The new symmetry of the loop dynamics of QCD is found. This is a local SUSY δs = θβ(s), δθ = β(s) of the superloop field Xμ(s, θ) = xμ(s) + θψμ(s). The remarkable thing is, there is no einbein-gravitino on this theory, which makes it a 1D topological supergravity, or locally SUSY quantum mechanics. Using this symmetry, we derive the large Nc loop equation in momentum superloop space. Introducin...

We investigate the functional equation ∑n i=1 aif(bix + ciy) = 0, where ai, bi, ci ∈ C, and the unknown function f is defined on the field K = Q(b1, . . . , bn, c1, . . . , cn). (It is easy to see that every solution on K can be extended to C as a solution.) Let S1 denote the set of additive solutions defined on K. We prove that S1 is spanned by S1 ∩ D, where D is the set of the functions φ ◦ D...

7.1 Quantum spin Let us consider a simple example of how Wess-Zumino effective Lagrangian appears from the “current algebra”. To simplify the story we take an example of quantum spin S. This is a quantum mechanical system with an SU(2) spin algebra playing the role of “current algebra” of quantum field theory. We have standard spin commutation relations [S, S] = i!S, (7.1) where a, b, c take va...

The Lemaître-Tolman-Bondi (LTB) model represents an inhomogeneous spherically symmetric universefilledwithfreelyfallingdustlikematterwithoutpressure. First,wehaveconsideredaFinslerian anstaz of (LTB) and have found a Finslerian exact solution of vacuum field equation. We have obtained the R(t,r) and S(t,r) with considering establish a new solution of Rµν = 0. Moreover, we attempttouseFinslergeo...

This paper presents a fast hybrid volume-surface integral equation approach for the computation of electromagnetic scattering from composed negative index media (NIM) such as split-ring-resonators (SRR) with wires. The volume electric field integral equation (EFIE) is applied to the dielectric region of this NIM, and the surface electric field integral equation is applied on the conducting surf...

In this paper we consider a neural field equation on LR × S, which models the activity of populations of spatially organized, orientation selective neurons. In particular, we show how spatially organized patterns of orientation tuning can emerge due to the presence of weak, long-range horizontal connections and how such patterns can be analyzed in terms of a reduced phase equation. The latter i...