A path integral for spinning particles is developed. It is a one-particle theory, equivalent to the usual quantum mechanics. Our method employs a classical model for spin which is quantized by path integration. The model, the spherical top, is a natural one from a group-theoretic point of view and has been used before in a similar context. The curvature and multiple connectedness of the top coordinate space [ $\mathrm{SO}(3)$ ] provide some interesting features in the sum over paths. The Green's function which results from this procedure propagates all spins, and recovery of the usual Pauli spinors from this formalism is achieved by projection to a specific spin subspace.A path integral for spinning particles is developed. It is a one-particle theory, equivalent to the usual quantum mechanics. Our method employs a classical model for spin which is quantized by path integration. The model, the spherical top, is a natural one from a group-theoretic point of view and has been used before in a similar context. The curvature and multiple connectedness of the top coordinate space [$\mathrm{SO}(3)$] provide some interesting features in the sum over paths. The Green's function which results from this procedure propagates all spins, and recovery of the usual Pauli spinors from this formalism is achieved by projection to a specific spin subspace.

Physical ReviewDec 25, 1968329 citations

The Spin Path Integral

Assa Auerbach

Graduate texts in contemporary physicsJan 1, 19940 citations

Coherent State Path Integral for the Harmonic Oscillator and a Spin Particle in a Constant Magnetic field

Mario Bergeron

Definition and formulas for harmonic oscillator coherent states and spin coherent states are reviewed in detail. The path integral formalism and its relation with the partition function of a system are also reviewed. The harmonic oscillator coherent state path integral is evaluated exactly at the discrete level and then used to find its continuum limit using various regularizations. The computation of the path integral for a particle of spin s put in a constant magnetic field is carried out using harmonic oscillator coherent states and spin coherent states, with a careful analysis of infinitesimal terms (in 1/N where N is the number of time slices) appearing in the Lagrangian. A mapping of the spin system into a CP1 model is shown explicitly. The theory of a spinless particle in the field of a magnetic monopole and its relation with the spin system are explained. The equivalence of these two models is established up to infinitesimal order by the introduction of an external field correction. This gives a new representation of a coherent state path integral in terms of a more familiar Feynman path integral.Definition and formulas for harmonic oscillator coherent states and spin coherent states are reviewed in detail. The path integral formalism and its relation with the partition function of a system are also reviewed. The harmonic oscillator coherent state path integral is evaluated exactly at the discrete level and then used to find its continuum limit using various regularizations. The computation of the path integral for a particle of spin s put in a constant magnetic field is carried out using harmonic oscillator coherent states and spin coherent states, with a careful analysis of infinitesimal terms (in 1/N where N is the number of time slices) appearing in the Lagrangian. A mapping of the spin system into a CP1 model is shown explicitly. The theory of a spinless particle in the field of a magnetic monopole and its relation with the spin system are explained. The equivalence of these two models is established up to infinitesimal order by the introduction of an external field correction. This gives a new representation of a coherent state path integral in terms of a more familiar Feynman path integral.

Fortschritte der Physik/Progress of PhysicsJan 1, 199211 citations

A path integral to quantize spin

H.B. Nielsen, Daniel Rohrlich

Nuclear Physics BApr 1, 198897 citations

Functional integrals for spin

Theoretical Physics

Annals of PhysicsApr 1, 19890 citations

\mathrm{SO}(3)

] provide some interesting features in the sum over paths. The Green's function which results from this procedure propagates all spins, and recovery of the usual Pauli spinors from this formalism is achieved by projection to a specific spin subspace.