It is shown that q-deformed quantummechanics (systems with q-deformed Heisenberg commutation relations) can be interpreted as an ordinary quantum mechanics on Kähler manifolds, or as a quantum theory with second (or first)-class constraints. 1. The q-deformed Heisenberg-Weyl algebras [1], [2] exhibiting the quantum group symmetries [3],[4] have attracted much attention of physicists and mathema...

‎In this study‎, ‎properties of spectral characteristic are investigated for‎ ‎singular Sturm-Liouville operators in the case where an eigen‎ ‎parameter not only appears in the differential equation but is‎ ‎also linearly contained in the jump conditions‎. ‎Also Weyl function‎ ‎for considering operator has been defined and the theorems which‎ ‎related to uniqueness of solution of inverse proble...

Let φ : M → Rn+p(c) be an n-dimensional submanifold in an (n + p)dimensional space form Rn+p(c) with the induced metric g. Willmore functional of φ is W (φ) = ∫M (S − nH2)n/2dv, where S = ∑ α,i, j (h α i j ) 2 is the square of the length of the second fundamental form, H is the mean curvature of M . The Weyl functional of (M, g) is ν(g) = ∫M |Wg|n/2dv, where |Wg|2 = ∑ i, j,k,l W 2 i jkl and Wi ...

Conformal invariant new forms of p-brane and Dp-brane actions are proposed. These are quadratic in ∂X for the p-brane case and for Dp-branes in the Abelian field strength. The fields content of these actions are: an induced metric, gauge fields, an auxiliary metric and an auxiliary scalar field. The proposed actions are Weyl invariant in any dimension and the elimination of the auxiliary metric...

The hypothesis that gravitational self-binding energy may be the source for the vacuum energy term of cosmology is studied in a Newtonian Ansatz. For spherical spaces the attractive force of gravitation and the negative pressure of the vacuum energy term form a self stabilizing system under very reasonable restrictions for the parameters, among them a characteristic coefficient β of self energy...

A general framework for the Weyl invariant quantization of Liouville field theory by means of an exact renormalization group equation is proposed. This flow equation describes the scale dependence of the effective average action which has a built-in infrared cutoff. For c < 1 it is solved approximately by a truncation of the space of action functionals. We derive the Ward identities associated ...

A system of PDOs(=Partial Differential Operators) has two non-commutativities, (i) one from [∂q, q] = 1 (Heisenberg relation), (ii) the other from [A, B] 6= 0 for A, B being matrices in general. Non-commutativity from Heisenberg relation is nicely controlled by using Fourier transformations (i.e. the theory of ΨDOs=pseudo-differential operators). Here, we give a new method of treating non-commu...

The envelope of the action of the symmetric group Sr on rank r tensors has dimension independent of the characteristic of the base field. M. Härterich proved this, using G.E. Murphy’s combinatorial basis of the Hecke algebra of Sr in order to describe an explicit basis for the the annihilator of tensor space. This leads to a proof of Schur-Weyl duality in positive characteristic, assuming the c...