Abstract
Spin-statistics transmutation is the phenomenon occurring when a “dressing” transformation introduced for physical reasons (e.g. gauge invariance) modifies the “bare” spin and statistics of particles or fields. Historically, it first appeared in Quantum Mechanics and in semiclassical approximation to Quantum Field Theory. After a brief historical introduction, we sketch how to describe such phenomenon in Quantum Field Theory beyond the semiclassical approximation, using a path-integral formulation of euclidean correlation functions, exemplifying with anyons, dyons and skyrmions.
Similar content being viewed by others
References
Tamm, I.: Die verallgemeinerten Kugelfunktionen und die Wellenfunktionen eines Elektrons im Felde eines Magnetpoles. Z. Phys. 71, 141–150 (1931)
Dirac, P.A.M.: Quantized Singularities in the Electromagnetic Field. Proc. R. Soc. A 133, 60–72 (1931)
Hurst, C.A.: Charge quantization and nonintegrable Lie algebras. Ann. Phys. 50, 51–75 (1968)
Jackiw, R., Rebbi, C.: Solitons with Fermion number 1/2. Phys. Rev. D 13, 3398–3409 (1976)
Jackiw, R., Rebbi, C.: Spin from isospin in a gauge theory. Phys. Rev. Lett. 36, 1116–1119 (1976)
Hasenfratz, P., ’t Hooft, G.: A Fermion-Boson puzzle in a gauge theory. Phys. Rev. Lett. 36, 1119–1122 (1976)
Goldhaber, A.: Connection of spin and statistics for charge-monopole composites. Phys. Rev. Lett. 36, 1122–1125 (1976)
Friedman, J.L., Sorkin, R.D.: Dyon spin and statistics: a fiber bundle theory of interacting magnetic and electric charges. Phys. Rev. D 20, 2511–2525 (1979)
Friedman, J.L., Sorkin, R.D.: A spin statistics theorem for composites containing both electric and magnetic charges. Commun. Math. Phys. 73, 161–196 (1980)
Wilczek, F.: Magnetic flux, angular momentum, and statistics. Phys. Rev. Lett. 48, 1144–1146 (1982)
Wilczek, F.: Quantum mechanics of fractional-spin particles. Phys. Rev. Lett. 49, 957–959 (1982)
Polyakov, A.M.: Fermi-Bose transmutations induced by gauge fields. Mod. Phys. Lett. A 3, 325–328 (1988)
Wilczek, F., Zee, A.: Linking numbers, spin, and statistics of solitons. Phys. Rev. Lett. 51, 2250–2252 (1983)
Finkelstein, D., Rubinstein, J.: Connection between spin, statistics, and kinks. J. Math. Phys. 9, 1762–1779 (1968)
Kauffman, L.H.: On Knots. Ann. Math. Studies, vol. 115. Princeton University Press, Princeton (1987)
Ehrenberg, W., Siday, R.E.: The refractive index in electron optics and the principles of dynamics. Proc. Phys. Soc. B 62, 8–21 (1949) ;
Aharonov, Y., Bohm, D.: Significance of electromagnetic potentials in quantum theory. Phys. Rev. 115, 485–491 (1959)
Bargmann, V.: Irreducible unitary representations of the Lorentz group. Ann. Math. 48, 568–640 (1947)
Birman, J.: Braids, Links and Mapping Class Group. Ann. Math. Studies, vol. 82. Princeton University Press, Princeton (1974)
Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Nuovo Cimento B 37, 1–23 (1977)
Goldin, G.A., Menikoff, R., Sharp, D.H.: Representations of a local current algebra in nonsimply connected space and the Aharonov-Bohm effect. J. Math. Phys. 22, 1664–1668 (1981)
Hatcher, A.: Algebraic Topology. Cambridge University Press, Cambridge (2002)
Skyrme, T.H.R.: A unified field theory of mesons and baryons. Nucl. Phys. 31, 556–569 (1962)
Witten, E.: Global aspects of current algebra. Nucl. Phys. B 223, 422–432 (1983)
Witten, E.: Current algebra, baryons, and quark confinement. Nucl. Phys. B 223, 433–444 (1983)
Feynman, R.P.: Space-time approach to nonrelativistic quantum mechanics. Rev. Mod. Phys. 20, 367–387 (1948)
Schwinger, J.: On gauge invariance and vacuum polarization. Phys. Rev. 82, 664–679 (1951)
Dirac, P.A.M.: Gauge invariant formulation of quantum electrodynamics. Can. J. Phys. 33, 650–660 (1955)
Strocchi, F.: Spontaneous symmetry breaking in local gauge quantum field theory: the Higgs mechanism. Commun. Math. Phys. 56, 57–78 (1977)
Morchio, G., Strocchi, F.: Infrared problem, Higgs phenomenon and long range interactions. In: Velo, G., et al. (eds.) Fundamental Problems of Gauge Field Theory (Erice 1985), pp. 301–344. Plenum, New York (1986)
Becchi, C., Rouet, A., Stora, R.: The Abelian Higgs-Kibble model. Unitarity of the S operator. Phys. Lett. B 52, 344–346 (1974)
Becchi, C., Rouet, A., Stora, R.: Renormalization of gauge theories. Ann. Phys. 98, 287–321 (1976)
Tyutin, I.V.: Gauge invariance in field theory and statistical mechanics. Lebedev preprint FIAN39 (1975)
Kugo, T., Ojima, I.: Local covariant operator formalism of nonAbelian gauge theories and quark confinement problem. Prog. Theor. Phys. Suppl. 66, 1–130 (1979)
