Related papers: Particle Mechanics Models with W-symmetries

A relation between an $Sp(2M)$ gauge particle model and the zero-curvature condition in a two-dimensional gauge theory is presented. For the $Sp(4)$ case we construct finite \W-transformations.

We prove that particle models whose action is given by the integrated $n$-th curvature function over the world line possess $n+1$ gauge invariances. A geometrical characterization of these symmetries is obtained via Frenet equations by…

In particle physics, the fundamental forces are subject to symmetries called gauge invariance. It is a redundancy in the mathematical description of any physical system. In this article I will demonstrate that the transformer architecture…

We consider a one-dimensional Osp($N|2M$) pseudoparticle mechanical model which may be written as a phase space gauge theory. We show how the pseudoparticle model naturally encodes and explains the two-dimensional zero curvature approach to…

We show how to obtain all covariant field equations for massless particles of arbitrary integer, or half-integer, helicity in four dimensions from the quantization of the rigid particle, whose action is given by the integrated extrinsic…

We prove that $\W_3$ is the gauge symmetry of the scale-invariant rigid particle, whose action is given by the integrated extrinsic curvature of its world line. This is achieved by showing that its equations of motion can be written in…

Using connection with quantum field theory, the infinitesimal covariant abelian gauge transformation laws of relativistic two-particle constraint theory wave functions and potentials are established and weak invariance of the corresponding…

We find the Lie point symmetries for non-relativistic two-dimensional charged particle motion. These symmetries comprise a quasi-invariance transformation, a time-dependent rotation, a time-dependent spatial translation and a dilation. The…

In these lectures, I discuss the role of symmetries in particle physics. I begin by discussing global symmetries and show that they can be realized differently in nature, depending on whether or not the vacuum state is left invariant by the…

We generalize the conformally invariant topological quantum mechanics of a particle propagating on a punctured plane by introducing a potential that breaks both the rotational and the conformal invariance down to a ${\bf Z}_2$…

We analyze the particle spectrum of a second-order (in derivatives) theory based on a rank-2 tensor field with both symmetric and antisymmetric components. By demanding the existence of a propagating massless spin-2 particle and invariance…

We show that non-relativistic Quantum Mechanics can be faithfully represented in terms of a classical diffusion process endowed with a gauge symmetry of group Z_4. The representation is based on a quantization condition for the realized…

In this article we provide a manifestly gauge-invariant approach to charged particles. It involves (1) Green functions of gauge-invariant operators and (2) Feynman rules which do not depend on any kind of gauge-fixing condition. First, we…

We show that Wigner's infinite spin particle classically is described by a reparametrization invariant higher order geometrical Lagrangian. The model exhibit unconventional features like tachyonic behaviour and momenta proportional to…

We review the current status of the long-term programme of numerical investigation of $Sp(2N)$ gauge theories with and without fermionic matter content. We start by introducing the phenomenological as well as theoretical motivations for…

The Gauge/Bethe correspondence relates Omega-deformed N=2 supersymmetric gauge theories to some quantum integrable models, in simple cases the integrable models can be treated as solvable quantum mechanics models. For SU(2) gauge theory…

We describe the deformed Poincare-conformal symmetries implying the covariance of the noncommutative space obeying Snyder's algebra. Relativistic particle models invariant under these deformed symmetries are presented. A gauge…

A gauge invariant mathematical formalism based on deformation quantization is outlined to model an $\mathcal{N}=2$ supersymmetric system of a spin $1/2$ charged particle placed in a nocommutative plane under the influence of a vertical…

In this paper we investigate electromagnetic interactions for massive spin 2 particles in (A)dS space at linear approximation using gauge invariant description for such massive particles. We follow bottom-up approach, i.e. we begin with the…

The two-by-two Sp(2) matrix has three parameters with unit determinant. Yet, there are no established procedures for diagonalizing this matrix. It is shown that this matrix can be written as a similarity transformation of the two-by-two…