Related papers: Geometric Quantization: Particles, Fields and Stri…
There are investigated several objects of an INFINITE DIMENSIONAL GEOMETRY appearing from the second quantization of a free string. The paper contains 2 chapters: 1st is devoted to the infinite dimensional geometry of flag, fundamental and…
In quantum metrology quantum properties such as squeezing and entanglement are exploited in the design of a new generation of clocks, sensors and other measurement devices that can outperform their classical counterparts. Applications of…
The covariant canonical method of quantization based on the De Donder-Weyl covariant canonical formalism is used to formulate a world-sheet covariant quantization of bosonic strings. To provide the consistency with the standard…
For any massless, irreducible representation of the covering of the proper, orthochronous Poincar\'e group we construct covariant, free quantum fields that generate the representation space from the vacuum and are localized in semi-infinite…
I present a method of quantization using cohomology groups extended via coefficient groups of different types. This is possible according to the Universal Coefficient Theorem (UCT). I also show that by using this method new features of…
In the free case, it is possible to define quantum fields which describe particles with integer or half-integer spin larger than one. It is shown that particles with integer spin must have Bose statistic and particles with half-integer-spin…
These notes offer a basic introduction to the primary mathematical concepts of quantum physics, and their physical significance, from the operator and Hilbert space point of view, highlighting more what are essentially the abstract…
In double field theory, the equation of motion for a point particle in the background field is considered. We find that the motion is described by a geodesic flow in the doubled geometry. Inspired by the analysis on the particle motion, we…
A new approach is proposed for an electromagnetic field geometrisation. We show that interacting Maxwell and Dirac fields can be considered as a single connected space-time 4-manifold. The Dirac spinors appear wihtin such approach as basic…
This note is supposed to be an introduction to those concepts of toric geometry that are necessary to understand applications in the context of string and F-theory dualities. The presentation is based on the definition of a toric variety in…
Spacetime geometry is supposed to be measured by identifying the trajectories of free test particles with geodesics. In practice, this cannot be done because, being described by Quantum Mechanics, particles do not follow trajectories. As a…
This note aims to subsume several apparently unrelated models under a common framework. Several examples of well-known quantum field theories are listed which are connected via stochastic quantization. We highlight the fact that the…
The Quantum Cosmology can be understand as the theory of an one object that is the Universe described in terms of fundamental mass groundstate of the free boson string, that is a tachyon - a hypothetical particle with negative mass square,…
An anomaly-free quantum theory of a relativistic string is constructed in two-dimensional space-time. The states of the string are found to be similar to the states of a massless chiral quantum particle. This result is obtained by…
The present paper is devoted to various objects of the infinite dimensional W-geometry of a second quantized free string. Our purpose is to include the W-symmetries into the general infinite dimensional geometrical picture related to the…
In this article, we will discuss geometric quantization of 2d QCD with fermionic and bosonic matter fields. We identify the respective large-N_c phase spaces as the infinite dimensional Grassmannian and the infinite dimensional Disc. The…
Candidate microstates of a spherically symmetric geometry are constructed in the group field theory formalism for quantum gravity, for models including both quantum geometric and scalar matter degrees of freedom. The latter are used as a…
We investigate the possibility that a background independent quantum theory of gravity is not a theory of quantum geometry. We provide a way for global spacetime symmetries to emerge from a background independent theory without geometry. In…
In this paper, I present a novel, purely differential geometric approach to the quantization of scalar fields, with a special focus on the familiar case of Minkowski spacetimes. This approach is based on using the natural geometric…
Stochastic field equations for linearized gravity are presented. The theory is compared with the usual quantum field theory and questions of Lorentz covariance are discussed. The classical radiation approximation is also presented.