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Jul 20, 2013
07/13

by
V. P. Nair

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Summation over hard thermal loops, by themselves and as insertions in higher order Feynman diagrams, is important in thermal perturbation theory for Quantum Chromodynamics, so that all contributions of a given order in the coupling constant can be consistently taken into account. I review some of the basic properties of hard thermal loops and how the generating functional for them is related to the eikonal for a Chern-Simons gauge theory, and using an auxiliary field, to the gauged...

Source: http://arxiv.org/abs/hep-th/9411220v1

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Sep 20, 2013
09/13

by
V. P. Nair

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These lectures fall into two distinct, although tenouously related, parts. The first part is about fuzzy and noncommutative spaces, and particle mechanics on such spaces, in other words, noncommutative mechanics. The second part is a discussion/review of twistors and how they can be used in the calculation of Yang-Mills amplitudes. The point of connection between these two topics, discussed in the last section, is in the realization of holomorphic maps as the lowest Landau level wave functions,...

Source: http://arxiv.org/abs/hep-th/0506120v1

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Sep 19, 2013
09/13

by
V. P. Nair

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Yang-Mills theories in 2+1 (or 3) dimensions are interesting as nontrivial gauge theories in their own right and as effective theories of QCD at high temperatures. I shall review the basics of our Hamiltonian approach to this theory, emphasizing symmetries with a short update on its status. We will show that the calculation of the vacuum wave function for Yang-Mills theory in 2+1 dimensions is in the lowest order of a systematic expansion. Expectation values of observables can be calculated...

Source: http://arxiv.org/abs/0910.3252v2

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Sep 21, 2013
09/13

by
V. P. Nair

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The effective action for hard thermal loops in QCD is related to a gauged WZNW theory. Some of the technical issues of this approach are clarified and the Hamiltonian formulation is presented. The two-point correlation function for the induced current in QCD is obtained; some simplifications of the dynamics of the longitudinal modes are also pointed out.

Source: http://arxiv.org/abs/hep-th/9403146v1

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Sep 22, 2013
09/13

by
V. P. Nair

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I review the analysis of (2+1)-dimensional Yang-Mills ($YM_{2+1})$ theory via the use of gauge-invariant matrix variables. The vacuum wavefunction, string tension, the propagator mass for gluons, its relation to the magnetic mass for $YM_{3+1}$ at nonzero temperature and the extension of our analysis to the Yang-Mills-Chern-Simons theory are discussed. A possible extension to 3+1 dimensions is also briefly considered.

Source: http://arxiv.org/abs/hep-th/0309061v1

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Sep 23, 2013
09/13

by
V. P. Nair

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A new class of twistor string theories were recently constructed by Abou-Zeid, Hull and Mason. The most interesting one of these theories has the particle content of N=8 supergravity. Arguments are given for the vanishing of the (+ - -)-helicity amplitude for gravitons which suggest that this theory describes a chiral N=8 supergravity rather than Einstein supergravity.

Source: http://arxiv.org/abs/0710.4961v1

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Sep 22, 2013
09/13

by
V. P. Nair

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We show how the maximally helicity violating (MHV) scattering amplitudes for gravitons can be related to current correlators and vertex operators in twistor space. This is similar to what happens in Yang-Mills theory and raises the possibility of a direct twistor-string-like construction for ${\cal N}=8$ supergravity.

Source: http://arxiv.org/abs/hep-th/0501143v1

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Sep 18, 2013
09/13

by
V. P. Nair

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Three topics, the self-consistent resummation of the perturbative expansion for thermal Yang-Mills (YM) theory, nonperturbative analysis of Yang-Mills theories in (2+1) dimensions and modification of the Bose distribution for gluons, are discussed. These topics are related to the magnetic mass or magnetic screening in the quark-gluon plasma. The value of the magnetic mass is argued to be close to $e^2N/2\pi=g^2TN/2\pi$ for an SU(N) gauge theory. An analytic calculation of the string tension for...

