nLab bosonic string



String theory


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Surveys, textbooks and lecture notes

theory (physics), model (physics)

experiment, measurement, computable physics



The incarnation of the concept of string without worldsheet supersymmetry is the bosonic string of bosonic string theory. In contrast to the spinning string/superstring.


In symplectic geometry / geometric quantization

See the reference below





The Polyakov action (but see there for more) for the bosonic string (and relation to Liouville theory in the non-critical case):

See the references at string theory for more.

Symplectic geometry and geometric quantization

The ordinary symplectic geometry and ordinary geometric quantization of the bosonic string sigma-model is discussed in the following references.

The symplectic structure and Kähler geometry of loop space is discussed in

  • M.J. Bowick, S.G. Rajeev, String theory as the Kähler geometry of loop space Phys. Rev. Lett. 58, 535-538 (1987)

  • M.J. Bowick, S.G. Rajeev, The holomorphic geometry of closed bosonic string theory and Diff(S 1)/S 1Diff(S^1)/S^1, Nucl. Phys. B293, 348-384 (1987)

  • Jouko Mickelsson, String quantization on group manifolds and the holomorphic geometry of Diff(S 1)/S 1Diff(S^1)/S^1 Commun. Math. Phys. 112, 653-661 (1987) (EUCLID)

with further comments in

  • Hendrik Grundlin, C. A. Hurst, The operator quantization of the open bosonic string: field algebra, Communications in mathematical physics 156 (1993) (pdf)

A correction of some points in these articles is discussed in

  • Sergei Merkulov, On the geometric quantization of bosonic string, Class. Quantum Grav. 9 2267 (1992) (IOP)

See also

  • Yue Yua, Han-Ying Guoa, On the geometric quantization and BRST quantization for bosonic strings, Physics Letters B Volume 216, Issues 1–2, (1989), Pages 68–74 (web)

  • Yu-liang Liu, Su-qing Chen,Guang-jiong Ni, Geometrical quantization of bosonic string with Wess-Zumino term on genus-g Riemann surface, Phys. Rev. D 41, 472–477 (1990)

  • A. D. Popov, Geometric quantization of strings and reparametrization invariance, Theoretical and Mathematical Physics, Volume 83, Number 3 (1990) (journal)

In multisymplectic geometry and higher geometric quantization

A discussion starting systematically with the correct symplectic form obtained by transgression from an multisymplectic extended phase space and including the BRST sector is in

  • Yue Yu, Symplectic geometry and geometric quantization for the open bosonic string in the BRST formalism, Physics Letters B, Volume 216, Issue 1-2, (1989) p. 75-80.

A detailed exposition of the multisymplectic geometry of the bosonic string together with its interpretation in 2-plectic geometry is in

and the appearance of the string Lie 2-algebra as the Heisenberg Lie 2-algebra of the string WZW-model in this context is discussed in



  • Jan Ambjørn?, Y. Makeenko, Stability of the nonperturbative bosonic string vacuum (arXiv:1703.05382)

Last revised on June 19, 2023 at 10:05:29. See the history of this page for a list of all contributions to it.