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In the paper [4] is presented a theory which unifies the gravitation theory and the mechanical effects, which is different from the Riemannian theories like GTR. Moreover it is built in the style of the electomagnetic field theory. This…
Electromagnetic fields are quantized in manifestly covariant way by means of a class of reducible representations of CCR. $A_a(x)$ transforms as a Hermitian four-vector field in Minkowski four-position space (no change of gauge), but in…
We argue that the quantized non-Abelian gauge theory can be obtained as the infrared limit of the corresponding classical gauge theory in a higher dimension. We show how the transformation from classical to quantum field theory emerges and…
We develop an unified algebraic approach to the description of gauge interactions within the framework of a new concept of quantum mechanics. The next step in generalizing the space-time and the action vector space is made. The gauge field…
The system of two relativistic particles with einbein fields is quantized as a constrained system.A method of the introduction of the Newton--Wigner collective coordinate is discussed in presence of different gauge fixing conditions. Some…
Quantization is studied from a viewpoint of field extension. If the dynamical fields and their action have a periodicity, the space of wave functions should be algebraically extended `a la Galois, so that it may be consistent with the…
Electromagnetism, the strong and the weak interaction are commonly formulated as gauge theories in a Lagrangian description. In this paper we present an alternative formal derivation of U(1)-gauge theory in a manifestly covariant Hamilton…
A framework is introduced for expressing electromagnetic (EM) potentials and fields of single atomic or molecular emitters modeled as oscillating dipoles, which follows a recently proposed method for solving inhomogeneous wave equations for…
We introduce the group field theory formalism for quantum gravity, mainly from the point of view of loop quantum gravity, stressing its promising aspects. We outline the foundations of the formalism, survey recent results and offer a…
A non-perturbative quantization of a paraxial electromagnetic field is achieved via a generalized dispersion relation imposed on the longitudinal and the transverse components of the photon wave vector. The theoretical formalism yields a…
The fallacies associated with the gauge concept in electromagnetism are illustrated. A clearer and more valid formulation of the basics of classical electromagnetism is provided by recognizing existing physical constraints as well as the…
In these lectures I review the status of gravity from the point of view of the gauge principle and renormalization, the main tools in the toolbox of theoretical particle physics. In the first lecture I start from the old question "in what…
A field theory with local transformations belonging to the quantum group SU_q(n) is defined on a classical spacetime, with gauge potentials belonging to a quantum Lie algebra. Gauge transformations are defined for the potentials which lead…
We show that the problem of unifying electromagnetism with gravity has an elegant solution in classical physics through the phenomenon of induction. By studying the way that induction leads to the formation of electromagnetic fields, we…
We describe a new class of exact square integrable solutions of the Pauli and Dirac equation in rotating electromagnetic fields. Solutions obtained by putting equations in the stationary form with help of a coordinate transformation…
A group theoretical mechanism for unification of local gauge and spacetime symmetries is introduced. No-go theorems prohibiting such unification are circumvented by slightly relaxing the usual requirement on the gauge group: only the so…
The Connes and Lott reformulation of the strong and electroweak model represents a promising application of noncommutative geometry. In this scheme the Higgs field naturally appears in the theory as a particular `gauge boson', connected to…
Quantization of systems with constraints can be carried on with several methods. In the Dirac formulation the classical generators of gauge transformations are required to annihilate physical quantum states to ensure their gauge invariance.…
The purpose of this article is to show that the standard method of introducing the quantum description of the electromagnetic field -- by canonical field quantization -- is not the only one. We have chosen instead as the starting point the…
The quantum gravity is formulated based on gauge principle. The model discussed in this paper has local gravitational gauge symmetry and gravitational field is represented by gauge potential. A preliminary study on gravitational gauge group…