Uniqueness of the coordinate independent state of Matrix Theory

Counting SO(9) × SU(2) representations in coordinate independent state space of SU(2) matrix theory

“…From the first row of Table 1, we see that SO(9) singlet states are decomposed into one singlet and one 13-dimensional representation of SU (2). This is consistent with the result of [1,2,4], and gives another proof of the uniqueness of SO(9)×SU(2) singlet.…”

“…Similar analyses have been made in [1] for SO(7)×SU(2) singlets, and in [3] for SU(N) gauge group singlets. As a byproduct of our calculation we can give another proof of the uniqueness of SO(9)×SU(2) singlet proven in [1,2].…”

“…Although θ a α is real, let us temporarily consider the case where θ a α is complex and their anticommutation relation is {θ a α , (θ b β ) † } = δ αβ δ ab . (In other words, θ a α is given by two copies of the real one θ (1) and θ (2) : θ a α = (θ…”

Towards the ground state of the supermembrane

“…Performing the Taylor expansion of the ground state about X = 0, the 0th order term (i.e. the coordinate independent one) for the SU(2) model has been constructed explicitly [17] and proven to be unique [18,19] which confirmed earlier symbolic results using Mathematica [20]. The 1st order term is now also available and turns out to be unique as well [21].…”

On Coordinate Independent State Space of Matrix Theory

“…In SU(2) case the leading term |φ has been constructed in 5) and 6), and shown that it is unique. 6), 7) In the following we shall construct the next leading term |φ a i . Coordinate independent states are constructed by acting creation operators made of θ a α on the vacuum.…”