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Light-cone gauge quantization procedures are given, for superstring theory on $AdS_3$ space charged with NS-NS background, both in NSR and GS formalism. The spacetime (super)conformal algebras are constructed in terms of the transversal…
It is shown that in two-state quantum theory, a generic quantum state can be described by a non-computable real number. In terms of this, the criterion for measurement outcome is simply and deterministically defined. This demonstration is…
We construct a Heisenberg-like algebra for the one dimensional quantum free Klein-Gordon equation defined on the interval of the real line of length $L$. Using the realization of the ladder operators of this type Heisenberg algebra in terms…
We discuss the problem of canonical quantization of a free real massive scalar field in the Schwarzschild spacetime. It is shown that a consistent procedure of canonical quantization of the field can be carried out without taking into…
We study how quantum field theory models are modified under the reparametrizations of the space-time coordinates and some simultaneous transformations of the field function. The transformations that turn the action of the massive field in…
This paper examines two cosmological models of quantum gravity (from string theory and loop quantum gravity) to investigate the foundational and conceptual issues arising from quantum treatments of the big bang. While the classical…
In the first part of this paper I review the construction of the realistic free fermionic models, as well as current attempts to study aspects of these models in the nonperturbative framework of M- and F-theories. I discuss the recent…
A fundamental length is introduced into physics in a way which respects the principles of relativity and quantum field theory. This improves the properties of quantum field theory: divergences are removed. How to quantize gravity is also…
We describe a theory amalgamating quantum theory and general relativity through the identification of a continuous 4-dimensional spacetime arena constructed from the substructures of a generalised multi-dimensional form for proper time. In…
These notes present an introduction to the method of geometric quantization. We discuss the main theorems in a style suitable for a theoretical physicist with an eye towards the physical motivation and the interpretation of the geometric…
We consider the set of controlled time-dependent backgrounds of general relativity and string theory describing ``bubbles of nothing'', obtained via double analytic continuation of black hole solutions. We analyze their quantum stability,…
Here the probability density of relativistic particles coordinates, satisfying the formal conditions of the quantum mechanics and the special relativity, is determined (under textbooks view, such density does not exist). It is specified for…
We argue that the conventional construction for quantum fields in curved spacetime has a grave drawback: It involves an uncountable set of physical field systems which are nonequivalent with respect to the Bogolubov transformations, and…
We study properties of a scalar quantum field theory on the two-dimensional noncommutative plane with $E_q(2)$ quantum symmetry. We start from the consideration of a firstly quantized quantum particle on the noncommutative plane. Then we…
It is shown that the averaged null energy condition is fulfilled for a dense, translationally invariant set of vector states in any local quantum field theory in two-dimensional Minkowski spacetime whenever the theory has a mass gap and…
We take quantum theory and replace $\mathbb{C}$ by $\mathbb{C}[\varepsilon]$ where $\varepsilon^2=0$, i.e. we extend quantum theory to the ring of dual complex numbers. The aim is to develop a common language in which to treat continuous…
An effective formalism for quantum constrained systems is presented which allows manageable derivations of solutions and observables, including a treatment of physical reality conditions without requiring full knowledge of the physical…
It is proven that the relativistic quantum fields obtained from analytic continuation of convoluted generalized (L\'evy type) noise fields have positive metric, if and only if the noise is Gaussian. This follows as an easy observation from…
We analyze the quantum phenomenon arising from the interaction of a spinless charged particle with a rotating cosmic string, under the action of a static and uniform magnetic field parallel to the string. We calculate the energy levels of…
The relativistic angular momentum is introduced as an extension of the non-relativistic analysis of allowed states in the phase space for a quantum particle. The paper shows the conceptual basis of the approach. An interesting feature of…