Manu Mathur
We construct the most general disorder operator for SU(N) lattice gauge theory in $(2+1)$ dimension by using exact duality transformations. These disorder operators, defined on the plaquettes and characterized by ($\text{N}-1$) angles, are…
We construct SU($N$) toric code model describing the dynamics of SU($N$) electric and magnetic fluxes on a two dimensional torus. We show that the model has $N^2$ topologically distinct ground states $|\psi_0\rangle_{({\mathsf p},{\mathsf…
We construct exact duality transformations in pure SU(N) Hamiltonian lattice gauge theory in (2+1) dimension. This duality is obtained by making a series of iterative canonical transformations on the SU(N) electric vector fields and their…
We exploit the spin network properties of the magnetic eigenstates of SU(2) Hamiltonian lattice gauge theory and use the Wilson loop operators to obtain a wide class of new identities amongst 3nj Wigner coefficients. We also show that the…
We resolve the SU(3) outer multiplicity problem by defining all possible $SU(3)\otimes SU(3)$ invariant operators in terms of SU(3) Schwinger bosons. We show that the elementary invariant operators relevant to the outer multiplicity problem…
We consider a local action with both the real scalar field and its dual in two Euclidean dimensions. The role of singular line discontinuities is emphasized. Exotic properties of the correlation of the field with its dual, the generation of…
The Wegner $Z_2$ gauge theory-$Z_2$ Ising spin model duality in $(2+1)$ dimensions is revisited and derived through a series of canonical transformations. The Kramers-Wannier duality is similarly obtained. The Wegner $Z_2$ gauge-spin…
We construct canonical transformations to reformulate SU(N) Kogut-Susskind lattice gauge theory in terms of a set of fundamental loop & string flux operators along with their canonically conjugate loop & string electric fields. We show that…
We construct canonical transformations to obtain a complete and most economical realization of the physical Hilbert space ${\cal H}^p$ of pure $SU(2)_{2+1}$ lattice gauge theory in terms of Wigner coupled Hilbert spaces of hydrogen atoms.…
We define coherent states carrying SU(N) charges by exploiting generalized Schwinger boson representation of SU(N) Lie algebra. These coherent states are defined on $2 (2^{N - 1} - 1)$ complex planes. They satisfy continuity property and…
We generalize Schwinger boson representation of SU(2) algebra to SU(N) and define coherent states of SU(N) using $2(2^{N-1}-1)$ bosonic harmonic oscillator creation and annihilation operators. We give an explicit construction of all (N-1)…
It is shown that SU(N) gauge theory coupled to adjoint Higgs can be explicitly re-written in terms of SU(N) gauge invariant dynamical variables with local physical interactions. The resultant theory has a novel compact abelian $U(1)^{(N -…
We construct SU(N) irreducible Schwinger bosons satisfying certain U(N-1) constraints which implement the symmetries of SU(N) Young tableaues. As a result all SU(N) irreducible representations are simple monomials of $(N-1)$ types of SU(N)…
We exploit SU(N) Schwinger bosons to construct and analyze the coupled irreducible representations of $SU(N) \times SU(N)$ in terms of the invariant group. The corresponding projection operators are constructed in terms of the invariant…
We exploit the SU(N) irreducible Schwinger boson to construct SU(N) coherent states. This construction of SU(N) coherent state is analogous to the construction of the simplest Heisenberg-Weyl coherent states. The coherent states belonging…
The SU(3) lattice gauge theory is reformulated in terms of SU(3) prepotential harmonic oscillators. This reformulation has enlarged $SU(3)\otimes U(1) \otimes U(1)$ gauge invariance under which the prepotential operators transform like…
We define coherent states carrying SU(2) charges by exploiting Schwinger boson representation of SU(2) Lie algebra. These coherent states satisfy continuity property and provide resolution of identity on $S^{3}$. We further generalize these…
We solve the Gauss law as well as the corresponding Mandelstam constraints of (d+1) dimensional SU(2) lattice gauge theory in terms of harmonic oscillator prepotentials. This enables us to explicitly construct a complete orthonormal and…
We write the SU(2) lattice gauge theory Hamiltonian in (d+1) dimensions in terms of prepotentials which are the SU(2) fundamental doublets of harmonic oscillators. The Hamiltonian in terms of prepotentials has $SU(2) \otimes U(1)$ local…
We define coherent states for SU(3) using six bosonic creation and annihilation operators. These coherent states are explicitly characterized by six complex numbers with constraints. For the completely symmetric representations (n,0) and…