Related papers: Exact uncertainty principle and quantization: impl…
The detection of quantum aspects of gravity remains one of the most elusive challenges in modern physics. In this paper, we develop a comprehensive theoretical framework for the gravitational Aharonov-Bohm (AB) effect, extending previous…
We present a line by line derivation of canonical quantum mechanics stemming from the compatibility of the statistical geometry of distinguishable observations with the canonical Poisson structure of Hamiltonian dynamics. This viewpoint can…
The connection between the canonical and the path integral formulations of Einstein's gravitational field is discussed using the Hamilton - Jacobi method. Unlike conventional methods, it is shown that our path integral method leads to…
In this paper the quantization of the 2$+$1-dimensional gravity couplet to the massless Dirac field is carried out. The problem is solved by the application of the new Dynamic Quantization Method [1,2]. It is well-known that in general…
Non-Abelian Gauss law is interpreted in terms of area bits described in a local frame which fit together into closed surfaces and the Non-Abelian Stokes law in terms of length bits described in a local frame which fit together into closed…
The Heisenberg Uncertainty Principle (HUP) limits the accuracy in the simultaneous measurements of the position and momentum variables of any quantum system. This is known to be true in the context of non-relativistic quantum mechanics.…
The basic features of the complex canonical formulation of general relativity and the recent developments in the quantum gravity program based on it are reviewed. The exposition is intended to be complementary to the review articles…
We review the definition of geometric quantization, which begins with defining a mathematical framework for the algebra of observables that holds equally well for classical and quantum mechanics. We then discuss prequantization, and go into…
One of the biggest challenges to theoretical physics of our time is to find a background-independent quantum theory of gravity. Today one encounters a profusion of different attempts at quantization, but no fully accepted - or acceptable,…
The non-perturbative, lattice field theory approach towards the quantization of Euclidean gravity is reviewed. Included is a tentative summary of the most significant results and a presentation of the current state of art.
Quantum cosmology in general denotes the application of quantum physics to the whole universe and thus gives rise to many realizations and examples, covering problems at different mathematical and conceptual levels. It is related to quantum…
There is a long-standing debate about whether gravity should be quantised. A powerful line of argument in favour of quantum gravity considers models of hybrid systems consisting of coupled quantum-classical sectors. The conclusion is that…
The infinite dimensional generalization of the quantum mechanics of extended objects, namely, the quantum field theory of extended objects is employed to address the hitherto nonrenormalizable gravitational interaction following which the…
The gravity is classically formulated as the geometric curvature of the space-time in general relativity which is completely different from the other well-known physical forces. Since seeking a quantum framework for the gravity is a great…
The main principle of affine quantum gravity is the strict positivity of the matrix \{\hat g_{ab}(x)\} composed of the spatial components of the local metric operator. Canonical commutation relations are incompatible with this principle,…
A recent proposal for quantizing gravity is investigated for self consistency. There are well-known difficulties in dealing with Einstein gravity when resorting to the perturbative techniques of quantum field theory. This however does not…
Studies of geometrical theories suggest that fundmental problems of quantization arise from the disparate usage of displacement operators. These may be the source of a concealed inconsistency in the accepted formalism of quantum physics.…
General relativity is a background-independent theory of a dynamical classical spacetime geometry. Quantum theory is formulated in a classical spacetime, as an intrinsically probabilistic, contextual theory of non-classical, interfering…
Experiments are beginning to probe the interaction of quantum particles with gravitational fields beyond the uniform-field regime. In non-relativistic quantum mechanics, the gravitational field in such experiments can be written as a…
A noncommutative geometric generalisation of the quantum field theoretical framework is developed by generalising the Heisenberg commutation relations. There appear nonzero minimal uncertainties in positions and in momenta. As the main…