scholarly journals COVARIANT PHASE SPACE FORMULATIONS OF SUPERPARTICLES AND SUPERSYMMETRIC WZW MODELS

1994 ◽  
Vol 09 (27) ◽  
pp. 2469-2480
Author(s):  
G. AU ◽  
B. SPENCE
Keyword(s):  
Phase Space ◽  
Poisson Brackets ◽  
Group Manifold ◽  
Current Algebras

We present new covariant phase space formulations of superparticles moving on a group manifold, deriving the fundamental Poisson brackets and current algebras. We show how these formulations naturally generalize to the supersymmetric Wess-Zumino-Witten models.

scholarly journals On the Dirac eigenvalues as observables of the on-shell N = 2D = 4 Euclidean supergravity

Open Physics ◽  
2008 ◽  
Vol 6 (4) ◽  
Author(s):  
Ion Vancea
Keyword(s):  
Phase Space ◽  
Equations Of Motion ◽  
Poisson Brackets ◽  
Gauge Transformations

AbstractWe generalize previous works on the Dirac eigenvalues as dynamical variables of Euclidean gravity and N =1 D = 4 supergravity to on-shell N = 2 D = 4 Euclidean supergravity. The covariant phase space of the theory is defined as the space of the solutions of the equations of motion modulo the on-shell gauge transformations. In this space we define the Poisson brackets and compute their value for the Dirac eigenvalues.

scholarly journals DIRAC BRACKETS FROM MAGNETIC BACKGROUNDS

2007 ◽  
Vol 04 (04) ◽  
pp. 523-532 ◽  
Author(s):  
JOSÉ M. ISIDRO
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Phase Space ◽  
Symplectic Form ◽  
Weak Magnetic Field ◽  
Complex Geometry ◽  
Poisson Brackets ◽  
Generalized Complex ◽  
Dirac Brackets ◽  
Classical Phase Space

In symplectic mechanics, the magnetic term describing the interaction between a charged particle and an external magnetic field has to be introduced by hand. On the contrary, in generalized complex geometry, such magnetic terms in the symplectic form arise naturally by means of B-transformations. Here we prove that, regarding classical phase space as a generalized complex manifold, the transformation law for the symplectic form under the action of a weak magnetic field gives rise to Dirac's prescription for Poisson brackets in the presence of constraints.

scholarly journals Poisson-Lie T-duality of WZW model via current algebra deformation

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Francesco Bascone ◽  
Franco Pezzella ◽  
Patrizia Vitale
Keyword(s):  
Phase Space ◽  
Configuration Space ◽  
Current Algebra ◽  
Degrees Of Freedom ◽  
Target Space ◽  
Moody Algebra ◽  
Hamiltonian Description ◽  
Direct Sum ◽  
Group Manifold ◽  
Two Parameter

Abstract Poisson-Lie T-duality of the Wess-Zumino-Witten (WZW) model having the group manifold of SU(2) as target space is investigated. The whole construction relies on the deformation of the affine current algebra of the model, the semi-direct sum $$ \mathfrak{su}(2)\left(\mathrm{\mathbb{R}}\right)\overset{\cdot }{\oplus}\mathfrak{a} $$ su 2 ℝ ⊕ ⋅ a , to the fully semisimple Kac-Moody algebra $$ \mathfrak{sl}\left(2,\mathrm{\mathbb{C}}\right)\left(\mathrm{\mathbb{R}}\right) $$ sl 2 ℂ ℝ . A two-parameter family of models with SL(2, ℂ) as target phase space is obtained so that Poisson-Lie T-duality is realised as an O(3, 3) rotation in the phase space. The dual family shares the same phase space but its configuration space is SB(2, ℂ), the Poisson-Lie dual of the group SU(2). A parent action with doubled degrees of freedom on SL(2, ℂ) is defined, together with its Hamiltonian description.

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.

Size of the early universe and GUP

2019 ◽  
Vol 34 (22) ◽  
pp. 1950178
Author(s):  
Ljubisa Nesic ◽  
Darko Radovancevic
Keyword(s):  
Phase Space ◽  
Cosmological Model ◽  
Early Universe ◽  
Generalized Uncertainty Principle ◽  
Poisson Algebra ◽  
Poisson Brackets ◽  
Energy Term ◽  
Classical Version ◽  
One Dimensional ◽  
Potential Energy Term

This paper presents the effects of the Generalized Uncertainty Principle (GUP), i.e. its classical version expressed through the deformed Poisson brackets in the phase–space of a one-dimensional minisuperspace Friedmann cosmological model with a mixture of non-interacting dust and radiation. It is shown, in the case of this model, that starting from the specific representation of the deformed Poisson algebra, which corresponds to the change of the potential energy term of the oscillator, the size of the early universe can be related to its inflationary GUP expansion.