Source: http://arxiv.org/abs/hep-th/9809086v3

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Jun 28, 2018
06/18

by
V. P. Nair

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Thermofield dynamics is presented in terms of a path-integral using coherent states, equivalently, using a coadjoint orbit action. A field theoretic formulation in terms of fields on a manifold ${\mathcal M} \times {\tilde{\mathcal M}}$ where the two components have opposite orientation is also presented. We propose formulating gravitational dynamics for noncommutative geometry using thermofield dynamics, doubling the Hilbert space modeling the noncommutative space. We consider 2+1 dimensions...

Topics: Quantum Physics, Mathematical Physics, Mathematics, High Energy Physics - Theory

Source: http://arxiv.org/abs/1508.00171

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Sep 18, 2013
09/13

by
V. P. Nair

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K\"ahler-Chern-Simons theory describes antiself-dual gauge fields on a four- dimensional K\"ahler manifold. The phase space is the space of gauge potentials, the symplectic reduction of which by the constraints of antiself-duality leads to the moduli space of antiself-dula instantons. We outline the theory highlighting the symmetries, their canonical realization and some properties of the quantum wave functions. The relationship to integrable systems via dimensional reduction is...

Source: http://arxiv.org/abs/hep-th/9110042v1

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Sep 21, 2013
09/13

by
V. P. Nair

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The generating functional for hard thermal loops in QCD is important in setting up a resummed perturbation theory. I review how this functional is related to the eikonal for a Chern-Simons theory, and using an auxiliary field, to the gauged WZNW-action. The induced current due to hard thermal loops, properly incorporating damping effects, is also briefly discussed. (Invited talk at the Third Worshop on Thermal Field Theories, Banff, Canada, August, 1993.)

Source: http://arxiv.org/abs/hep-th/9403145v1

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Sep 19, 2013
09/13

by
V. P. Nair

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Recent progress in understanding (2+1)-dimensional Yang-Mills (YM_{2+1}) theory via the use of gauge-invariant variables is reviewed. Among other things, we discuss the vacuum wavefunction, an analytic calculation of the string tension and the propagator mass for gluons and its relation to the magnetic mass for YM_{3+1} at nonzero temperature.

Source: http://arxiv.org/abs/hep-th/9911061v1

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Sep 18, 2013
09/13

by
V. P. Nair

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We consider different large ${\cal N}$ limits of the one-dimensional Chern-Simons action $i\int dt~ \Tr (\del_0 +A_0)$ where $A_0$ is an ${\cal N}\times{\cal N}$ antihermitian matrix. The Hilbert space on which $A_0$ acts as a linear transformation is taken as the quantization of a $2k$-dimensional phase space ${\cal M}$ with different gauge field backgrounds. For slowly varying fields, the large ${\cal N}$ limit of the one-dimensional CS action is equal to the $(2k+1)$-dimensional CS theory on...

Source: http://arxiv.org/abs/hep-th/0605007v2

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Sep 18, 2013
09/13

by
V. P. Nair

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We consider the quantum mechanics of a particle on a noncommutative two-sphere with the coordinates obeying an SU(2)-algebra. The momentum operator can be constructed in terms of an $SU(2)\times SU(2)$-extension and the Heisenberg algebra recovered in the smooth manifold limit. Similar considerations apply to the more general SU(n) case.

Source: http://arxiv.org/abs/hep-th/0008027v2

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Sep 20, 2013
09/13

by
V. P. Nair

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The analysis of (2+1)-dimensional Yang-Mills ($YM_{2+1})$ theory via the use of gauge-invariant matrix variables is reviewed. The vacuum wavefunction, string tension, the propagator mass for gluons, its relation to the magnetic mass for $YM_{3+1}$ at nonzero temperature and the extension of our analysis to the Yang-Mills-Chern-Simons theory are discussed.

Source: http://arxiv.org/abs/hep-th/0204063v1

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Sep 23, 2013
09/13

by
V. P. Nair

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We consider the hard thermal loops of QCD for a moving quark-gluon plasma. Generalizing from this we suggest a candidate for the magnetic mass term. This term may also be useful in understanding the mass gap of three-dimensional non-Abelian gauge theories.

