arXiv subjects
Publications and source records attributed to Ramesh Anishetty.
We solve the local Gauss law in lattice QCD in the presence of matter charges. This corresponds to constructing singlet states using Schwinger Bosons and Fermions of SU(3) group at each vertex of the lattice. We also calculate the action of various invariant operators on these states required for studying the dynamics.
We construct the singlet Hilbert space associated with addition of SU(3) generators. This corresponds to the solution of Gauss law in lattice QCD. The normalized basis states are explicitly constructed using Schwinger Bosons. Further, we compute the action of basic singlet operators on these basis states.
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.
Intermolecular correlations in liquid water at ambient conditions have generally been characterized through short range density fluctuations described through the atomic pair distribution functions (PDF). Recent numerical and experimental results have suggested that such a description of order or structure in liquid water is incomplete and there exists considerably longer ranged orientational correlations in water that can be studied through dipolar correlations. In this study, using large scale classical, atomistic molecular dynamics (MD) simulations using TIP4P-Ew and TIP3P models of water, we show that salts such as sodium chloride (NaCl), potassium chloride (KCl), caesium chloride (CsCl) and magnesium chloride (MgCl$_2$) have a long range effect on the dipolar correlations, which can not be explained by the notion of structure making and breaking by dissolved ions. The relative effects of cations on dipolar correlations are observed to be consistent with the well-known Hofmeister series. Observed effects are explained through orientational stratification of water molecules around ions, and their long range coupling to the global hydrogen bond network by virtue of the sum rule for water. The observations for single hydrophilic solutes are contrasted with the same for a single methane (CH$_4$) molecule. We observe that even a single small hydrophobe can result in enhancement of long range orientational correlations in liquid water,- contrary to the case of dissolved ions, which have been observed to have a reducing effect. The observations from this study are discussed in the context of hydrophobic effect.
Within the Hamiltonian formulation of Lattice gauge theories, prepotentials, belonging to the fundamental representation of the gauge group and defined locally at each site of the lattice, enables us to construct local loop operators and loop states. We propose a set of diagrammatic rules for the action of local gauge invariant operators on arbitrary loop states. Moreover We propose a new set of fusion variables within the prepotential aproach suitable for approaching the weak coupling limit.
We use Schwinger Bosons as prepotentials for lattice gauge theory to define local linking oper- ators and calculate their action on linking states for 2 + 1 dimensional SU(2) lattice gauge theory. We develop a diagrammatic technique and associate a set of (lattice Feynman) rules to compute the entire loop dynamics diagrammatically. The physical loop space is shown to contain only non- intersecting loop configurations after solving the Mandelstam constraint. The smallest plaquette loops are contained in the physical loop space and other configurations are generated by the action of a set of fusion operators on this basic loop states enabling one to charaterize any arbitrary loop by the basic plaquette together with the fusion variables. Consequently, the full Kogut-Susskind Hamiltonian and the dynamics of all possible non-intersecting physical loops are formulated in terms of these fusion variables.
In this paper we study the coupled system of non-abelian gauge fields with higher-derivative gravity. Charge renormalization is investigated in this coupled system. It is found that the leading term in the gauge coupling beta function comes due to interaction of gauge fields with gravitons. This is shown to be a universal quantity in the sense that it doesn't depend on the gauge coupling and the gauge group, but may depend on the other couplings of the action (gravitational and matter). The coupled system is studied at one-loop. It is found that the leading term of gauge beta function is zero at one-loop in four dimensions. The effect of gauge fields on the running of gravitational couplings is investigated. The coupled system of gauge field with higher-derivative gravity is shown to satisfy unitarity when quantum corrections are taken in to account. Moreover, it is found that Newton constant goes to zero at short distances. In this renormalizable and unitary theory of gauge field coupled with higher-derivative gravity, the leading term of the gauge beta function, found to be universal for all gauge groups, is further studied in more detail by isolating it in the context of abelian gauge theories coupled with gravity in four dimensions. Using self-duality of abelian gauge theories in four dimensions, this term of the gauge beta function is shown to be zero to all loops. This is found to be independent of the gravity action, regularization scheme and gauge fixing condition. An explicit one-loop computation for arbitrary gravity action further demonstrates the vanishing of this term in the gauge beta function in four dimensions, independent of the regularization scheme and gauge fixing condition. Consequences of this are discussed.
The leading term in the gauge coupling beta function comes due to interaction of gauge field with gravitons. It is shown to be a universal quantity for all gauge theories. At one-loop it is found to be zero in four dimensions. This is independent of the gravity action with metric as the field variable, gauge fixing condition and regularization scheme. This term being universally same for all gauge groups is further studied in the case of abelian gauge theories, where due to self-duality this term is shown to be zero to all loops, on-shell. Consequences of this are discussed.