QUANTIZED SUPERTWISTORS, HIGHER SPIN SUPERALGEBRAS AND SUPERSINGLETONS

1990 ◽  
Vol 05 (06) ◽  
pp. 439-451 ◽  
Author(s):  
WOLFGANG HEIDENREICH ◽  
JERZY LUKIERSKI
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Poisson Brackets ◽  
Canonical Coordinates ◽  
Higher Spin

We introduce supertwistors in D=3 and D=4 as describing the canonical coordinates in two models of fundamental phase space with respectively OSP(N; 4) and u(2, 2; N) invariant fundamental Poisson brackets. The infinite superalgebra of normally ordered polynomials in quantized supertwistor variables can be identified with recently proposed D=3 and D=4 higher spin superalgebras. We consider the supersingleton representations of OSP(N, 4), and OSP(2N, 8) as describing fundamental realizations of D=3 and D=4 supertwistor quantum mechanics.

scholarly journals FINITE ORDER BFFT METHOD

2003 ◽  
Vol 18 (30) ◽  
pp. 5613-5625 ◽  
Author(s):  
M. MONEMZADEH ◽  
A. SHIRZAD
Keyword(s):  
Phase Space ◽  
Finite Order ◽  
Infinite Series ◽  
Poisson Brackets ◽  
Extended Phase Space ◽  
Extended Phase ◽  
The Matrix ◽  
Chiral Bosons ◽  
Physical Quantities

We propose a method in the context of BFFT approach that leads to truncation of the infinite series regarded as constraints in the extended phase space, as well as other physical quantities (such as Hamiltonian). This has been done for cases where the matrix of Poisson brackets among the constraints is symplectic or constant. The method is applied to the Proca model, single self dual chiral bosons and chiral Schwinger models as examples.

scholarly journals A GENERALIZATION OF THE JORDAN-SCHWINGER MAP: THE CLASSICAL VERSION AND ITS q DEFORMATION

1994 ◽  
Vol 09 (31) ◽  
pp. 5541-5561 ◽  
Author(s):  
V.I. MAN’KO ◽  
G. MARMO ◽  
P. VITALE ◽  
F. ZACCARIA
Keyword(s):  
Phase Space ◽  
Lie Algebras ◽  
Three Dimensional ◽  
Poisson Brackets ◽  
Classical Version ◽  
Deformed Algebras

For all three-dimensional Lie algebras the construction of generators in terms of functions on four-dimensional real phase space is given with a realization of the Lie product in terms of Poisson brackets. This is the classical Jordan-Schwinger map, which is also given for the deformed algebras [Formula: see text], ℰq(2) and ℋq(1). The algebra [Formula: see text] is discussed in the same context.

GAUGE INVARIANCE AND CONSTRAINTS

1989 ◽  
Vol 04 (13) ◽  
pp. 3211-3228 ◽  
Author(s):  
P.N. PYATOV ◽  
A.V. RAZUMOV
Keyword(s):  
Phase Space ◽  
Wide Class ◽  
Gauge Invariance ◽  
Lagrangian Systems ◽  
Poisson Brackets ◽  
Hamiltonian Description ◽  
Gauge Invariant ◽  
Primary Constraint ◽  
Extension Of Functions ◽  
Constraint Surface

It is shown that in the Hamiltonian description of a wide class of gauge invariant Lagrangian systems there arise only primary and secondary constraints and they are all first class. The explicit expressions for the Poisson brackets of the Hamiltonian and the constraints are obtained by introducing the so-called “standard” extension of functions originally defined on the primary constraint surface to the whole phase space.

scholarly journals CHIRAL QUANTIZATION ON A GROUP MANIFOLD

1994 ◽  
Vol 09 (23) ◽  
pp. 4149-4168 ◽  
Author(s):  
ZBIGNIEW HASIEWICZ ◽  
PRZEMYSLAW SIEMION ◽  
WALTER TROOST
Keyword(s):  
Hilbert Space ◽  
Phase Space ◽  
Geometric Quantization ◽  
Quadratic Relation ◽  
Classical Analysis ◽  
Quantum Sphere ◽  
Exchange Algebra ◽  
Group Manifold ◽  
Left And Right ◽  
The One

The phase space of a particle on a group manifold can be split into left and right sectors, in close analogy with the chiral sectors in Wess–Zumino–Witten models. We perform a classical analysis of the sectors, and geometric quantization in the case of SU(2). The quadratic relation, classically identifying SU(2) as the sphere S3, is replaced quantum-mechanically by a similar condition on noncommutative operators ("quantum sphere"). The resulting quantum exchange algebra of the chiral group variables is quartic, not quadratic. The fusion of the sectors leads to a Hilbert space that is subtly different from the one obtained through a more direct (unsplit) quantization.

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