In a variety of situations, integrals of products of eigenfunctions have faster decay than smoothness entails. This phenomenon does not appear for abelian or compact groups, since irreducibles are finite-dimensional, so the decomposition of a tensor product of irreducibles is finite. In contrast, for non-compact, nonabelian groups irreducibles are typically infinite-dimensional, and the decompo...

We formulate a new class of tensor gauge field theories in any dimension that is hybrid between symmetric higher-rank theory (i.e., higher-spin theory) and anti-symmetric topological theory. Our describes mixed unitary phase interplaying gapless gapped order phases (which can live with or without Euclidean, Poincar\'e anisotropic symmetry, at least ultraviolet high intermediate energy theory, b...

A group is called square-like if it is universally equivalent to its direct square. It is known that the class of all square-like groups admits an explicit first order axiomatization but its theory is undecidable. We prove that the theory of square-like abelian groups is decidable. This answers a question posed by D. Spellman.

In this paper, we study universal central extensions and non-abelian tensor product of hom-Lie–Rinehart algebras. We discuss $\alpha $-central extensions, the lifting automorphisms $-derivations to hom-Li

We analyze the gauge symmetry of a topological mass generating action in four dimensions which contains both a vector and a second rank antisymmetric tensor fields. In the Abelian case, this system induces an effective mass for the vector gauge field via a topological coupling B ∧ F in the presence of a kinetic term for the antisymmetric tensor field B, while maintaining a gauge symmetry. On th...

Dimensional reduction of a self-dual tensor gauge field in 6d gives an Abelian vector gauge field in 5d. We derive the conditions under which an interacting 5d theory of an Abelian vector gauge field is the dimensional reduction of a 6d Lorentz invariant interacting theory of a self-dual tensor. Then we specialize to the particular 6d theory that gives 5d Born–Infeld theory. The field equation ...

We extend a conjecture of Kimberley-Robertson on the abelian-izations of certain square complex groups.

In SU(2) gluodynamics we calculate the gluon polarization tensor in an Abelian homogeneous magnetic field in one-loop order in the Lorentz background field gauge. It turned out to be non transversal and consisting of ten tensor structures and corresponding form factors four in color neutral and six in color charged sector. Seven tensor structures are transversal, three are not. The non transver...

It is shown that if C1 and C2 are maximal abelian self-adjoint subalgebras (masas) of C*-algebras A1 and A2, respectively, then the completion C1 ⊗ C2 of the algebraic tensor product C1 ⊙ C2 of C1 and C2 in any C*-tensor product A1 ⊗β A2 is maximal abelian provided that C1 has the extension property of Kadison and Singer and C2 contains an approximate identity for A2. Examples are given to show...

Using the corner-transfer matrix renormalization group to contract tensor network that describes its partition function, we investigate nature of phase transitions hard-square model, one exactly solved models statistical physics for which Baxter has found an integrable manifold. The motivation is twofold: assess power networks such models, and probe 2D classical analog a 1D quantum model hard-c...