Source: http://arxiv.org/abs/hep-th/9406073v1

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Sep 18, 2013
09/13

by
V. P. Nair

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The one-dimensional ${\cal N}\times {\cal N}$-matrix Chern-Simons action is given, for large ${\cal N}$ and for slowly varying fields, by the $(2k+1)$-dimensional Chern-Simons action $S_{CS}$, where the gauge fields in $S_{CS}$ parametrize the different ways in which the large ${\cal N}$ limit can be taken. Since some of these gauge fields correspond to the isometries of the space, we argue that gravity on fuzzy spaces can be described by the one-dimensional matrix Chern-Simons action at finite...

Source: http://arxiv.org/abs/hep-th/0605008v2

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Sep 23, 2013
09/13

by
V. P. Nair

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We explore the relationship between the quantum effective action and the ground state (and excited state) wave functions of a field theory. Applied to the Yang-Mills theory in 2+1 dimensions, we find the leading terms of the effective action from the ground state wave function previously obtained in the Hamiltonian formalism by solving the Schrodinger equation.

Source: http://arxiv.org/abs/1109.6376v2

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8.0

Jun 29, 2018
06/18

by
V. P. Nair

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These lecture notes (from the Second Autumn School in High Energy Physics and Quantum Field Theory, Yerevan 2014) cover a number of topics related to geometric quantization. Most of the material is presented from a physicist's point of view. The original notes are posted at \verb+http://theorphyslab-ysu.info/VW_ASW-2014/uploads/ArmeniaLectures.pdf+. The have been revised with some additions and changes, although referencing is still somewhat dated. These notes are posted here as they may be...

Topics: High Energy Physics - Theory, Quantum Physics, Condensed Matter, Mathematics, Mesoscale and...

Source: http://arxiv.org/abs/1606.06407

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51

Sep 19, 2013
09/13

by
V. P. Nair

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The generating functional for hard thermal loops in QCD is rewritten in terms of a gauged WZNW action by introducing an auxiliary field. This shows in a simple way that the contribution of hard thermal loops to the energy of the quark-gluon plasma is positive.

Source: http://arxiv.org/abs/hep-ph/9307326v1

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Sep 18, 2013
09/13

by
V. P. Nair

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We outline a method of relating the quantum effective action and the ground state wave function of a field theory. This method, along with a gauge-invariant mass term and the previously obtained vacuum wave function, is used to arrive at the leading terms of the 3d-covariant quantum effective action for the Yang-Mills theory in three (or 2+1) dimensions. Some features of this effective action are also discussed.

Source: http://arxiv.org/abs/1201.0977v1

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3.0

Jun 30, 2018
06/18

by
Dimitra Karabali; V. P. Nair

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We consider relativistic charged particle dynamics and relativistic magnetohydrodynamics using symplectic structures and actions given in terms of co-adjoint orbits of the Poincar\'e group. The particle case is meant to clarify some points such as how minimal coupling (as defined in text) leads to a gyromagnetic ratio of $2$, and to set the stage for fluid dynamics. The general group-theoretic framework is further explained and is then used to set up Abelian magnetohydrodynamics including spin...

Topic: High Energy Physics - Theory

Source: http://arxiv.org/abs/1406.1551

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41

Jul 20, 2013
07/13

by
Dimitra Karabali; V. P. Nair

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The effect of edges and apertures on the Casimir energy of an arrangement of plates and boundaries can be calculated in terms of an effective nonlocal lower-dimensional field theory that lives on the boundary. This formalism has been developed in a number of previous papers and applied to specific examples with Dirichlet boundary conditions. Here we generalize the formalism to arbitrary boundary conditions. As a specific example, the geometry of a flat plate and a half-plate placed parallel to...

Source: http://arxiv.org/abs/1304.0511v1

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4.0

Jun 29, 2018
06/18

by
Dimitra Karabali; V. P. Nair

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We present a general formula for the topological part of the effective action for quantum Hall systems in higher dimensions, including fluctuations of the gauge field and metric around background fields of a specified topological class. The result is based on a procedure of integrating up from the Dolbeault index density which applies for the degeneracies of Landau levels, combined with some input from the standard descent procedure for anomalies. Features of the topological action in (2+1),...

Topics: Mathematics, High Energy Physics - Theory, Mathematical Physics, Condensed Matter, Strongly...

