Related papers: The Magnificent Realm of Affine Quantization: vali…
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…
A discussion of the meaning of a physical concept cannot be separated from discussion of the conditions for its ideal measurement. We assert that quantization is no more than the invocation of the quantum of action in the explanation of…
Enhanced quantization is an improved program for overcoming difficulties which may arise during an ordinary canonical quantization procedure. We review here how this program applies for a particle on circle.
This is an introduction to quantum gravity, aimed at a fairly general audience and concentrating on what have historically two main approaches to quantum gravity: the covariant and canonical programs (string theory is not covered). The…
A theoretical framework for the quantization of gravity has been an elusive Holy Grail since the birth of quantum theory and general relativity. While generations of scientists have attempted solutions to this deep riddle, an alternative…
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…
In this manuscript, we will discuss the construction of covariant derivative operator in quantum gravity. We will find it is more perceptive alternative to use affine connections more general than metric compatible connections in quantum…
Second quantization has been widely used in quantum mechanics and quantum chemistry, which is trivial and error-prone for researchers. Fortunately it is a good candidate for automatic evaluation with its simple, trivial and intrinsic…
The nature of the classical canonical phase-space variables for gravity suggests that the associated quantum field operators should obey affine commutation relations rather than canonical commutation relations. Prior to the introduction of…
In order to test the canonical quantization programme for general relativity we introduce a reduced model for a real sector of complexified Ashtekar gravity which captures important properties of the full theory. While it does not…
The paper presents shortly the geometric approach to the problem of a general quantization formalism, both physically meaningful and mathematically consistent.
As a canonical and generally covariant gauge theory, loop quantum gravity requires special techniques to derive effective actions or equations. If the proper constructions are taken into account, the theory, in spite of considerable…
The gravitational field is usually neglected in the calculation of atomic energy levels as its effect is much weaker than the electromagnetic field, but that is not the case for a particle orbiting a black hole. In this work, the canonical…
We study a system of two pointlike particles coupled to three dimensional Einstein gravity. The reduced phase space can be considered as a deformed version of the phase space of two special-relativistic point particles in the centre of mass…
A new approach is demonstrated that QFTs can be UV finite if they are viewed as the low energy effective theories of a fundamental underlying theory (that is complete and well-defined in all respects) according to the nowaday's standard…
This paper is a review of our recent work on three notorious problems of non-relativistic quantum mechanics: realist interpretation, quantum theory of classical properties and the problem of quantum measurement. A considerable progress has…
We proceed to the canonical quantization of the complex scalar field without making use of its real and imaginary parts. Our motivation is to formally connect, as tightly as possible, the quantum-field notions of particle and antiparticle -…
Application of the so-called refined algebraic quantization scheme for constrained systems to the relativistic particle provides an inner product that defines a unique Fock representation for a scalar field in curved space-time. The…
..."but we do not have quantum gravity." This phrase is often used when analysis of a physical problem enters the regime in which quantum gravity effects should be taken into account. In fact, there are several models of the gravitational…
We examine the possibility of dealing with gravitational singularities on a quantum level through the use of coherent state or wavelet quantization instead of canonical quantization. We consider the Robertson-Walker metric coupled to a…