Related papers: Conic Constrained Particle Quantization within the…
Based on the results of a recent reexamination of the quantization of systems with first-class and second-class constraints from the point of view of coherent-state phase-space path integration, we give additional examples of the…
A canonical analysis of RG improved action of the Einstein-Hilbert functional is performed. The gravitational and cosmological constants as function of the space-time coordinates are treated as external non-geometrical fields. Dirac's…
In [1] we initiated an approach towards quantizing the Hamiltonian constraint in Loop Quantum Gravity (LQG) by requiring that it generates an anomaly-free representation of constraint algebra off-shell. We investigated this issue in the…
Over the last two years, the canonical approach to quantum gravity based on connections and triads has been put on a firm mathematical footing through the development and application of a new functional calculus on the space of gauge…
In the first-order formulation, general relativity could be formally viewed as the topological $BF$ theory with a specific constraint, the Plebanski constraint. $BF$ theory is expected to be the classical limit of the Crane-Yetter~(CY)…
Recently, it has been observed that a certain class of classical theories with constraints can be quantized by a mathematical procedure known as Rieffel induction. After a short exposition of this idea, we apply the new quantization theory…
The method of the BRST quantization is considered for the system of constraints, which form a Lie algebra. When some of the Cartan generators do not imply any conditions on the physical states, the system contains the first and the second…
Quadratic gravity in two dimensions can be formulated as a Background Field (BF) theory plus an interaction term which is polynomial in both, the gauge and Background fields. This formulation is similar to the one given by Freidel and…
We show that the constraint structure in the chain by chain method can be investigated within the symplectic analysis of Faddeev-Jackiw formalism.
Dirac algorithm allows to construct Hamiltonian systems for singular systems, and so contributing to its successful quantization. A drawback of this method is that the resulting quantized theory does not have manifest Lorentz invariance.…
We study algebras constructed by quantum Hamiltonian reduction associated with symplectic quotients of symplectic vector spaces, including deformed preprojective algebras, symplectic reflection algebras (rational Cherednik algebras), and…
We give a short review of the algebraic procedure known as deformation quantisation, which replaces a commutative algebra with a non-commutative algebra. We use this framework to examine how the objects known as wavefunctions, as known in…
The Batalin-Fradkin-Tyutin (BFT) scheme, which is an improved version of Dirac quantization, is applied to the $CP^1$ model, and the compact form of a nontrivial first-class Hamiltonian is directly obtained by introducing the BFT physical…
A generalization of the Dirac's canonical quantization theory for a system with second-class constraints is proposed as the fundamental commutation relations that are constituted by all commutators between positions, momenta and Hamiltonian…
The models of New General Relativity have recently got attention of research community, and there are some works studying their dynamical properties. The formal aspects of this investigation have been mostly restricted to the primary…
We start from the Barnes-Coleman slave-particle description, where the Hubbard operators $X$ are decomposed into a product of fermionic ($f_{\alpha}$) and bosonic ($b$) operators. The quantum mechanical constraint $b^{\dagger} b +…
We construct a quantum mechanics based on the hypothesis of existing compact extra dimensions for a particle that wants to detect it. By introducing a probability function, we express the transition of particle to the extra 2d window. The…
Numerical simulations of the full quantum properties of interacting many-body systems by means of field-theoretic Monte-Carlo techniques are often limited due to a sign problem. Here we simulate properties of a dilute two-dimensional Bose…
The Spinning Particle Model for anyon is analysed in the Batalin-Tyutin scheme of quantisation in extended phase space. Here additional degrees of freedom are introduced in the phase space such that all the constraints in the theory are…
When the gauge group of a theory has infinite volume, defining the inner product on physical states becomes subtle. This is the case for gravity, even in exactly solvable models such as minisuperspace or low-dimensional theories: the…