Dirac Quantization of t’Hooft-Polyakov Monopole Field: Axial Hamiltonization

Quantization of Dirac Field

covariant quantization and the Dirac field

Canonical Hamiltonian field theory in curved spacetime is formulated in a manifestly covariant way. Second quantization is achieved invoking a correspondence principle between the Poisson bracket of classical fields and the commutator of the corresponding quantum operators. The Dirac theory is investigated and it is shown that, in contrast to the case of bosonic fields, in curved spacetime, the...

Ray Optics in the Field of Non-minimal Dirac Monopole

Based on the analogy with non-minimal SU(2) symmetric Wu-Yang monopole with regular metric, the solution describing a non-minimal U(1) symmetric Dirac monopole is obtained. In order to take into account the curvature coupling of gravitational and electromagnetic fields, we reconstruct the effective metrics of two types: the so-called associated and optical metrics. The optical metrics display e...

Dequantization of the Dirac monopole

In his classical paper on quantization of magnetic poles, Dirac (1931) remarked that ‘Non-euclidean geometry and non-commutative algebra, which were at one time considered to be purely fictions of the mind and pastimes for logical thinkers, have now been found to be very necessary for the description of general facts of the physical world. It seems likely that this process of increasing abstrac...

Mass of a quantum ’t Hooft-Polyakov monopole

The quantum mechanical mass of ’t Hooft-Polyakov monopoles in the fourdimensional Georgi-Glashow is calculated non-perturbatively using lattice Monte Carlo simulations. This is done by imposing twisted boundary conditions that ensure there is one unit of magnetic charge on the lattice, and measuring the free energy difference between this ensemble and the vacuum. In the weak-coupling limit, the...