In what follows, we study the speed of sound of a two-component pseudospin-[up arrow], [down arrow] fermionic gas loaded on a square optical lattice with a non-Abelian

gauge field A = ([alpha][[sigma].sub.y], - [alpha][[sigma].sub.x]) in the presence of a Zeeman field, where a is independently tunable parameter, and [[sigma].sub.i], i = x, y, z are the Pauli matrices.

In QG research, it is known that general relativity with nonzero cosmological constant ([LAMBDA] [not equal to] 0) can be obtained from a so-called BF model (a topological field theory) for a

gauge field, valued in either SO(3,2) (for [LAMBDA] < 0) or a SO(4,1) (for [LAMBDA] > 0), by a symmetry breaking mechanism [6,7].

Here, [psi](t, x) : [R.sup.1+2] [right arrow] C is the matter field, N(t, x) : [R.sup.1+2] [right arrow] r is the neutral field, and [A.sub.[mu]](t, x) : [R.sup.1+2] [right arrow] R is the

gauge field. [D.sub.[mu]] = [[partial derivative].sub.[mu]] - [A.sub.[mu]] is the covariant derivative, i = [square root of (-1)], [mathematical expression not reproducible], and [DELTA] = [[partial derivative].sub.j][[partial derivative].sub.j].

The vector field derived from the gauge term, the

gauge field, makes the adjustment via the field force acting on the charge of symmetry.

propose a model in which the early universe is dominated by a

gauge field that interacts with a fermion current.

Frampton,

Gauge Field Theories, 3ra Ed., Wiley-VCH Verlag GmbH & Co.

Quantum chromodynamics is a non-Abelian

gauge field theory that can describe the strong interactions of fundamental particles, he explains, and he introduces the field to first-year graduate students, introducing gauge theory as a whole at the same time.

On such a lattice, we are given values on each edge in the form of a "U(1)

gauge field", U = {[u.sub.j] := [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] | j = 1, ..., [n.sub.e]}, where the values [[theta].sub.j] are prescribed based on some known distribution, discussed momentarily, and the "gauge links", [u.sub.j], live on the edges of the lattice.

By comparing the second-order differential equation that has been obtained from Dirac equation with Schrodinger equation for the well-known potential such as Scarff-II, Poshel-Teller, Morse, 3D-oscillator, and shift-oscillator potentials, the

gauge field potential can be written based on the well-known superpotentials that are related to the mentioned potentials.

The doublet corresponds to two charge states that convert one into another at the vertices, suggesting the SU(2) group for transformations of the inner (charge) space in the

gauge field theory, but now it appears as an indispensable mechanism to realize the regular lattice by means of the motion-to-motion gauge.

Colleagues remember Austrian theoretical physicist Kummer (1935-2007) with 25 papers on

gauge field theory and particle physics, classical and quantum gravity, and his place in the physics community.

This involves traditional gauge fixing (of the component

gauge field), as well as elimination of the anti-fields.