Electronic Resource
Springer
International journal of theoretical physics
25 (1986), S. 959-971
ISSN:
1572-9575
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract The analytic structure of gauge fields in the presence of fermions is studied in arbitrary symmetry. A Hamiltonian formalism is developed which relates Cauchy-Riemann equations to the symmetry. The formalism is applied to three problems in (2+1)-dimensional Euclidean space: (1) a free fermion, (2) a fermion interacting with a massless scalar field, and (3) a fermion interacting with a vector field. We find that the Hamiltonian for the free fermion is analytic and single-valued in a finite region of momentum space. With the addition of an auxiliary field, the Hamiltonian can be analytic in the entire momentum space. The scalar field then acquires spin-dependent coordinates by interaction with the fermion; the interactions break the Abelian symmetry ofφ so thatφ →φ 1∼ 1/(x1 −-im 1 −1 (x1 −-im 1 −1 ), wherem 1 are spin-dependent and multivalued. There are four solutions for each chirality eigenvalue of the fermion. For spinless fermionsφ gives the Jackiw-Nohl-Rebbi solution and is separable into Coulomb-like 1/x analytic functions on the first and fourth quadrants. For a vector field the results are similar except that the coordinates are not spindependent or multivalued; interactions break the initial symmetry andA μ(x μ)→A μ 1 (x μ) and theA μ 1 have a non-Abelian algebra. Thel indices represent directions fixed by spin matrices in a spin-dependent color space.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00668824
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