Source: http://arxiv.org/abs/1604.00722

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49

Sep 21, 2013
09/13

by
R. Jackiw; V. P. Nair

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In their recent letter, Chaichian et.~al. present a Lagrangian for a massive ($m$) point particle on the plane, with which they claim to realize anyon statistics. However, we find that there are some inaccuracies in their formulation and, when these are taken care of, well-known results are reproduced, which already exist in the literature.

Source: http://arxiv.org/abs/hep-th/9403010v1

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46

Sep 18, 2013
09/13

by
Dimitra Karabali; V. P. Nair

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In the first part of this paper, we present a set of simple arguments to show that the two-dimensional gauge anomaly and the (2+1)-dimensional Lorentz symmetry determine the leading Gaussian term in the vacuum wave function of (2+1)-dimensional Yang-Mills theory. This is to highlight the robustness of the wave function and its relative insensitivity to the choice of regularizations. We then comment on the correspondence with the explicit calculations done in earlier papers. We also make some...

Source: http://arxiv.org/abs/0705.2898v1

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Jun 28, 2018
06/18

by
Dimitra Karabali; V. P. Nair

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The possibility of treating boundary conditions in terms of a bilocal dynamical field is formalized in terms of a boundary action. This allows for a simple path-integral perturbation theory approach to physical effects such as radiation from a time-dependent boundary. The nature of the action which governs the dynamics of the bilocal field is investigated for a limited case (which includes the Robin boundary conditions).

Topics: Quantum Physics, High Energy Physics - Theory

Source: http://arxiv.org/abs/1507.03880

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Sep 21, 2013
09/13

by
R. Jackiw; V. P. Nair

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We describe the relationship between time-ordered and retarded response functions in a plasma. We obtain an expression, including the proper $i\epsilon$-prescription, for the induced current due to hard thermal loops in a non-Abelian theory, thus giving the non-Abelian generalization of the Kubo formula. The result is closely related to the eikonal for a Chern-Simons theory and is relevant for a gauge-invariant description of Landau damping in the quark-gluon plasma at high temperature.

Source: http://arxiv.org/abs/hep-ph/9305241v1

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45

Sep 19, 2013
09/13

by
V. P. Nair; A. Yelnikov

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We consider a gauge-invariant Hamiltonian analysis for Yang-Mills theories in three spatial dimensions. The gauge potentials are parametrized in terms of a matrix variable which facilitates the elimination of the gauge degrees of freedom. We develop an approximate calculation of the volume element on the gauge-invariant configuration space. We also make a rough estimate of the ratio of $0^{++}$ glueball mass and the square root of string tension by comparison with $(2+1)$-dimensional Yang-Mills...

Source: http://arxiv.org/abs/hep-th/0302176v2

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Sep 23, 2013
09/13

by
R. Efraty; V. P. Nair

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We show that the generating functional for hard thermal loops with external gluons in QCD is essentially given by the eikonal for a Chern-Simons gauge theory. This action, determined essentially by gauge invariance arguments, also gives an efficient way of obtaining the hard thermal loop contributions without the more involved calculation of Feynman diagrams.

Source: http://arxiv.org/abs/hep-th/9201058v2

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81

Jul 24, 2013
07/13

by
Abhishek Agarwal; V. P. Nair

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Pure Yang-Mills theory on ${\mathbb R} \times S^2$ is analyzed in a gauge-invariant Hamiltonian formalism. Using a suitable coordinatization for the sphere and a gauge-invariant matrix parametrization for the gauge potentials, we develop the Hamiltonian formalism in a manner that closely parallels previous analysis on ${\mathbb R}^3$. The volume measure on the physical configuration space of the gauge theory, the nonperturbative mass-gap and the leading term of the vacuum wave functional are...

Source: http://arxiv.org/abs/0807.2131v1

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55

Sep 21, 2013
09/13

by
Dimitra Karabali; V. P. Nair

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Following recent work on the quantum Hall effect on $S^4$, we solve the Landau problem on the complex projective spaces ${\bf C}P^k$ and discuss quantum Hall states for such spaces. Unlike the case of $S^4$, a finite spatial density can be obtained with a finite number of internal states for each particle. We treat the case of ${\bf C}P^2$ in some detail considering both Abelian and nonabelian background fields. The wavefunctions are obtained and incompressibility of the Hall states is shown....

