### Abstract

The quantum field theory of particles with both electric and magnetic charges is developed as an obvious extension of Schwinger's quantum field theory of particles with either electric or magnetic charge. Two new results immediately follow. The first is the chiral equivalence theorem which states the unitary equivalence of the Hamiltonians describing the system of particles with electric and magnetic charges en, gn and the system with charges en′=cosθ, en+sinθ gn, gn′=-sinθ en+cosθ gn. This result holds in particular in the absence of physical magnetic charges. The second result is that if physical magnetic charges do occur, then, in consequence of chiral equivalence, the charge quantization condition applies, not to the separate products emgn, but to the combinations emgn-gmen, which must be integral multiples of 4π. The general solution of this condition leads to the introduction of a second elementary quantum of electric charge e2, the electric charge on the Dirac monopole, besides the first elementary charge e1, the charge on the electron. There are no other free parameters.

Original language | English (US) |
---|---|

Pages (from-to) | 1489-1495 |

Number of pages | 7 |

Journal | Physical Review |

Volume | 176 |

Issue number | 5 |

DOIs | |

State | Published - 1968 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Physical Review*,

*176*(5), 1489-1495. https://doi.org/10.1103/PhysRev.176.1489

**Quantum field theory of particles with both electric and magnetic charges.** / Zwanziger, Daniel.

Research output: Contribution to journal › Article

*Physical Review*, vol. 176, no. 5, pp. 1489-1495. https://doi.org/10.1103/PhysRev.176.1489

}

TY - JOUR

T1 - Quantum field theory of particles with both electric and magnetic charges

AU - Zwanziger, Daniel

PY - 1968

Y1 - 1968

N2 - The quantum field theory of particles with both electric and magnetic charges is developed as an obvious extension of Schwinger's quantum field theory of particles with either electric or magnetic charge. Two new results immediately follow. The first is the chiral equivalence theorem which states the unitary equivalence of the Hamiltonians describing the system of particles with electric and magnetic charges en, gn and the system with charges en′=cosθ, en+sinθ gn, gn′=-sinθ en+cosθ gn. This result holds in particular in the absence of physical magnetic charges. The second result is that if physical magnetic charges do occur, then, in consequence of chiral equivalence, the charge quantization condition applies, not to the separate products emgn, but to the combinations emgn-gmen, which must be integral multiples of 4π. The general solution of this condition leads to the introduction of a second elementary quantum of electric charge e2, the electric charge on the Dirac monopole, besides the first elementary charge e1, the charge on the electron. There are no other free parameters.

AB - The quantum field theory of particles with both electric and magnetic charges is developed as an obvious extension of Schwinger's quantum field theory of particles with either electric or magnetic charge. Two new results immediately follow. The first is the chiral equivalence theorem which states the unitary equivalence of the Hamiltonians describing the system of particles with electric and magnetic charges en, gn and the system with charges en′=cosθ, en+sinθ gn, gn′=-sinθ en+cosθ gn. This result holds in particular in the absence of physical magnetic charges. The second result is that if physical magnetic charges do occur, then, in consequence of chiral equivalence, the charge quantization condition applies, not to the separate products emgn, but to the combinations emgn-gmen, which must be integral multiples of 4π. The general solution of this condition leads to the introduction of a second elementary quantum of electric charge e2, the electric charge on the Dirac monopole, besides the first elementary charge e1, the charge on the electron. There are no other free parameters.

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U2 - 10.1103/PhysRev.176.1489

DO - 10.1103/PhysRev.176.1489

M3 - Article

VL - 176

SP - 1489

EP - 1495

JO - Physical Review

JF - Physical Review

SN - 0031-899X

IS - 5

ER -