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Manu Mathur

Publications and source records attributed to Manu Mathur.

32 records · Page 2Linked to original sources
arXiv2004

Harmonic Oscillator Prepotentials in SU(2) Lattice Gauge Theory

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 gauge invariance. In the strong coupling limit, the color confinement in this formulation is due to the U(1) gauge group. We further solve the $SU(2) \otimes U(1)$ Gauss law to characterize the physical Hilbert space in terms of a set of gauge invariant integers. We also obtain certain novel gauge invariant operators in terms of the above oscillators. The corresponding prepotential formulation of SU(N) lattice gauge theory is also simple and discussed.

hep-lat↗
arXiv2003

Coherent States with SU(N) Charges

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 provide resolution of identity. We also exploit this technique to construct the corresponding non-linear SU(N) coherent states.

quant-ph↗
arXiv2002

SU(N) Coherent States

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) Casimirs of SU(N) in terms of these creation and annihilation operators. The SU(N) coherent states belonging to any irreducible representations of SU(N) are labelled by the eigenvalues of the Casimir operators and are characterized by (N-1) complex orthonormal vectors describing the SU(N) manifold. The coherent states provide a resolution of identity, satisfy the continuity property, and possess a variety of group theoretic properties.

quant-ph↗
arXiv2000

Coherent States For SU(3)

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 (0,m), only three of the bosonic operators are required. For mixed representations (n,m), all six operators are required. The coherent states provide a resolution of identity, satisfy the continuity property, and possess a variety of group theoretic properties. We introduce an explicit parameterization of the group SU(3) and the corresponding integration measure. Finally, we discuss the path integral formalism for a problem in which the Hamiltonian is a function of SU(3) operators at each site.

quant-ph↗
arXiv1999

Z_2 Monopoles, Vortices and the Universality of the SU(2) Deconfinement Transition

We investigate the effect of $Z_2$ magnetic monopoles and vortices on the finite temperature deconfinement phase transition in the fundamental - adjoint SU(2) lattice gauge theory. In the limit of complete suppression of the $Z_2$ monopoles, the mixed action for the SU(2) theory in its Villain form is shown to be self-dual under the exchange of the fundamental and adjoint couplings. By further suppressing the $Z_2$ vortices we show that the extended model reduces to the Wilson action with a modified coupling. The universality of the SU(2) deconfinement phase transition with the Ising model is therefore expected to remain intact in the entire plane of the fundamental-adjoint couplings in the continuum limit. The self-duality arguments related to the suppression of $Z_2$ monopoles are also applicable to the Villain form of mixed action for the SU(N) theory with $Z_{N}$ magnetic monopoles.

hep-lat↗
arXiv1998

Abelianization of Low Energy SU(2) Effective Action

Recently Faddeev and Niemi proposed a low energy effective action for pure SU(2) Yang Mills theory in 4 dimension to describe its long distance physics. The effective action is O(3) $σ$ model with a mass parameter, a dimensionless coupling constant e and a topological term. In this work, choosing a new set of variables, we relate this $σ$ model to a U(1) gauge theory with electric and magnetic charges of charge e and $4 πe^{-1}$ respectively. In the new formulation the connection of the mass parameter with the monopole condensate is discussed. This theory after lattice regularisation is the compact U(1) gauge theory coupled to electric charges.

hep-th↗
arXiv1998

Abelianization of SU(N) Gauge Theory with Gauge Invariant Dynamical Variables and Magnetic Monopoles

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 $U(1)^{(N - 1)}$ gauge invariance. The above abelian gauge invariance is related to the adjoint Higgs field and not to the gauge group SU(N). In this abelianized version the magnetic monopoles carrying the magnetic charges of $(N-1)$ types have a natural origin and therefore appear explicitly in the partition function as Dirac monopoles along with their strings. The gauge invariant electric and magnetic charges with respect to $U(1)^{(N-1)}$ gauge groups are shown to be vectors in root and co-root lattices of SU(N) respectively. Therefore, the Dirac quantization condition corresponds to SU(N) Cartan matrix elements being integers. We also study the effect of the $θ$ term in the abelian version of the theory.

