Four-Dimensional Yang-Mills Theory in Local Gauge Invariant Variables

Lunev, F. A.

doi:10.1142/s0217732394002148

Cited by 24 publications

(20 citation statements)

References 5 publications

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“…At this point there seems to be nothing special in this choice, but we will see that according to the arguments of Ref. [18] and [39], the barrier at r = 1/C will only absolutely confine a particle if λ ≥ g while for λ < g there will be some probability for the test particle to tunnel through the barrier. Combining all the preceding assumptions we find…”

Section: Motion Of Tests Particles In Schwarzschild-like Potentialmentioning

confidence: 89%

“…(9). The Schwarzschild-like solution, with its singular spherical surface, has been speculated to have some connection with the confinement phenomenon for quarks [15] [17] [18] [20] [21]. By studying the motion of a test particle which moves in the potentials given by the minus sign solution in Eq.…”

Section: A Solutions With Spherical Singularitiesmentioning

confidence: 99%

“…First we will take our test particle to be a scalar particle as in Ref. [18] [20]. One reason for making this choice is to illustrate the spin from isospin [38] effect that occurs with these solutions.…”

Section: Motion Of Tests Particles In Schwarzschild-like Potentialmentioning

confidence: 99%

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General relativistic analogue solutions for the Yang-Mills theory

Singleton

1998

Theor Math Phys

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Finding solutions to non-linear field theories, such as Yang-Mills theories or general relativity, is usually difficult. The field equations of Yang-Mills theories and general relativity are known to share some mathematical similarities, and this connection can be used to find solutions to one theory using known solutions of the other theory. For example, the Schwarzschild solution of general relativity can be shown to have a mathematically similar counterpart in Yang-Mills theory. In this article we will discuss several solutions to the Yang-Mills equations which can be found using this connection between general relativity and Yang-Mills theory. Some comments about the possible physical meaning of these solutions will be discussed. In particular it will be argued that some of these analog solutions of Yang-Mills theory may have some connection with the confinement phenomenon. To this end we will briefly look at the motion of test particles moving in the background potential of the Schwarzschild analog solution. * For the memorial issue of Theo. Math. Phys. in memory of F.A. Lunev

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Section: Motion Of Tests Particles In Schwarzschild-like Potentialmentioning

confidence: 89%

Section: A Solutions With Spherical Singularitiesmentioning

confidence: 99%

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General relativistic analogue solutions for the Yang-Mills theory

Singleton

1998

Theor Math Phys

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“…This idea first appeared in [3] [4], and has recently gained new momentum with the work in [5] [6] [7] [8] [9] [10] [11] [12] [13], and references therein. In [8], one constructs a change of variables that will allow us to replace the coordinates A a i by new coordinates u a i that have the property of transforming covariantly under the gauge group, as opposed to as a gauge connection.…”

Section: Introductionmentioning

confidence: 99%

Supersymmetric Yang-Mills theory and Riemannian Geometry

Schiappa¹

1998

Nuclear Physics B

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We introduce new local gauge invariant variables for N = 1 supersymmetric Yang-Mills theory, explicitly parameterizing the physical Hilbert space of the theory. We show that these gauge invariant variables have a geometrical interpretation, and can be constructed such that the emergent geometry is that of N = 1 supergravity: a Riemannian geometry with vector-spinor generated torsion. Full geometrization of supersymmetric Yang-Mills theory is carried out, and geometry independent divergences associated to the inversion of a differential operator with zero modes -that were encountered in the non-supersymmetric case -do not arise in this situation.

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“…A similar approach was tried out for 3+1 dimensions in [7], but the theory turned out to be quite complicated. Here we do a manifestly gauge invariant formulation of 3+1 dimensional Yang-Mills theory using Ashtekar like variables.…”

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confidence: 99%

Reformulating Yang-Mills theory in terms of local gauge invariant variables

Majumdar

Sharatchandra

2001

Nuclear Physics B - Proceedings Supplements

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An explicit canonical transformation is constructed to relate the physical subspace of Yang-Mills theory to the phase space of the ADM variables of general relativity. This maps 3+1 dimensional Yang-Mills theory to local evolution of metrics on 3 manifolds.A long standing problem in Yang-Mills theories is whether its dynamics can be written in terms of gauge invariant variables. This is very important for our understanding of confinement in QCD. One option is to write the theory as dynamics of Wilson loops. However these are nonlocal variables and their evolution equations are difficult to handle. Another approach has been to use composite variables constructed out of the non-Abelian electric [1][2][3] or magnetic fields [4,5].In three dimensions, gauge invariant formulation of Yang-Mills theory was carried out in close analogy to gravity in [6]. A similar approach was tried out for 3+1 dimensions in [7], but the theory turned out to be quite complicated. Here we do a manifestly gauge invariant formulation of 3+1 dimensional Yang-Mills theory using Ashtekar like variables. This formulation is also closely related to ADM formulation of gravity. We identify the physical variables and the Gauss law and then rewrite the Hamiltonian in terms of the new variables.Starting with the usual Euclidean partition function, we introduce an auxiliary field E ia and integrate over A a 0 to obtain(1) * Present address:

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Four-Dimensional Yang-Mills Theory in Local Gauge Invariant Variables

Cited by 24 publications

References 5 publications

General relativistic analogue solutions for the Yang-Mills theory

General relativistic analogue solutions for the Yang-Mills theory

Supersymmetric Yang-Mills theory and Riemannian Geometry

Reformulating Yang-Mills theory in terms of local gauge invariant variables

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