Related papers: Beyond Analog Gravity: The Case of Exceptional Dyn…
We study the interaction of gauge fields of arbitrary half-integer spins with the homogeneous electromagnetic field. We reduce the problem of obtaining the gauge-invariant Lagrangian and transformations of the half-integer spin fields in…
In this paper, we show how to study the evolution of a system, given imprecise knowledge about the state of the system and the dynamics laws. Our approach is based on Fuzzy Set Theory, and it will be shown that the \emph{Fuzzy Dynamics} of…
The interaction between singular and regular fields is considered for Lorentz-invariant scalar and vector wave equations. The singular field is generated by a Dirac source term. Its dynamics are deduced from the total field Lagrangian. At…
We establish a new model, which takes into account a dynamic (inertial) self-interaction of gravitating systems. The model is formulated by introduction of a new function depending on the square of the covariant derivative of the velocity…
Electromagnetic phenomena can be described by Maxwell equations written for the vectors of electric and magnetic field. Equivalently, electrodynamics can be reformulated in terms of an electromagnetic vector potential. We demonstrate that…
We construct the non-standard Lagrangian, called the multiplicative form, of the homogeneous scalar field and fermion field through the inverse calculus of variations, which the equation of motion still satisfies the Klein-Gordon and Dirac…
A general affine connection has enough degrees of freedom to describe the classical gravitational and electromagnetic fields in the metric-affine formulation of gravity. The gravitational field is represented in the Lagrangian by the…
This thesis covers several developments performed in metric-affine gravity. This alternative framework extends General Relativity by considering a more general connection than the one induced by the metric (i.e., arbitrary torsion and…
A charged particle in a suitably strong magnetic field spirals along the field lines while slowly drifting transversely. This note provides a brief derivation of an effective Lagrangian formulation for the guiding-centre approximation that…
A new approach to model the biomatter dynamics based on the field theory is presented. It is shown that some well known tools in field theory can be utilized to describe the physical phenomena in life matters, in particular at elementary…
We consider a classical field theory whose equations of motion follow from the least action principle, but the class of admissible trajectories is restricted by differential equations. The key element of the proposed construction is the…
This work is an application of the second order gauge theory for the Lorentz group, where a description of the gravitational interaction is obtained which includes derivatives of the curvature. We analyze the form of the second field…
A class of theories of gravity based on a Lagrangian which depends on the curvature and metric - but not on the derivatives of the curvature tensor - is of interest in several contexts including in the development of the paradigm that…
We discuss the problems of dynamics of the gravitational field and try to solve them according to quantum field theory by suggesting canonical states for the gravitational field and its conjugate field. To solve the problem of quantization…
We consider an interacting system of spinor and electromagnetic field, explicitly depending on the electromagnetic potentials, i.e., interaction with broken gauge invariance. The Lagrangian for interaction is chosen in such a way that the…
Two problems of the Standard Model, associated with the introduction of non-gauge interactions and with the introduction of an electromagnetic field as a linear combination of fields on which various gauge groups are implemented, are…
Action-dependent field theories are systems where the Lagrangian or Hamiltonian depends on new variables that encode the action. They model a larger class of field theories, including non-conservative behavior, while maintaining a…
The field equations of a generalized $f(R)$ type gravity model, in which there is an arbitrary coupling between matter and geometry, are obtained. The equations of motion for test particles are derived from a variational principle in the…
We propose a new theory of gravitation, in which the affine connection is the only dynamical variable describing the gravitational field. We construct the simplest dynamical Lagrangian density that is entirely composed from the connection,…
We consider a self-interacting scalar field theory in a slowly varying gravitational background field. Using zeta-function regularization and heat-kernel techniques, we derive the one-loop effective Lagrangian up to second order in the…