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Related papers: Pohlmeyer reduction revisited

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By using the general framework of affine Gaudin models, we construct a new class of integrable sigma models. They are defined on a coset of the direct product of $N$ copies of a Lie group over some diagonal subgroup and they depend on…

High Energy Physics - Theory · Physics 2021-03-09 Gleb Arutyunov , Cristian Bassi , Sylvain Lacroix

The AdS/CFT correspondence relates the expectation value of Wilson loops in N=4 SYM to the area of minimal surfaces in AdS_5 In this paper we consider minimal area surfaces in generic Euclidean AdS_{n+1} using the Pohlmeyer reduction in a…

High Energy Physics - Theory · Physics 2018-03-14 Yifei He , Changyu Huang , Martin Kruczenski

The main result of this article provides a characterization of reductive homogeneous spaces equipped with some geometric structure (non necessarily pseudo-Riemannian) in terms of the existence of certain connection. The result generalizes…

Differential Geometry · Mathematics 2021-08-20 J. L. Carmona Jimenez , M. Castrillon Lopez

We construct the moduli spaces associated to the solutions of equations of motion (modulo gauge transformations) of the Poisson sigma model with target being an integrable Poisson manifold. The construction can be easily extended to a case…

Symplectic Geometry · Mathematics 2008-11-26 Francesco Bonechi , Maxim Zabzine

The main result of this paper is a convexity theorem for momentum mappings of certain hamiltonian actions of noncompact semisimple Lie groups. The image is required to fall within a certain open subset D of the (dual of the) Lie algebra,…

Symplectic Geometry · Mathematics 2007-05-23 Alan Weinstein

We introduce a phase space with spinorial momenta, corresponding to fermionic derivatives, for a 2d supersymmetric (1, 1) sigma model. We show that there is a generalisation of the covariant De Donder-Weyl Hamiltonian formulation on this…

High Energy Physics - Theory · Physics 2020-04-03 Ulf Lindström

We formulate Euler-Poincar\'e and Lagrange-Poincar\'e equations for systems with broken symmetry. We specialize the general theory to present explicit equations of motion for nematic systems, ranging from single nematic molecules to biaxial…

Chaotic Dynamics · Physics 2010-07-21 François Gay-Balmaz , Cesare Tronci

The motion of a rigid body in a quadratic potential is an important example of an integrable Hamiltonian system on a dual to a semidirect product Lie algebra so(n) x Symm(n). We give a Lagrangian derivation of the corresponding equations of…

solv-int · Physics 2007-05-23 Yuri B. Suris

In Einstein's gravitational theory, the spacetime is Riemannian, that is, it has vanishing torsion and vanishing nonmetricity (covariant derivative of the metric). In the gauging of the general affine group ${A}(4,R)$ and of its subgroup…

General Relativity and Quantum Cosmology · Physics 2008-11-26 F. W. Hehl , J. D. McCrea , E. W. Mielke , Y. Ne'eman

For a discrete mechanical system on a Lie group $G$ determined by a (reduced) Lagrangian $\ell$ we define a Poisson structure via the pull-back of the Lie-Poisson structure on the dual of the Lie algebra ${\mathfrak g}^*$ by the…

Numerical Analysis · Mathematics 2025-10-20 Jerrold E. Marsden , Sergey Pekarsky , Steve Shkoller

Anti-Hermitian mass terms are considered, in addition to Hermitian ones, for PT-symmetric complex-scalar and fermionic field theories. In both cases, the Lagrangian can be written in a manifestly symmetric form in terms of the PT-conjugate…

High Energy Physics - Theory · Physics 2017-10-02 Jean Alexandre , Peter Millington , Dries Seynaeve

Various classical solutions to lower dimensional IKKT-like Lorentzian matrix models are examined in their commutative limit. Poisson manifolds emerge in this limit, and their associated induced and effective metrics are computed. Signature…

High Energy Physics - Theory · Physics 2018-10-22 A. Stern , Chuang Xu

For Hamiltonian field theories on polysymplectic manifolds with a symmetry group action and a momentum map, we explore the redundancy in a set of necessary conditions that has appeared in the literature, for a generalized version of the…

Mathematical Physics · Physics 2023-08-01 Eduardo García-Toraño Andrés , Tom Mestdag

In this article, we analyze the Pontryagin model adopting different geometric-covariant approaches. In particular, we focus on the manner in which boundary conditions must be imposed on the background manifold in order to reproduce an…

General Relativity and Quantum Cosmology · Physics 2025-02-21 Jasel Berra-Montiel , Iñaki de Santos , Alberto Molgado

This note gives an overview on the construction of symplectic groupoids as reduced phase spaces of Poisson sigma models and its generalization in the infinite dimensional setting (before reduction).

Symplectic Geometry · Mathematics 2020-05-19 Ivan Contreras , Alberto S. Cattaneo

This paper is a continuation and elaboration of our work quant-ph/0206057 (Nucl. Phys. B, 1968, 7, 79) where some approach to the variable-mass problem were proposed. Here we have found a concret realization of irreducible representations…

Quantum Physics · Physics 2007-05-23 Wilhelm I. Fushchych , Ivan Yu. Krivsky

A condition of geometric modular action is proposed as a selection principle for physically interesting states on general space-times. This condition is naturally associated with transformation groups of partially ordered sets and provides…

Mathematical Physics · Physics 2007-05-23 Detlev Buchholz , Olaf Dreyer , Martin Florig , Stephen J. Summers

A completely Lorentz-invariant Bohmian model has been proposed recently for the case of a system of non-interacting spinless particles, obeying Klein-Gordon equations. It is based on a multi-temporal formalism and on the idea of treating…

Quantum Physics · Physics 2014-11-21 Sergio Hernandez-Zapata , Ernesto Hernandez-Zapata

In this paper, we investigate the reduction process of a contact Lagrangian system whose Lagrangian is invariant under a group of symmetries. We give explicit coordinate expressions of the resulting reduced differential equations, the…

Mathematical Physics · Physics 2024-08-14 Alexandre Anahory Simoes , Leonardo Colombo , Manuel de Leon , Modesto Salgado , Silvia Souto

Let U be a real form of a complex semisimple Lie group, and tau, sigma, a pair of commuting involutions on U. This data corresponds to a reflective submanifold of a symmetric space, U/K. We define an associated integrable system, and…

Differential Geometry · Mathematics 2007-10-06 David Brander