Related papers: Shintani's invariant via cyclic quantum dilogarith…
For the chiral QCD_2 on a cylinder, we give a construction of a quantum theory consistent with anomaly. We construct the algebra of the Poincare generators and show that it differs from the Poincare one.
We investigate a variation of $q$-Wolstenholme's theorem, which extends the $q$-analogue of Wolstenholme's theorem due to Shi and Pan [Amer. Math. Monthly 114 (2007), 529--531]. The proof makes use of the Ramanujan sum and higher order…
We present a bicovariant differential calculus on the quantum Poincare group in two dimensions. Gravity theories on quantum groups are discussed.
The quantum deformed (1+1) Poincare' algebra is shown to be the kinematical symmetry of the harmonic chain, whose spacing is given by the deformation parameter. Phonons with their symmetries as well as multiphonon processes are derived from…
A theorem of G\"ottsche establishes a connection between cohomological invariants of a complex projective surface $S$ and corresponding invariants of the Hilbert scheme of $n$ points on $S.$ This relationship is encoded in certain infinite…
In this short note, we give an algorithm to get an explicit expression of the Luroth invariant in terms of the Dixmier-Ohno invariants. We also get the explicit factorized expression on the locus of Ciani quartics in terms of the…
A consistent classical mechanics formulation is presented in such a way that, under quantization, it gives a noncommutative quantum theory with interesting new features. The Dirac formalism for constrained Hamiltonian systems is strongly…
Further properties of a recently proposed higher order infinite spin particle model are derived. Infinitely many classically equivalent but different Hamiltonian formulations are shown to exist. This leads to a condition of uniqueness in…
We give a construction of a state sum invariant of a closed spin 3-manifold based on a super 3-cocycle $(\widetilde{\alpha}, \omega)$ and a combinatorial representation of a spin 3-manifold, where $\omega$ is a $\mathbb{Z}_2$-valued cocycle…
A new complete invariant for acyclic graphs is presented
The coupling of spin 0 and spin 1 external fields to Dirac fermions defines a theory which displays gauge chiral symmetry. Quantum mechanically, functional integration of the fermions yields the determinant of the Dirac operator, known as…
We apply the constructions of "The p-adic Shintani cocycle" to the Shintani cocycle of Charollois-Dasgupta-Greenberg, obtaining cocycles on arithmetic subgroups of GL_n(Q$ valued in maps from "deformation vectors" R^n-Q^n to p-adic…
We show that Tim Cochran's invariants $\beta^i(L)$ of a $2$-component link $L$ in the $3$--sphere can be computed as intersection invariants of certain 2-complexes in the $4$--ball with boundary $L$. These 2-complexes are special types of…
This article is concerned with the representation of curves by means of integral invariants. In contrast to the classical differential invariants they have the advantage of being less sensitive with respect to noise. The integral invariant…
Using differential and integral calculi on the quantum plane which are invariant with respect to quantum inhomogeneous Euclidean group E(2)q , we construct path integral representation for the quantum mechanical evolution operator kernel of…
Assuming the spin-independence for confining force, we give a covariant quark representation of general composite meson systems with definite Lorentz transformation properties. For benefit of this representation we are able to deduce…
Second order supersymmetric approach is taken to the system describing motion of a quantum particle in a potential endowed with position-dependent effective mass. It is shown that the intertwining relations between second order partner…
We calculate the Chern-Simons invariants of the twist knot orbifolds using the Schl\"{a}fli formula for the generalized Chern-Simons function on the family of the twist knot cone-manifold structures. Following the general instruction of…
We introduce new skein invariants of links based on a procedure where we first apply the skein relation only to crossings of distinct components, so as to produce collections of unlinked knots. We then evaluate the resulting knots using a…
A covariant formulation for the Newton-Hooke particle is presented by following an algorithm developed by us \cite{BMM1, BMM2, BMM3}. It naturally leads to a coupling with the Newton-Cartan geometry. From this result we provide an…