Abstract
We further develop the quantization of topological solitons in two-dimensional quantum field theory in terms of Euclidean region functional integrals. Our approach is nonperturbative and mathematically rigorous. We apply it to construct physical states with fractional fermion number in models of interacting bosons and fermions without recurring to a semiclassical approximation. A related issue discussed in this paper is two-dimensional chiral bosonization.
Similar content being viewed by others
References
Fröhlich, J.: New super-selection sectors (“soliton states”) in two dimensional Bose quantum field models. Commun. Math. Phys.47, 269 (1976)
Fröhlich, J.: In Current problems in elementary particle and mathematical physics. (Schladming 1976), Acta Phys. Austriaca [Suppl.]XV (1976)
Bellissard, J., Fröhlich, J., Gidas, B.: Soliton mass and surface tension in the (λ|φ|4)2 quantum field model. Commun. Math. Phys.60, 37 (1978)
Fröhlich, J.: In Invariant wave equations. Lecture Notes in Physics, Vol. 73. Berlin, Heidelberg, New York: Springer 1978
Fröhlich, J., Marchetti, P.A.: Soliton quantization in lattice field theories. Commun. Math. Phys.112, 343 (1987)
Fröhlich, J.: In Recent developments in gauge theories. (Cargèse 1979) t'Hooft, G. et al. (eds.). New York: Plenum Press 1980
Marino, E.C., Swieca, J.A.: Order, disorder and generalized statistics. Nucl. Phys. B170, [FS1], 175 (1980); Marino, E.C., Schroer, B., Swieca, J.A.: Euclidean functional integral approach for disorder variables and kinks. Nucl. Phys. B200 [FS4], 473 (1982)
Kadanoff, L.P., Ceva, H.: Determination of an operator algebra for the two-dimensional Ising model. Phys. Rev. B3, 3918 (1971)
Wegner, F.: Duality in generalized Ising models and phase transitions without local order parameters. J. Math. Phys.12, 2259 (1971)
t'Hooft, G.: On the phase transition towards permanent quark confinement. Nucl. Phys. B138, 1 (1978)
Glimm, J., Jaffe, A.: Quantum physics. A functional integral point of view, 2nd edn. Berlin, Heidelberg, New York: Springer 1978
Glimm, J., Jaffe, A., Spencer, T.: A convergent expansion about mean field theory. I. The expansion. Ann. Phys.101, 610 (1976)
Simon, B.: TheP(φ)2 Euclidean (Quantum) field theory. Princeton, N.J.: Princeton University Press 1976
Osterwalder, K., Schrader, R.: Axioms for Euclidean Green's functions. Commun. Math. Phys.31, 83 (1973); Axioms for Euclidean Green's functions. II,42, 281 (1975)
Glaser, V.: Commun. Math. Phys.37, 257 (1974)
Fröhlich, J., Osterwalder, K., Seiler, E.: Ann. Math.118, 461 (1983)
Marchetti, P.A.: Constructing quantum kinks by differential geometry and statistical mechanics. To appear in Europhys. Lett., and paper in preparation
Constantinescu, F., Thalheimer, W.: Euclidean Green's functions for Jaffe fields. Commun. Math. Phys.38, 299 (1974);
Seiler, E.: Gauge theories as a problem of constructive quantum field theory and statistical mechanics. Lecture Notes in Physics, Vol. 159. Berlin, Heidelberg, New York: Springer 1982
Köberle, R., Marino, E.C.: Duality, mass spectrum and vacuum expectation values. Phys. Lett.126, 475 (1983)
Fröhlich, J.: Classical and quantum statistical mechanics in one and two dimensions: Two-component Yukawa- and Coulomb systems. Commun. Math. Phys.47, 233 (1976)
Fröhlich, J.: In Renormalization theory. (Erice 1975) Velo, G., Wightman, A.S. (eds.), NATO Advanced Study Institutes Series C23 1976
Fröhlich, J., Park, Y.M.: Remarks on exponential interactions and the quantum sine-Gordon equation in two space-time dimensions. Helv. Phys. Acta50, 315 (1977)
