ON THE CANONICAL FORMULATION OF SUPERSYMMETRIC YANG-MILLS THEORIES

1987 ◽  
Vol 02 (07) ◽  
pp. 487-497 ◽  
Author(s):  
ROSANNE DI STEFANO ◽  
MAXIMILIAN KREUZER ◽  
ANTON REBHAN
Keyword(s):  
Phase Space ◽  
Gauge Invariant ◽  
Yang Mills ◽  
Canonical Formulation ◽  
Higher Dimensional ◽  
Supersymmetric Theories

We treat supersymmetric Yang-Mills theories in the canonical formulation. By a gauge invariant and Lorentz covariant ansatz for the canonical supersymmetry generators we rederive that supersymmetric theories based on spin 1 and spin [Formula: see text] exist only in dimensions 4, 6, and 10. Moreover we find that the algebra of these supersymmetry generators closes on the phase space without the need of auxiliary fields. This holds true also for the higher-dimensional theories where it is not possible to find auxiliary fields making the algebra close off-shell on the Lagrangian level.

scholarly journals POISSON ALGEBRA OF WILSON LOOPS IN FOUR-DIMENSIONAL YANG-MILLS THEORY

1995 ◽  
Vol 10 (17) ◽  
pp. 2479-2505 ◽  
Author(s):  
S.G. RAJEEV ◽  
O.T. TURGUT
Keyword(s):  
Phase Space ◽  
Gauge Theories ◽  
Poisson Algebra ◽  
Coadjoint Orbit ◽  
Quadratic Algebra ◽  
Wilson Loops ◽  
Poisson Brackets ◽  
Canonical Structure ◽  
Gauge Invariant ◽  
Yang Mills

We formulate the canonical structure of Yang-Mills theory in terms of Poisson brackets of gauge-invariant observables analogous to Wilson loops. This algebra is nontrivial and tractable in a light cone formulation. For U (N) gauge theories the result is a Lie algebra while for SU (N) gauge theories it is a quadratic algebra. We also study the identities satisfied by the gauge-invariant observables. We suggest that the phase space of a Yang-Mills theory is a coadjoint orbit of our Poisson algebra; some partial results in this direction are obtained.

scholarly journals 2 + 1 ABELIAN "GAUGE THEORY" INSPIRED BY IDEAL HYDRODYNAMICS

2006 ◽  
Vol 21 (18) ◽  
pp. 3771-3808
Author(s):  
GOVIND S. KRISHNASWAMI
Keyword(s):  
Phase Space ◽  
Magnetic Energy ◽  
Poisson Algebra ◽  
Integrable Model ◽  
Coadjoint Orbit ◽  
Diffeomorphism Group ◽  
Noncommutative Space ◽  
Abelian Gauge ◽  
Gauge Invariant ◽  
Yang Mills

We study a possibly integrable model of Abelian gauge fields on a two-dimensional surface M, with volume form μ. It has the same phase-space as ideal hydrodynamics, a coadjoint orbit of the volume-preserving diffeomorphism group of M. Gauge field Poisson brackets differ from the Heisenberg algebra, but are reminiscent of Yang–Mills theory on a null surface. Enstrophy invariants are Casimirs of the Poisson algebra of gauge invariant observables. Some symplectic leaves of the Poisson manifold are identified. The Hamiltonian is a magnetic energy, similar to that of electrodynamics, and depends on a metric whose volume element is not a multiple of μ. The magnetic field evolves by a quadratically nonlinear "Euler" equation, which may also be regarded as describing geodesic flow on SDiff (M, μ). Static solutions are obtained. For uniform μ, an infinite sequence of local conserved charges beginning with the Hamiltonian are found. The charges are shown to be in involution, suggesting integrability. Besides being a theory of a novel kind of ideal flow, this is a toy-model for Yang–Mills theory and matrix field theories, whose gauge-invariant phase-space is conjectured to be a coadjoint orbit of the diffeomorphism group of a noncommutative space.

scholarly journals Study of the gauge invariant, nonlocal mass operatorTr∫d4xFμν(D2)−1Fμνin Yang-Mills theories

2005 ◽  
Vol 72 (10) ◽  
Author(s):  
M. A. L. Capri ◽  
D. Dudal ◽  
J. A. Gracey ◽  
V. E. R. Lemes ◽  
R. F. Sobreiro ◽  
...  
Keyword(s):  
Gauge Invariant ◽  
Yang Mills

scholarly journals A MANIFESTLY GAUGE INVARIANT AND UNIVERSAL CALCULUS FORSU(N) YANG–MILLS

2006 ◽  
Vol 21 (23n24) ◽  
pp. 4627-4761 ◽  
Author(s):  
OLIVER J. ROSTEN
Keyword(s):  
Perturbation Theory ◽  
Renormalization Group ◽  
Explicit Dependence ◽  
Gauge Invariant ◽  
Yang Mills ◽  
Group A ◽  
Β Function ◽  
Exact Renormalization Group

Within the framework of the Exact Renormalization Group, a manifestly gauge invariant calculus is constructed for SU (N) Yang–Mills. The methodology is comprehensively illustrated with a proof, to all orders in perturbation theory, that the β function has no explicit dependence on either the seed action or details of the covariantization of the cutoff. The cancellation of these nonuniversal contributions is done in an entirely diagrammatic fashion.

