Related papers: Can the canonical quantization be accomplished wit…
Symplectic quantization is a functional approach to quantum field theory that allows sampling of quantum fluctuations directly in Minkowski space time by means of a generalized Hamiltonian dynamics in an extra time variable $\tau$ which, at…
From the point of view of canonical quantum gravity, it has become imperative to find a framework for quantization which provides a {\em general} prescription to find the physical inner product, and is flexible enough to accommodate…
We formulate a new quantum equivalence principle by which a path integral for a particle in a general metric-affine space is obtained from that in a flat space by a non-holonomic coordinate transformation. The new path integral is free of…
By virtue of the Noether theorems, the vast gauge redundancy of general relativity provides us with a rich algebra of boundary charges that generate physical symmetries. These charges are located at codimension-2 entangling surfaces called…
We study canonical quantization of a closed Euclidean universe with a cosmological constant and a massless scalar field. The closed Euclidean universe with an ordinary matter state can be matched at a finite radius only with the closed…
Quantum mechanics is among the most important and successful mathematical model for describing our physical reality. The traditional formulation of quantum mechanics is linear and algebraic. In contrast classical mechanics is a geometrical…
The manifold of pure quantum states is a complex projective space endowed with the unitary-invariant geometry of Fubini and Study. According to the principles of geometric quantum mechanics, the detailed physical characteristics of a given…
Quantum computing has demonstrated potential for solving complex optimization problems; however, its application to spatial regionalization remains underexplored. Spatial contiguity, a fundamental constraint requiring spatial entities to…
In this series of papers we aim to provide a mathematically comprehensive framework to the Hamiltonian pictures of quantum field theory in curved spacetimes. Our final goal is to study the kinematics and the dynamics of the theory from the…
In this initial paper in a series, we first discuss why classical motions of small particles should be treated statistically. Then we show that any attempted statistical description of any nonrelativistic classical system inevitably yields…
A general classical theorem is presented according to which all invariant relations among the space time metric scalars, when turned into functions on the Phase Space of full Pure Gravity (using the Canonical Equations of motion), become…
Finite-dimensional Quantum Mechanics can be geometrically formulated as a proper classical-like Hamiltonian theory in a projective Hilbert space. The description of composite quantum systems within the geometric Hamiltonian framework is…
The quantization rules recently proposed by M. Navarro (and independently I.V. Kanatchikov) for a finite-dimensional formulation of quantum field theory are applied to the Klein-Gordon and the Dirac fields to obtain the quantum equations of…
The scalar matter and gravity are unified into the geometric scalar matter and quantized. The quantum with a definite 3-metric has definite energy but does not have well-defined momentum. The quantum theory resolves singularities.
Dirac's method of classical analogy is employed to incorporate quantum degrees of freedom into modern nonequilibrium thermodynamics. The proposed formulation of dissipative quantum mechanics builds entirely upon the geometric structures…
Quantum machine learning is often motivated by the idea that quantum systems can expose useful high-dimensional structure that is difficult to access with classical models. We isolate one central component of this claim: the fixed…
The quantization of classical theories that admit more than one Hamiltonian description is considered. This is done from a geometrical viewpoint, both at the quantization level (geometric quantization) and at the level of the dynamics of…
By virtue of harmonic maps on two-dimensional spheres (S$^{2}$), a topological quantization in spacetime is proposed. The discrete character of all physical quantities follows naturally. A Schwarzschild black hole, non-black hole and…
We show how quantum many-body systems on hyperbolic lattices with nearest-neighbor hopping and local interactions can be mapped onto quantum field theories in continuous negatively curved space. The underlying lattices have recently been…
While there does not at this time exist a complete canonical theory of full 3+1 quantum gravity, there does appear to be a satisfactory canonical quantization of minisuperspace models. The method requires no `choice of time variable' and…