Froehlich, J., Marchetti, P.A.: Superselection sectors in quantum field models: Kinks in Phi4 in two-dimensions and charged states in lattice (Q.E.D.) in four-dimensions. In: Kastler, D. (ed.) Algebraic Theory of Superselection Sectors. Introduction and Recent Results, pp. 428–484. World Scientific, Singapore (1990)
Candlin, D.J.: On sums over trajactories for systems with Fermi statistics. Nuovo Cimento 4, 231–239 (1956)
Berezin, A.: The Method of Second Quantization. Academic Press, New York (1966)
Osterwalder, K., Schrader, R.: Axioms for Euclidean Green’s functions. Commun. Math. Phys. 31, 83–112 (1973)
Osterwalder, K., Schrader, R.: Axioms for Euclidean Green’s functions. 2. Commun. Math. Phys. 42, 281–305 (1975)
Seiler, E.: Gauge Theories as a Problem in Constructive Quantum Field Theory and Statistical Mechanics. Lecture Notes in Physics, vol. 159. Springer, Berlin (1982)
Froehlich, J., Marchetti, P.A.: Quantum field theory of anyons. Lett. Math. Phys. 16, 347–358 (1988)
Froehlich, J., Marchetti, P.A.: Quantum field theories of vortices and anyons. Commun. Math. Phys. 121, 177–223 (1989)
Lechner, K., Marchetti, P.A.: Spin statistics transmutation in relativistic quantum field theories of dyons. J. High Energy Phys. 0012, 028 (2000). doi:10.1088/1126-6708/2000/12/028
Froehlich, J., Marchetti, P.A.: Quantum skyrmions. Nucl. Phys. B 335, 1–22 (1990)
Kruczenski, M., Oxman, L.: Covariant quantization of the skyrmion. Nucl. Phys. B 488, 513–538 (1997)
Laughlin, R.B.: Anomalous quantum Hall effect: An incompressible quantum fluid with fractionally charged excitations. Phys. Rev. Lett. 50, 1395–1398 (1983)
Chakraborty, T., Pietilainen, P.: The Fractional Quantum Hall Effect. Springer, Berlin (1988)
Chern, S.-S., Simons, J.: Characteristic forms and geometric invariants. Ann. Math. 99, 48–69 (1974)
Marchetti, P.A.: Bosonization and duality in condensed matter systems. In: Barone, A., Devoto, A. (eds.) Proceedings of “Common Trends in Condensed Matter and High Energy Physics”, Chia Laguna 1995, pp. 178–188. Istituto Italiano per gli studi Filosofici, Napoli (2000) (Also in arXiv:hep-th/9511100)
Schonfeld, J.F.: A mass term for three-dimensional gauge fields. Nucl. Phys. B 185, 157–171 (1981)
Deser, S., Jackiw, R., Templeton, S.: Topologically massive gauge theories. Ann. Phys. 140, 372–411 (1982)
Buchholz, D., Fredenhagen, K.: Locality and the structure of particle states. Commun. Math. Phys. 84, 1–54 (1982)
Seiberg, N., Witten, E.: Electric—magnetic duality, monopole condensation, and confinement in N=2 supersymmetric Yang-Mills theory. Nucl. Phys. B 426, 19–52 (1994)
Dirac, P.A.M.: The theory of magnetic poles. Phys. Rev. 74, 817–830 (1948)
Schwinger, J.: Magnetic charge and quantum field theory. Phys. Rev. 144, 1087–1093 (1966)
Schwinger, J.: Magnetic charge and the charge quantization condition. Phys. Rev. D 12, 3105–3111 (1975)
de Rham, G.: Differentiable Manifolds. Forms, Currents, Harmonic Forms. Springer, Berlin (1984)
Mandelstam, S.: Quantum electrodynamics without potentials. Ann. Phys. 19, 1–24 (1962)
Froehlich, J., Marchetti, P.A.: Gauge invariant charged, monopole and dyon fields in gauge theories. Nucl. Phys. B 511, 770–812 (1999)
Belavin, V.A., Chernodub, M.N., Polikarpov, M.I.: Numerical study of Froehlich and Marchetti monopole creation operator. Nucl. Phys. Proc. Suppl. 106, 610–612 (2002)
Froehlich, J., Marchetti, P.A.: Soliton quantization in lattice field theories. Commun. Math. Phys. 112, 343–383 (1987)
Froehlich, J., Marchetti, P.A.: Bosonization, topological solitons and fractional charges in two-dimensional quantum field theory. Commun. Math. Phys. 116, 127–173 (1988)
Marino, E.C., Schroer, B., Swieca, J.A.: Euclidean functional integral approach for disorder variables and kinks. Nucl. Phys. B 200, 473–497 (1982)
Belavin, A.A., Polyakov, A.M., Schwartz, A.S., Tyupkin, Y.S.: Pseudoparticle solution of the Yang-Mills equations. Phys. Lett. B 59, 85–87 (1975)
Wess, J., Zumino, B.: Consequences of anomalous Ward identities. Phys. Lett. B 37, 95–97 (1971)
Chou, K., Guo, H., Wu, K.: On the gauge invariance and anomaly free condition of Wess-Zumino-Witten effective action. Phys. Lett. B 134, 67–69 (1984)
Balachandran, A.P., Lizzi, F., Rodgers, V.E.J., Stern, A.: Dibaryons as chiral solitons. Nucl. Phys. B 256, 525–556 (1985)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Marchetti, P.A. Spin-Statistics Transmutation in Quantum Field Theory. Found Phys 40, 746–764 (2010). https://doi.org/10.1007/s10701-009-9345-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10701-009-9345-2