The paper contains a complete theory of factors for ray representations acting in a Hilbert bundle, which is a generalization of the known Bargmann's theory. With the help of it we have reformulated the standard quantum theory such that the gauge freedom emerges naturally from the very nature of quantum laws. The theory is of primary importance in the investigations of covariance (in contradistinction to symmetry) of a quantum theory which possesses a nontrivial gauge freedom. In that case the group in question is not any symmetry group but it is a covariance group only -that case which has not been deeply investigated. It is shown in the paper that the factor of its representation depends on space and time when the system in question possesses a gauge freedom. In the nonrelativistic theories the factor depends on the time only. In the relativistic theory the Hilbert bundle is over the spacetime and in the nonrelativistic one it is over the time.We explain two applications of this generalization: in the theory of a quantum particle in the gravitational field in the nonrelativistic limit and in the quantum electrodynamics.
We analyze the angular distributions for the (α, 3 He) and (α, t) reactions on 28 Si for projectile energies ranging from 50 to 120 MeV based on the partial-wave representation of the transfer amplitude expressed in terms of the S-matrices for the entrance and exit channels, with an emphasis on identifying Airy minima of various orders. The calculations have been performed using a six-parameter S-matrix model and S-matrix parameters obtained from the analysis of elastic scattering data. The first-and (or) second-order Airy minima are clearly identified in the analyzed transfer reaction angular distributions at intermediate angles. The detected Airy minima are found to be due to the interference between several inner and surface partial waves. The impact parameters of these waves are in the range of 1-6 fm, the upper boundary of which is less than the strong absorption radius.
The paper has the form of a proposal concerned with the relationship between the three mathematically rigorous approaches to quantum field theory: (1) local algebraic formulation of Haag, (2) Wightman formulation and (3) the perturbative formulation based on the microlocal renormalization method. In this project we investigate the relationship between (1) and (3) and utilize the known relationships between (1) and (2). The main goal of the proposal lies in obtaining obstructions for the existence of the adiabatic limit (confinement problem in the phenomenological standard model approach). We extend the method of deformation of Dütsch and Fredenhagen (in the Bordeman-Waldmann sense) and apply Fedosov construction of the formal index-an analog of the index for deformed symplectic manifolds, generalizing the Atiyah-Singer index. We present some first steps in realization of the proposal.
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