Source: http://arxiv.org/abs/hep-th/0203264v1

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Sep 20, 2013
09/13

by
Ravit Efraty; V. P. Nair

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The generating functional for hard thermal loops in QCD is important in setting up a resummed perturbation theory, so that all terms of a given order in the coupling constant can be consistently taken into account. It is also the functional which leads to a gauge invariant description of Debye screening and plasma waves in the quark-gluon plasma. We have recently shown that this functional is closely related to the eikonal for a Chern-Simons gauge theory. In this paper, this relationship is...

Source: http://arxiv.org/abs/hep-th/9212068v1

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Sep 18, 2013
09/13

by
Dimitra Karabali; V. P. Nair

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The Hamiltonian formulation for a non-Abelian gauge theory in two spatial dimensions is carried out in terms of a gauge-invariant matrix parametrization of the fields. The Jacobian for the relevant transformation of variables is given in terms of the WZW-action for a hermitian matrix field. Some gauge-invariant eigenstates of the kinetic term of the Hamiltonian are given; these have zero charge and exhibit a mass gap.

Source: http://arxiv.org/abs/hep-th/9510157v3

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Sep 18, 2013
09/13

by
G. Alexanian; V. P. Nair

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We discuss how magnetic screening can be systematically included in a self-consistent way for Chromodynamics at high temperatures. The resulting gap equation, which gives the summation of self-energy iterations, is calculated to one-loop order and leads to a nonzero value for the magnetic mass.

Source: http://arxiv.org/abs/hep-ph/9504256v1

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Jul 22, 2013
07/13

by
Ioannis Giannakis; V. P. Nair

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We discuss symplectic structures for the chiral boson in (1+1) dimensions and the self-dual field in (4k+2) dimensions. Dimensional reduction of the six-dimensional field on a torus is also considered.

Source: http://arxiv.org/abs/hep-th/9702024v2

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Sep 18, 2013
09/13

by
Dimitra Karabali; V. P. Nair

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We give a brief review of quantum Hall effect in higher dimensions and its relation to fuzzy spaces. For a quantum Hall system, the lowest Landau level dynamics is given by a one-dimensional matrix action whose large $N$ limit produces an effective action describing the gauge interactions of a higher dimensional quantum Hall droplet. The bulk action is a Chern-Simons type term whose anomaly is exactly cancelled by the boundary action given in terms of a chiral, gauged Wess-Zumino-Witten theory...

Source: http://arxiv.org/abs/hep-th/0606161v1

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Sep 20, 2013
09/13

by
Dimitra Karabali; V. P. Nair

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In terms of a gauge-invariant matrix parametrization of the fields, we give an analysis of how the mass gap could arise in non-Abelian gauge theories in two spatial dimensions.

Source: http://arxiv.org/abs/hep-th/9610002v2

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Sep 21, 2013
09/13

by
D. Metaxas; V. P. Nair

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Yang-Mills theory at finite temperature is rewritten as a theory of plasmons which provides a Hamiltonian framework for perturbation theory with resummation of hard thermal loops.

Source: http://arxiv.org/abs/hep-ph/9905569v2

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Sep 22, 2013
09/13

by
Dimitra Karabali; V. P. Nair

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We consider quantum Hall droplets on complex projective spaces with a combination of abelian and nonabelian background magnetic fields. Carrying out an analysis similar to what was done for abelian backgrounds, we show that the effective action for the edge excitations is given by a chiral, gauged Wess-Zumino-Witten (WZW) theory generalized to higher dimensions.

Source: http://arxiv.org/abs/hep-th/0403111v2

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Sep 22, 2013
09/13

by
Dimitra Karabali; V. P. Nair

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An analysis of how the mass gap could arise in pure Yang-Mills theories in two spatial dimensions is given

Source: http://arxiv.org/abs/hep-th/9602155v1

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Sep 23, 2013
09/13

by
D. Minic; V. P. Nair

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We analyze the renormalization of wave functionals and energy eigenvalues in field theory. A discussion of the structure of the renormalization group equation for a general Hamiltonian system is also given.

