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Fractional Hamilton’s equations of motion in fractional time

100%
Muslih S., Baleanu D., Rabei E.
Open Physics
|
2007
|
vol. 5
|
issue 4
549-557
EN
The Hamiltonian formulation for mechanical systems containing Riemman-Liouville fractional derivatives are investigated in fractional time. The fractional Hamilton’s equations are obtained and two examples are investigated in detail.
2
Content available remote

The Yang-Mills fields - from the gauge theory to the mechanical model

81%
Constantinescu R., Ionescu C.
Open Physics
|
2009
|
vol. 7
|
issue 4
711-720
EN
The paper presents some mechanical models of gauge theories, i.e. gauge fields transposed in a space with a finite number of degree of freedom. The main focus is on how a global symmetry as the BRST one could be transferred in this context. The mechanical Yang-Mills model modified by taking the ghost type variables into account will be considered as an example of nonlinear dynamical systems.
3
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Atom as a “dressed” nucleus

52%
Kalitvianski V.
Open Physics
|
2009
|
vol. 7
|
issue 1
1-11
EN
We show that the electrostatic potential of an atomic nucleus “seen” by a fast charged projectile at short distances is quantum mechanically smeared due to nucleus motion around the atomic center of inertia. For example, the size of the “positive charge cloud” in the Hydrogen ground state is much larger than the proper proton size. For target atoms in excited initial states, the effect is even larger. The elastic scattering at large angles is generally weaker than the Rutherford scattering since the effective potential at short distances is softer than the Colombian one due to a natural “cutoff”. In addition, the large-angle scattering leads to target atom excitations due to pushing the nucleus (⇒ inelastic processes). The Rutherford cross section is in fact inclusive rather than elastic. These results are analogous to those from QED. Non-relativistic atomic calculations are presented. The difference and the value of these calculations arise from nonperturbatively (exact) nucleus “dressing” that immediately leads to correct physical results and to significant technical simplifications. In these respects a nucleus bound in an atom is a simple but rather realistic model of a “dressed” charge in the QFT. This idea is briefly demonstrated on a real electron model (electronium) which is free from infinities.
4
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Unification Principle and a Geometric Field Theory

52%
Wanas M. I., Osman S. N., El-Kholy R. I.
Open Physics
|
2015
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vol. 13
|
issue 1
EN
In the context of the geometrization philosophy, a covariant field theory is constructed. The theory satisfies the unification principle. The field equations of the theory are constructed depending on a general differential identity in the geometry used. The Lagrangian scalar used in the formalism is neither curvature scalar nor torsion scalar, but an alloy made of both, the W-scalar. The physical contents of the theory are explored depending on different methods. The analysis shows that the theory is capable of dealing with gravity, electromagnetism and material distribution with possible mutual interactions. The theory is shown to cover the domain of general relativity under certain conditions.
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