Related papers: Poisson Brackets for some Coulomb Branches
In this paper, we present an explicit construction of twisted traces for quantum Coulomb branches of conical theories. We develop an operator representation of the Coulomb branch algebra and use it to derive integral formulas for the…
The binary bracket of a Courant algebroid structure on $(E,\langle \cdot,\cdot \rangle)$ can be extended to a $n$-ary bracket on $\Gamma(E)$, yielding a multi-Courant algebroid. These $n$-ary brackets form a Poisson algebra and were…
We combine the projective geometry approach to Schroedinger equations on the circle and differential Galois theory with the theory of Poisson Lie groups to construct a natural Poisson structure on the space of wave functions (at the zero…
Poisson bracket relations for generators of canonical transformations are derived directly from the Galilei and Poincar\'e groups of changes of space-time coordinates. The method is simple but rigorous. The meaning of each step is clear…
As a generalization of the linear Poisson bracket on the dual space of a Lie algebra, we introduce certain non-linear Poisson brackets which are ``cocycle perturbations'' of the linear Poisson bracket. We show that these special Poisson…
We use brane configurations and SL(2,Z) symmetry of the type IIB string to construct mirror N=2 supersymmetric gauge theories in three dimensions. The mirror map exchanges Higgs and Coulomb branches, Fayet-Iliopoulos and mass parameters and…
We introduce the notion of a multiplicative Poisson $\lambda$-bracket, which plays the same role in the theory of Hamiltonian differential-difference equations as the usual Poisson $\lambda$-bracket plays in the theory of Hamiltonian PDE.…
The purpose of this paper is to discuss a number of issues that crop up in the computation of Poisson brackets in field theories. This is specially important for the canonical approaches to quantization and, in particular, for loop quantum…
The model of D4 open string with non-Grassmann spinning variables is considered. The non-linear gauge, which is invariant both Poincar\'e and scale transformations of the space-time, is used for subsequent studies. It is shown that the…
The technique of orthosymplectic quotient quiver subtraction is introduced. This involves subtraction of an orthosymplectic quotient quiver from a $3d\;\mathcal N=4$ orthosymplectic quiver gauge theory which has the effect of gauging…
In the context of averaging method, we describe a reconstruction of invariant connection-dependent Poisson structures from canonical actions of compact Lie groups on fibered phase spaces. Some symmetry properties of Wong's type equations…
The widely accepted approach to the foundation of quantum mechanics is that the Poisson bracket, governing the non-commutative algebra of operators, is taken as a postulate with no underlying physics. In this manuscript, it is shown that…
In this paper we study the problem of Hamiltonization of nonholonomic systems from a geometric point of view. We use gauge transformations by 2-forms (in the sense of Severa and Weinstein [29]) to construct different almost Poisson…
This paper investigates different Poisson structures that have been proposed to give a Hamiltonian formulation to evolution equations issued from fluid mechanics. Our aim is to explore the main brackets which have been proposed and to…
Coulomb branches of a set of $3d\ \mathcal{N}=4$ supersymmetric gauge theories are closures of nilpotent orbits of the algebra $\mathfrak{so}(n)$. From the point of view of string theory, these quantum field theories can be understood as…
The multiplicative structure of the trivial symplectic groupoid over $\mathbb R^d$ associated to the zero Poisson structure can be expressed in terms of a generating function. We address the problem of deforming such a generating function…
Relation between the Peierls and the Poisson bracket is derived in classical mechanics of time-dependent systems. Equal-time Peierls brackets are seen to be the same as the Poisson brackets in simple cases but a proof for a general…
We propose a construction of the Coulomb branch of a $3d\ {\mathcal N}=4$ gauge theory corresponding to a choice of a connected reductive group $G$ and a symplectic finite-dimensional reprsentation $\mathbf M$ of $G$, satisfying certain…
We consider the problem of constructing Poisson brackets on smooth manifolds $M$ with prescribed Casimir functions. If $M$ is of even dimension, we achieve our construction by considering a suitable almost symplectic structure on $M$,…
We derive first-order and second-order field equations from ambitwistor spaces as phase spaces of massless particles. In particular, the second-order field equations of Yang-Mills theory and general relativity are formulated in a unified…