We construct the RG equations for the scattering amplitudes and effective potential
In a a set of non-renormalizable theories. We show that they are a consequence of locality
rather than multiplicative renormalizability. These RG equations sum up the leading log terms
in all orders of PT and allow one to explore the high energy/field behaviour.
The gauge symmetry is said unfree if the gauge transformation leaves the action
functional unchanged provided for the gauge parameters are constrained by the system of partial
differential equations. The best known example of this phenomenon is the volume preserving
diffeomorphism being the gauge symmetry of unimodular gravity (UG). Various extensions are
known of the UG, including the higher...
Wrenches and twists are considered as generalizations of the concepts of force and angular velocity, respectively, and the corresponding mathematical formalism is reviewed. Manifolds of forces or angular velocities that naturally emerge in the screw theory are compared with the Grassmann manifold associated with the Penrose twistor space.
We analyzed mathematical conditions that are used in obtaining the eigenvalue spectrum of the orbital angular momentum operator in non-relativistic quantum mechanics. As it turns out, if one retains only those conditions that are the mathematical realization of physical requirements, the eigenvalue spectrum is discrete, admitting integer, as well as non-integer eigenvalues. Relation for the...
A description of the evolution of a quantum system is considered. Within the framework of the path integration method, the probability of a system transition between quantum states is determined as a double functional integral of a real functional. Its interpretation from the point of view of probability theory is given. The transition probability is the sum of the probabilities of pairwise...
