Compare Papers
Paper 1
Continuous-time quantum Monte Carlo for fermion-boson lattice models: Improved bosonic estimators and application to the Holstein model
Manuel Weber, Fakher F. Assaad, Martin Hohenadler
- Year
- 2016
- Journal
- Physical Review B
- DOI
- 10.1103/physrevb.94.245138
- arXiv
- -
No abstract.
Open paperPaper 2
Group theoretic quantization of punctured plane
Manvendra Somvanshi, D. Jaffino Stargen
- Year
- 2025
- Journal
- arXiv preprint
- DOI
- arXiv:2510.25794
- arXiv
- 2510.25794
We quantize punctured plane, $X=\mathbb{R}^2-\{0\}$, employing Isham's group theoretic quantization procedure. After sketching out a brief review of group theoretic quantization procedure, we apply the quantization scheme to the phase space, $M=X \times \R^2$, corresponding to the punctured plane, $X$. Particularly, we find the canonical Lie group, $\mathscr{G}$, corresponding to the phase space, $M=X \times \R^2$, to be $\mathscr{G} = \R^2 \rtimes (SO(2)\times \R^+)$. We establish an algebra homomorphism between the Lie algebra corresponding to the canonical group, $\mathscr{G} = \R^2 \rtimes (SO(2)\times \R^+)$, and the smooth functions, $f\in C^{\infty}(M)$, in the phase space, $M=X \times \R^2$. Making use of this homomorphism and unitary representation of the canonical group, $\mathscr{G} = \R^2 \rtimes (SO(2)\times \R^+)$, we deduce a quantization map that maps a subspace of classical observables, $f\in C^{\infty}(M)$, to self-adjoint operators on the Hilbert space, $\mathscr{H}$, which is the space of all square integrable functions on $X=\mathbb{R}^2-\{0\}$ with respect to the measure $\dd μ= \dd φ\ddρ/(2πρ)$.
Open paper