Brydges, D., Federbush, P.: Debye screening. Commun. Math. Phys.73, 197 (1980)
Coleman, S.: Quantum sine-Gordon equation as the massive Thirring model. Phys. Rev. D11, 2088 (1975)
Fröhlich, J., Seiler, E.: The massive Thirring-Schwinger model (QED2): convergence of perturbation theory and particle structure. Helv. Phys. Acta49, 889 (1976)
Gallavotti, G., Nicolò, F.: The “screening phase transitions” in the two-dimensional Coulomb gas. J. Stat. Phys.39, 133 (1985)
Nicolò, F., Renn, J., Steinmann, A.: On the massive sine-Gordon equation in all regions of collapse. Commun. Math. Phys.105, 291 (1985)
Fröhlich, J., Spencer, T.: The Kosterlitz-Thouless transition in two-dimensional abelian spin systems and the Coulomb gas. Commun. Math. Phys.81, 527 (1981)
Allendoerfer, C.B., Eells, J.: Commun. Math. Helv.32, 165 (1958)
Bricmont, J., Fröhlich, J.: Statistical mechanical methods in particle structure analysis of lattice field theories. I. General theory. Nucl. Phys. B251 [FS13], 517 (1985); Statistical mechanical methods in particle structure analysis of lattice field theories. II. Scalar and surface models. Commun. Math. Phys.98, 553 (1985)
Artin, E.: Theorie der Zöpfe. Hamburg Abh.4, 47 (1925)
Birman, J.S.: Braids, links and mapping class groups. Annals of Mathematics Studies, Vol. 82. Princeton, NJ.: Princeton University Press 1974
Bost, J.: In Proceedings of “VIII-th International Congress” in Mathematical Physics, Mebkhout, M., Sénéor, R. (eds.). Singapore: World Scientific 1987, and references therein
Schroer, B., Truong, T.T.: The relativistic quantum fields of theD=2 Ising model. Phys. Lett.72, 731 (1978); Direct construction of the quantum field operators of theD=2 Ising model.73 B, 149 (1978)
Seiler, E., Simon, B.: Nelson's symmetry and all that in the Yukawa2 and (φ4)3 field theories. Ann. Phys.97, 470 (1976)
Bałaban, T., Gawedzki, K.: A low temperature expansion for the pseudoscalar Yukawa model of quantum fields in two space-time dimensions. Ann. Inst. H. Poincaré36, 271 (1982) and references therein
Jackiw, R., Rebbi, C.: Solitons with fermi number 1/2. Phys. Rev. D13, 3398 (1976)
Jackiw, R.: In Quantum structure of space and time. Duff, M.J., Isham, C.J. (eds.). London: Cambridge University Press 1982
Niemi, A.J., Semenoff, G.W.: Spectral asymmetry on an open space. Phys. Rev. D30, 809 (1984)
Goldstone, J., Wilczek, F.: Fractional quantum number on solitons. Phys. Rev. Lett.47, 986 (1981)
Frishman, R., Gepner, D., Yankielowicz, S.: Fractional charge and anomalous commutators. Phys. Lett.130, 66 (1983)
Su, W.P., Schrieffer, J.R., Heeger, A.J.: Soliton excitations in polyacetylene. Phys. Rev. B22, 2099 (1980)
Jackiw, R., Schrieffer, J.R.: Solitons with fermion number 1/2 in condensed matter and relativistic field theories. Nucl. Phys. B190, [FS 3], 253 (1981)
See e.g. Eguchi, T., Gilkey, P.B., Hanson, A.J.: Gravitation, gauge theories and differential geometry. Phys. Rep.66, 213 (1980)
Marchetti, P.A.: Particle structure analysis of soliton sectors in massive lattice field theories (preprint) PD (1987)
Author information
Authors and Affiliations
Additional information
Communicated by A. Jaffe
Rights and permissions
About this article
Cite this article
Fröhlich, J., Marchetti, P. Bosonization, topological solitons and fractional charges in two-dimensional quantum field theory. Commun.Math. Phys. 116, 127–173 (1988). https://doi.org/10.1007/BF01239028
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01239028