Search results for "Canonical quantization"
showing 10 items of 20 documents
Quantum cosmological approach to 2d dilaton gravity
1993
We study the canonical quantization of the induced 2d-gravity and the pure gravity CGHS-model on a closed spatial section. The Wheeler-DeWitt equations are solved in (spatially homogeneous) choices of the internal time variable and the space of solutions is properly truncated to provide the physical Hilbert space. We establish the quantum equivalence of both models and relate the results with the covariant phase-space quantization. We also discuss the relation between the quantum wavefunctions and the classical space-time solutions and propose the wave function representing the ground state.
Coordinate-free quantization of first-class constrained systems
1996
The coordinate-free formulation of canonical quantization, achieved by a flat-space Brownian motion regularization of phase-space path integrals, is extended to a special class of closed first-class constrained systems that is broad enough to include Yang-Mills type theories with an arbitrary compact gauge group. Central to this extension are the use of coherent state path integrals and of Lagrange multiplier integrations that engender projection operators onto the subspace of gauge invariant states.
Electronic Processes in Solid State: Dirac Framework
2019
The present paper proposes canonical Dirac framework adapted for application to the electronic processes in solid state. The concern is a spatially periodic structure of atoms distinguished by birth and annihilation of particle states excited due to interaction with the electromagnetic field. This implies replacing the conventional energy-momentum relation specific of the canonical Dirac framework and permissible for particle physics by a case specific relation available for the solid state. The advancement is a unified and consistent mathematical framework incorporating the Hilbert space, the quantum field, and the special relativity. Essential details of the birth and annihilation of the …
A Quantum Mechanical Model of the Reissner-Nordstrom Black Hole
1997
We consider a Hamiltonian quantum theory of spherically symmetric, asymptotically flat electrovacuum spacetimes. The physical phase space of such spacetimes is spanned by the mass and the charge parameters $M$ and $Q$ of the Reissner-Nordstr\"{o}m black hole, together with the corresponding canonical momenta. In this four-dimensional phase space, we perform a canonical transformation such that the resulting configuration variables describe the dynamical properties of Reissner-Nordstr\"{o}m black holes in a natural manner. The classical Hamiltonian written in terms of these variables and their conjugate momenta is replaced by the corresponding self-adjoint Hamiltonian operator, and an eigenv…
Covariant phase-space quantization of the induced 2D gravity
1993
Abstract We study in a parallel way the induced 2D gravity and the Jackiw-Teitelboimmodel on the cylinder from the viewpoint of the covariant description of canonical formalism. We compute explicity thhe symplectic structure of both theories showing that their (reduced) phase spaces are finite-dimensional cotangent bundles. For the Jackiw-Teitelboim model the base space (configuration space) is the space of conjugacy classes of the PSL(2, R ) group. For the induced 2D gravity, and Λ > 0, the (reduced) phase space consist of two (identical) connected components each one isomorphic to the contangent bundle of the space of hyperbolic conjugacy classes of the PSL (2, R ) group, whereas for Λ R …
The Usefulness of Lie Brackets: From Classical and Quantum Mechanics to Quantum Electrodynamics
2020
We know that in Hamiltonian systems a dynamic function f(q, p) develops in time according to
Fundamental Principles of Quantum Mechanics
2001
There are two alternative methods of quantizing a system: a) quantization via the Feynman Path Integral (equivalent to Schwinger’s Action Principle); b) canonical quantization.
A no-go result for the quantum damped harmonic oscillator
2019
Abstract In this letter we show that it is not possible to set up a canonical quantization for the damped harmonic oscillator using the Bateman Lagrangian. In particular, we prove that no square integrable vacuum exists for the natural ladder operators of the system, and that the only vacua can be found as distributions. This implies that the procedure proposed by some authors is only formally correct, and requires a much deeper analysis to be made rigorous.
From where do quantum groups come?
1993
The phase space realizations of quantum groups are discussed using *-products. We show that on phase space, quantum groups appear necessarily as two-parameter deformation structures, one parameter (v) being concerned with the quantization in phase space, the other (η) expressing the quantum groups as “deformation” of their Lie counterparts. Introducing a strong invariance condition, we show the uniqueness of the η-deformation. This suggests that the strong invariance condition is a possible origin of the quantum groups.
Perturbative quantum field theory
2000
pQFT In this chapter we repeat the main steps towards a derivation of the Feynman rules, following the well-known path of canonical quantization. This is standard material, and readers who are not acquainted with such topics are referred to [Bjorken and Drell 1965, Bogoliubov and Shirkov 1980, Itzykson and Zuber 1980, Kaku 1993, Weinberg 1995, Peskin and Schroeder 1995, Teller 1997]. We hope that the short summary given here, similar to that in [Kreimer 1997a], is helpful for readers who want to refresh their memory. Having introduced Feynman rules, we next introduce Schwinger–Dyson equations as a motivation for the introduction of Z -factors. We remark on dimensional regularization and giv…