In 3+1 space-time dimensions, fourth order derivative gravity is perturbatively renormalizable. Here it is shown that it describes a unitary theory of gravitons (with/without an additional scalar) in a limited coupling parameter space which includes standard cosmology. The running of gravitational constant which includes contribution of graviton is computed. It is shown that generically Newton's constant vanishes at short distance in this perturbatively renormalizable and unitary theory.
Fourth order derivative gravity in 3+1-dimensions is perturbatively renormalizable and is shown to describe a unitary theory of gravitons in a limited coupling parameter space. The running gravitational constant which includes graviton contribution is computed. Generically, gravitational Newton's constant vanishes at short distances in this perturbatively renormalizable and unitary theory.
Hydrophobic force, interfacial tension, transverse density profile in confined water system are addressed from first principles of statistical mechanics in a lattice model for water. Using molecular mean field theory technique we deduce explicit expressions for each of the above mentioned phenomena and show that hydrophobic force is a manifestation of Casimir-like effect due to hydrogen bond fluctuations in confined water. It is largely influenced by the long range correlations of orientational fluctuations. All the computations are parameter-free and we compare favorably with results of molecular dynamics simulations and experiments.
Attractive bonding interactions between molecules typically have inherent conservation laws which influence the statistical properties of such systems in terms of corresponding sum rules. We considered lattice water as an example and enunciated the consequences of the sum rule through a general computational procedure called "Molecular mean field" theory. Fluctuations about mean field are computed and many of the liquid properties have been deduced and compared with Monte Carlo simulation, molecular dynamics and experimental results. Large correlation lengths are seen to be a consequence of the sum rule in liquid phase. Long range Coulomb interactions are shown to have minor effects on our results.
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) irreducible Schwinger bosons. Further, we show that these representations are free of multiplicity problems. Thus all SU(N) representations are made as simple as SU(2).
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 matter fields. The Hilbert space of SU(3) lattice gauge theory is shown to be equivalent to the Hilbert space of the prepotential formulation satisfying certain color invariant Sp(2,R) constraints. The SU(3) irreducible prepotential operators which solve these Sp(2,R) constraints are used to construct SU(3) gauge invariant Hilbert spaces at every lattice site in terms of SU(3) gauge invariant vertex operators. The electric fields and the link operators are reconstructed in terms of these SU(3) irreducible prepotential operators. We show that all the SU(3) Mandelstam constraints become local and take very simple form within this approach. We also discuss the construction of all possible linearly independent SU(3) loop states which solve the Mandelstam constraints. The techniques can be easily generalized to SU(N).
Liquid water, at ambient conditions, has short-range density correlations which are well known in literature. Surprisingly, large scale molecular dynamics simulations reveal an unusually long-distance correlation in `longitudinal' part of dipole-dipole orientational correlations. It is non-vanishing even at 75 Å and falls-off exponentially with a correlation length of about 24 Å beyond solvation region. Numerical evidence suggests that the long range nature of dipole-dipole correlation is due to underlying fluctuating network of hydrogen-bonds in the liquid phase. This correlation is shown to give a shape dependant attraction between two hydrophobic surfaces at large distances of separation and the range of this attractive force is in agreement with experiments. In addition it is seen that quadrupolar fluctuations vanish within the first solvation peak (3 Å)
We develop simple computational techniques for constructing all possible SU(3) representations in terms of irreducible SU(3) Schwinger bosons. We show that these irreducible Schwinger oscillators make SU(3) representation theory as simple as SU(2). The new Schwinger oscillators satisfy certain Sp(2,R) constraints and solve the multiplicity problem as well. These SU(3) techniques can be generalized to SU(N).
We investigate light meson bound state contributions to six quark Green's functions and establish that the latter has poles corresponding to baryon bound states. We estimate light baryon masses including the Roper resonance. Constituent quark model and the Parton model are natural consequences of this quantum field theoretic picture. We elaborate this analysis to pentaquarks and heptaquarks. An almost model independent prediction for the mass of $θ$ pentaquark is $1.57Gev$.
General properties of the light and heavy quark propagators have been investigated in the context of string tension interaction. Confinement, chiral symmetry breaking, spectral properties of the propagator are analytically studied and numerically validated. We show that the propagator is analytic in the infrared region even for massless quarks with a non zero radius of convergence. Emergence of more than one mass scale is exemplified. Massless limit of the quark propagator does exhibit critical behaviour.