arXiv subjects

T. P. Sreeraj

Publications and source records attributed to T. P. Sreeraj.

6 recordsLinked to original sources

arXiv2024

Imperfect Measurements and Conjugate Observables

In the standard von Neumann interaction used in Quantum measurements, the chosen observable to which the environment (apparatus) entangles is exactly reproduced in the state of the environment, thereby decohering the quantum system in the eigenbasis of the observable. We relax this by allowing for imperfect measurements whereby the environment evolves to a state that approximately, but not exactly, reflects the state of the system. In this scheme it is possible to attain approximate decoherence of conjugate quantities that resembles classical physics, which we demonstrate using an example.

quant-ph↗

arXiv2019

Resolution of SU(3) Outer Multiplicity Problem and the $SU(3)\otimes SU(3)$ Invariant Group $SO(4,2)$

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 form SO(4,2) algebra. Further, they enable us to construct a family of operators any one of which can be used to distinguish repeating representations present in the reduction of the direct product of two SU(3) irreducible representations.

math-ph↗

arXiv2018

Mass gap in the weak coupling limit of $(2+1)$ SU(2) lattice gauge theory

We develop the dual description of $2+1$ SU(2) lattice gauge theory as interacting `abelian like' electric loops by using Schwinger bosons. "Point splitting" of the lattice enables us to construct explicit Hilbert space for the gauge invariant theory which in turn makes dynamics more transparent. Using path integral representation in phase space, the interacting closed loop dynamics is analyzed in the weak coupling limit to get the mass gap.

hep-lat↗

arXiv2016

Lattice Gauge Theories and Spin Models

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 duality is directly generalized to SU(N) lattice gauge theory in $(2+1)$ dimensions to obtain the SU(N) spin model in terms of the SU(N) magnetic fields and their conjugate SU(N) electric scalar potentials. The exact and complete solutions of the $Z_2, U(1), SU(N)$ Gauss law constraints in terms of the corresponding spin or dual potential operators are given. The gauge-spin duality naturally leads to a new gauge invariant magnetic disorder operator for SU(N) lattice gauge theory which produces a magnetic vortex on the plaquette. A variational ground state of the SU(2) spin model with nearest neighbor interactions is constructed to analyze SU(2) gauge theory.

hep-lat↗

arXiv2015

Canonical Transformations and Loop Formulation of SU(N) Lattice Gauge Theories

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 as a consequence of SU(N) Gauss laws all SU(N) string degrees of freedom become cyclic and decouple from the physical Hilbert space ${\cal H}^p$. The canonical relations between the initial SU(N) link operators and the final SU(N) loop & string operators over the entire lattice are worked out in a self consistent manner. The Kogut-Susskind Hamiltonian rewritten in terms of the fundamental physical loop operators has global SU(N) invariance. There are no gauge fields. We further show that the $(1/g^2)$ magnetic field terms on plaquettes create and annihilate the fundamental plaquette loop fluxes while the $(g^2)$ electric field terms describe all their interactions. In the weak coupling ($g^2 \rightarrow 0$) continuum limit the SU(N) loop dynamics is described by SU(N) spin Hamiltonian with nearest neighbour interactions. In the simplest SU(2) case, where the canonical transformations map the SU(2) loop Hilbert space into the Hilbert spaces of hydrogen atoms, we analyze the special role of the hydrogen atom dynamical symmetry group $SO(4,2)$ in the loop dynamics and the spectrum. A simple tensor network ansatz in the SU(2) gauge invariant hydrogen atom loop basis is discussed.

hep-lat↗

arXiv2015

From Lattice Gauge Theories to Hydrogen Atoms

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. One hydrogen atom is assigned to every plaquette of the lattice. A complete orthonormal description of the Wilson loop basis in ${\cal H}^p$ is obtained by all possible angular momentum Wigner couplings of hydrogen atom energy eigenstates $\vert n~l~m\rangle$ describing electric fluxes on the loops. The SU(2) gauge invariance implies that the total angular momenta of all hydrogen atoms vanish. The canonical transformations also enable us to rewrite the Kogut-Susskind Hamiltonian in terms of fundamental Wilson loop operators and their conjugate electric fields. The resulting loop Hamiltonian has a global SU(2) invariance and a simple weak coupling ($g^2\rightarrow 0$) continuum limit. The canonical transformations leading to the loop Hamiltonian are valid for any SU(N). The ideas and techniques can also be extended to higher dimension.

hep-lat↗