Related papers: Quantization and Coherent States over Lagrangian S…
A formalism is presented in which quantum particle dynamics can be developed on its own rather than `quantization' of an underlying classical theory. It is proposed that the unification of probability and dynamics should be considered as…
In this work, we explore the implications of applying the formalism of symplectic geometry to quantum mechanics, particularly focusing on many-particle systems. We extend the concept of a symplectic indicator of entanglement, originally…
An algebraic formulation of Riemannian geometry on quantum spaces is presented, where Riemannian metric, distance, Laplacian, connection, and curvature have their counterparts. This description is also extended to complex manifolds.…
Ricci-type symplectic manifolds have been introduced and extensively studied by M. Cahen et al.. In this note, we describe their deformation quantizations in the split solvable symmetric case. In particular, we introduce the notion of…
Certain many-particle Hardy inequalities are derived in a simple and systematic way using the so-called ground state representation for the Laplacian on a subdomain of $\mathbb{R}^n$. This includes geometric extensions of the standard Hardy…
A novel algebra underlying integrable systems is shown to generate and unify a large class of quantum integrable models with given $R$-matrix, through reductions of an ancestor Lax operator and its different realizations. Along with known…
The aim of this article is to study the functorial properties of the ``formal geometric quantization'' procedure which is defined for non-compact Hamiltonian manifolds (when the moment map is proper). For this purpose, we introduce a…
We study quantum corrections to hypersurfaces of dimension $d+1>2$ embedded in generic higher-dimensional spacetimes. Manifest covariance is maintained throughout the analysis and our methods are valid for arbitrary co-dimension and…
The purpose of this contribution is to provide an introduction for a general physics audience to the recent results of Emile Grgin that unifies quantum mechanics and relativity into the same mathematical structure. This structure is the…
We develop a Lagrangian approach for constructing a symplectic structure for singular systems. It gives a simple and unified framework for understanding the origin of the pathologies that appear in the Dirac-Bergmann formalism, and offers a…
Filtration of real gases described by Peng-Robinson equations of state in 3-dimensional space is studied. Thermodynamic states are considered as either Legendrian submanifolds in contact space, or Lagrangian submanifolds in symplectic…
A general prescription for the treatment of constrained quantum motion is outlined. We consider in particular constraints defined by algebraic submanifolds of the quantum state space. The resulting formalism is applied to obtain solutions…
We introduce geometric quantization in the setting of shifted symplectic structures. We define Lagrangian fibrations and prequantizations of shifted symplectic stacks and their geometric quantization. In addition, we study many examples…
Symplectic unitary representations for the Poincar\'{e} group are studied. The formalism is based on the noncommutative structure of the star-product, and using group theory approach as a guide, a consistent physical theory in phase space…
This paper has the purpose of presenting in an organic way a new approach to integrable (1+1)-dimensional field systems and their systematic quantization emerging from intersection theory of the moduli space of stable algebraic curves and,…
A quantization scheme based on the extension of phase space with application of constrained quantization technic is considered. The obtained method is similar to the geometric quantization. For constrained systems the problem of scalar…
A regularization renormalization method ($RRM$) in quantum field theory ($QFT$) is discussed with simple rules: Once a divergent integral $I$ is encountered, we first take its derivative with respect to some mass parameter enough times,…
The standard (Berezin-Toeplitz) geometric quantization of a compact Kaehler manifold is restricted by integrality conditions. These restrictions can be circumvented by passing to the universal covering space, provided that the lift of the…
A cosmological model describing the evolution of n Ricci-flat spaces (n>1) in the presence of 1-component perfect-fluid and minimally coupled scalar field is considered. When the pressures in all spaces are proportional to the density, the…
We consider a general approach for the process of Lagrangian and Hamiltonian reduction by symmetries in chiral gauge models. This approach is used to show the complete integrability of several one dimensional texture equations arising in…