Gauge-Invariant Characterization of Yang–Mills–Higgs Equations

2006 ◽  
Vol 8 (1) ◽  
pp. 203-217 ◽  
Author(s):  
Marco Castrillón López ◽  
Jaime Muñoz Masqué
Keyword(s):  
Gauge Invariant ◽  
Yang Mills ◽  
Invariant Characterization

scholarly journals Gauge-invariant quantum circuits for U (1) and Yang-Mills lattice gauge theories

2021 ◽  
Vol 3 (4) ◽  
Author(s):  
Giulia Mazzola ◽  
Simon V. Mathis ◽  
Guglielmo Mazzola ◽  
Ivano Tavernelli
Keyword(s):  
Gauge Theories ◽  
Quantum Circuits ◽  
Gauge Invariant ◽  
Yang Mills ◽  
Lattice Gauge ◽  
Lattice Gauge Theories ◽  
Invariant Quantum

Quantum statistical physics: Functional integration formalism

2021 ◽  
pp. 64-89
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Phase Space ◽  
Integral Representation ◽  
Density Matrix ◽  
Thermal Equilibrium ◽  
Degrees Of Freedom ◽  
Functional Integral ◽  
Complex Variables ◽  
Path Integral Representation ◽  
Canonical Formulation ◽  
Grand Canonical

The functional integral representation of the density matrix at thermal equilibrium in non-relativistic quantum mechanics (QM) with many degrees of freedom, in the grand canonical formulation is introduced. In QM, Hamiltonians H(p,q) can be also expressed in terms of creation and annihilation operators, a method adapted to the study of perturbed harmonic oscillators. In the holomorphic formalism, quantum operators act by multiplication and differentiation on a vector space of analytic functions. Alternatively, they can also be represented by kernels, functions of complex variables that correspond in the classical limit to a complex parametrization of phase space. The formalism is adapted to the description of many-body boson systems. To this formalism corresponds a path integral representation of the density matrix at thermal equilibrium, where paths belong to complex spaces, instead of the more usual position–momentum phase space. A parallel formalism can be set up to describe systems with many fermion degrees of freedom, with Grassmann variables replacing complex variables. Both formalisms can be generalized to quantum gases of Bose and Fermi particles in the grand canonical formulation. Field integral representations of the corresponding quantum partition functions are derived.

scholarly journals xAct Implementation of the Theory of Cosmological Perturbation in Bianchi I Spacetimes

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 290 ◽  
Author(s):  
Ivan Agullo ◽  
Javier Olmedo ◽  
Vijayakumar Sreenath
Keyword(s):  
Phase Space ◽  
Degrees Of Freedom ◽  
Computational Algorithm ◽  
Tensor Algebra ◽  
Cosmological Perturbation ◽  
Gauge Invariant ◽  
Bianchi I ◽  
Space Formulation

This paper presents a computational algorithm to derive the theory of linear gauge invariant perturbations on anisotropic cosmological spacetimes of the Bianchi I type. Our code is based on the tensor algebra packages xTensor and xPert, within the computational infrastructure of xAct written in Mathematica. The algorithm is based on a Hamiltonian, or phase space formulation, and it provides an efficient and transparent way of isolating the gauge invariant degrees of freedom in the perturbation fields and to obtain the Hamiltonian generating their dynamics. The restriction to Friedmann–Lemaître–Robertson–Walker spacetimes is straightforward.

The interaction of molecular multipoles with the electromagnetic field in the canonical formulation of non-covariant quantum electrodynamics

1970 ◽  
Vol 319 (1539) ◽  
pp. 549-563 ◽  
Keyword(s):  
Electromagnetic Field ◽  
Physical Interpretation ◽  
Quantum Electrodynamics ◽  
Unitary Transformation ◽  
Canonical Quantization ◽  
Multipole Moments ◽  
Gauge Invariant ◽  
Covariant Quantum ◽  
Canonical Formulation ◽  
Gauge Conditions

The procedure devised by Dirac for the canonical quantization of systems described by degenerate lagrangians is used to construct the hamiltonian for molecules interacting with the electromagnetic field. The hamiltonian obtained is expressed in terms of the gauge invariant field strengths and the electric and magnetic multipole moments of the molecules. The Coulomb gauge is introduced but other gauge conditions could be used. Finally, a physical interpretation of the unitary transformation that may be used to generate the multipole hamiltonian is given.

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