Source: http://arxiv.org/abs/hep-th/9406074v1

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Jun 29, 2018
06/18

by
Dimitra Karabali; V. P. Nair

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The topological terms of the bulk effective action for the integer quantum Hall effect, capturing the dynamics of gauge and gravitational fluctuations, reveal a curiosity, namely, the Abelian potential for the magnetic field appears in a particular combination with the Abelian spin connection. This seems to hold for quantum Hall effect on complex projective spaces of arbitrary dimensions. An interpretation of this in terms of the algebra of symplectic transformations is given. This can also be...

Topics: High Energy Physics - Theory, Mesoscale and Nanoscale Physics, Mathematical Physics, Condensed...

Source: http://arxiv.org/abs/1606.06405

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Jun 27, 2018
06/18

by
Abhishek Agarwal; V. P. Nair

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A gauge-invariant reformulation of QCD in three spacetime dimensions is presented within a Hamiltonian formalism, extending previous work to include fermion fields in the adjoint and fundamental representations. A priori there are several ways to define the gauge-invariant versions of the fermions; a consistent prescription for choosing the fermionic variables is presented. The fermionic contribution to the volume element of the gauge orbit space and the gluonic mass-gap is computed exactly and...

Topic: High Energy Physics - Theory

Source: http://arxiv.org/abs/1504.07201

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Sep 23, 2013
09/13

by
Chanju Kim; V. P. Nair

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We present a functional derivation of recursion rules for scattering amplitudes in a non-Abelian gauge theory in a form valid to arbitrary loop order. The tree-level and one-loop recursion rules are explicitly displayed.

Source: http://arxiv.org/abs/hep-th/9608156v2

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Sep 18, 2013
09/13

by
Abhishek Agarwal; V. P. Nair

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A Hamiltonian formulation of Yang-Mills-Chern-Simons theories with $0\leq N\leq 4$ supersymmetry in terms of gauge-invariant variables is presented, generalizing earlier work on nonsupersymmetric gauge theories. Special attention is paid to the volume measure of integration (over the gauge orbit space of the fields) which occurs in the inner product for the wave functions and arguments relating it to the renormalization of the Chern-Simons level number and to mass-gaps in the spectrum of the...

Source: http://arxiv.org/abs/1201.6609v2

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Sep 22, 2013
09/13

by
V. P. Nair; Rashmi Ray

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We analyze the canonical structure of a continuum model of ferromagnets and clarify known difficulties in defining a momentum density. The moments of the momentum density corresponding to volume-preserving coordinate transformations can be defined, but a nonsingular definition of the other moments requires an enlargement of the phase space which illuminates a close relation to fluid mechanics. We also discuss the nontrivial connectivity of the phase space for two and three dimensions and show...

Source: http://arxiv.org/abs/hep-th/0309087v1

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Jul 19, 2013
07/13

by
V. P. Nair; Alexandr Yelnikov

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We point out that there is a nonabelian instability for a nonabelian plasma which does not allow both for a net nonzero color charge and the existence of field configurations which are coherent over a volume $v$ whose size is determined by the chemical potential. The basic process which leads to this result is the Schwinger decay of chromoelectric fields, for the case where the field arises from commutators of constant potentials, rather than as the curl of spacetime dependent potentials. In...

Source: http://arxiv.org/abs/1005.2582v1

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49

Sep 21, 2013
09/13

by
G. Alexanian; V. P. Nair

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The Thomas-Fermi screening of non-Abelian gauge fields by fermions or screening of gluon fields in quark matter is discussed. It is described by an effective mass term which is, as with hard thermal loops, related to the eikonal for a Chern-Simons theory and the Wess-Zumino-Witten action.

Source: http://arxiv.org/abs/hep-th/9609011v2

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Sep 18, 2013
09/13

by
Jian Dai; V. P. Nair

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We consider the general formulation of nonabelian fluid dynamics based on symmetry considerations. We point out that, quite generally, this admits solitonic excitations which are the color analog of skyrmions. Some general properties of the solitons are discussed.

Source: http://arxiv.org/abs/hep-ph/0605090v2