993). World Sci Publ, River Edge, pp 163–175

    Google Scholar 

  • Kim YW, Lee CY, Kim SK (2004) Symplectic embedding of amassive vector–tensor theory with topological coupling. Eur Phys J C 34:383–392

    Article  Google Scholar 

  • Monemzadeh M, Ebrahimi AS (2012) Embedding of noncommutative massive QED. Mod Phys Lett A 27(14):5163–5176

    Article  Google Scholar 

  • Monemzadeh M, Ebrahimi AS, Sramadi S, Dehghani M (2014) Gauging of non–abelian Chern–Simons model. Mod Phys Lett A 29(5):1450028, 9 pp

    Article  Google Scholar 

  • Montani H (1993) Symplectic analysis of constrained systems. Inter J Mod Phys A 8(24):4319–4337

    Article  Google Scholar 

  • Neto JA, Neves C, Oliveira W (2001) Gauging the SU(2) Skyrme model. Phys Rev D 63(8):5018–5027

    Article  Google Scholar 

  • Paschalis JE, Porfyriadis PI (1996) BFV analysis of the U-em(1) Gauged SU(3) WZW model and the Faddeev-Jackiw approach. THES-TP 96/07

    Google Scholar 

  • Shirzad A, Mojiri M (2001) Constraint structure in modified Faddeev-Jackiw method. Mod Phys Lett A 16(38):2439–2448

    Article  Google Scholar 

  • Shirzad A, Monemzadeh M (2004) The BFT method with chain structure. Phys Lett B 584(1–2):220–224

    Article  Google Scholar 

  • Shirzad A, Monemzadeh M (2005) BFT method for mixed constrained systems and Chern-Simons theory. Phys Rev D 72:045004

    Article  Google Scholar 

  • Shirzad A, Shabani Moghadam M (1999) Explicit form of the gauge transformation generator in terms of constraints. J Phys A 32(46):8185–8195

    Article  Google Scholar 

  • Wess J, Zumino B (1971) Consequences of anomalous ward identities. Phys Lett 37B:95–97

    Article  Google Scholar 

  • Woodhouse NMJ (1992) Geometric quantization, 2nd edn, Oxford mathematical monographs. Oxford Science Publications/The Clarendon Press/Oxford University Press, New York

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Particle Physics and Gravity, Faculty of Physics, University of Kashan, Kashan, 87317-53153, Iran

    Salman Abarghouei Nejad & Majid Monemzadeh

Authors
  1. Salman Abarghouei Nejad
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Majid Monemzadeh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Majid Monemzadeh .

Editor information

Editors and Affiliations

  1. Department of Nanocomputing, Institute of Nanoscience and Nanotechnology, University of Kashan, Kashan, Iran

    Ali Reza Ashrafi

  2. Department of Chemistry, Faculty of Chemistry and Chemical Engineering, Babes-Bolyai University, Cluj-Napoca, Romania

    Mircea V. Diudea

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Nejad, S.A., Monemzadeh, M. (2016). Enhancing Gauge Symmetries Via the Symplectic Embedding Approach. In: Ashrafi, A., Diudea, M. (eds) Distance, Symmetry, and Topology in Carbon Nanomaterials. Carbon Materials: Chemistry and Physics, vol 9. Springer, Cham. https://doi.org/10.1007/978-3-319-31584-3_25

Download citation

Publish with us

Policies and ethics

Search

Navigation