hep-th↗
arXiv1997

More On The SU(2) Deconfinement Transition In The Mixed Action

We examine certain issues related to the universality of the SU(2) lattice gauge theory at non-zero temperatures. Using Monte Carlo simulations and strong coupling expansions, we study the behavior of the deconfinement transition in an extended coupling plane (beta, beta_A) around the tricritical point where the deconfinement transition changes from second to first order. Our numerical results on N_tau =2,4,6,8 lattices show that the tricritical point first moves down towards the Wilson axis and and then moves slowly upwards, if at all, as the lattice spacing is reduced. Lattices with very large N_tau seem to be therefore necessary for the mixed action to exhibit the critical exponents of the three dimensional Ising model for positive values of the adjoint coupling.

hep-lat↗
arXiv1997

Magnetic Monopoles, Gauge Invariant Dynamical Variables and Georgi Glashow Model

We investigate Georgi-Glashow model in terms of a set of explicitly SO(3) gauge invariant dynamical variables. In the new description a novel compact abelian gauge invariance emerges naturally. As a consequence magnetic monopoles occur as point like "defects" in space time. Their non-perturbative contribution to the partition function is explicitly included. This procedure corresponds to dynamical "abelian projection" without gauge fixing. In the Higgs phase the above abelian invariance is to be identified with electromagnetism. We also study the effect of $θ$ term in the above abelian theory.

hep-th↗
arXiv1995

Finite Temperature Phase Transition in SU(2) Lattice Gauge Theory with Extended Action

We study the three dimensional fundamental-adjoint $SU(2)$ lattice gauge theory at finite temperature by Monte Carlo simulations. We find that the finite temperature deconfinement phase transition line joins the first order bulk phase transition line at its endpoint. Moreover, across the bulk transition line, the Polyakov loop undergoes a discontinuous jump implying the existence of both confining and deconfining phases on its two sides. Implications for universality and the nature of the confining-deconfining transition are discussed.

hep-lat↗
arXiv1995

Landau Ginzberg model and deconfinement transition for extended SU(2) action

We compute the effective action in terms of the Polyakov loop for the 3-dimensional pure fundamental-adjoint SU(2) lattice gauge theory at non-zero temperatures using the strong coupling expansion. In the extended coupling plane we show the existence of a tricritical point where the nature of the deconfinement transition undergoes a change from second to first order. The resulting phase structure is in excellent agreement with the Monte Carlo results both in the fundamental and adjoint directions. The possible consequences of our results on universality are discussed.

hep-lat↗
arXiv1994

Universality and the Deconfinement Phase Transition in SU(2) Lattice Gauge Theory

We study the three dimensional fundamental-adjoint $SU(2)$ lattice gauge theory at non-zero temperatures by Monte Carlo simulations. On an $8^3 \times 2$ lattice, at $β_A = 1.1$, where $β_A$ is the adjoint coupling, we find no evidence of any transition at the location of a previously known bulk phase transition around $β= 1.33$. Moreover, the deconfinement transition at $ β_A = 1.1$ occurs at $β=1.20$ and is of first order for $β_A \ge 1.1$, thus implying a change of universality class from that of the Wilson action at $β_A=0$. Computations of the plaquette susceptibility and the temporal and spatial Polyakov loops on $8^3 \times 4$ and $16^3 \times 8$ lattices at $β_A = 1.1$ further support these conclusions and suggest that the previously claimed bulk transition around $β= 1.33$ is, in fact, the first order deconfinement transition. Simulations at larger $β_A$ and the measurements of the mass gaps from the correlation functions of temporal and spatial Polyakov loops also confirm the temperature dependent nature of the above transition. The consequences of our results on universality are discussed.

hep-lat↗
arXiv1992

Dual of 3-dimensional pure SU(2) Lattice Gauge Theory and the Ponzano-Regge Model

By carrying out character expansion and integration over all link variables, the partition function of 3-dimensional pure SU(2) lattice gauge theory is rewritten in terms of 6j symbols. The result is Ponzano-Regge model of 3-dimensional gravity with a term that explicitly breaks general coordinate invariance. Conversely, we show that dual of Ponzano-Regge model is an SU(2) lattice gauge theory where all plaquette variables are constrained to the identity matrix and therefore the model needs no further regularization. Our techniques are applicable to other models with non-abelian symmetries in any dimension and provide duality transform for the partition function.

hep-lat↗