相关论文: Order Parameters, Free Fermions, and Conservation …

A connection between the gauge fixed dynamics of protected operators in superconformal Yang-Mills theory in four dimensions and Calogero systems is established. This connection generalizes the free Fermion description of the chiral primary…

We give the generalization of a recent variational formulation for nonconservative classical mechanics, for fermionic and sypersymmetric systems. Both cases require slightly modified boundary conditions. The supersymmetric version is given…

${\rm SU}(2|1)$ supersymmetric multi-particle quantum mechanics with additional semi-dynamical spin degrees of freedom is considered. In particular, we provide an $\mathcal{N}{=}\,4$ supersymmetrization of the quantum ${\rm U}(2)$ spin…

A natural N=1 supersymmetric extension of the Euler top, which introduces exactly one fermionic counterpart for each bosonic degree of freedom, is considered. The equations of motion, their symmetries and integrals of motion are given. It…

We consider elliptic systems of order $2m$ in dimension $2m$ which are generalizations of extrinsic and intrinsic polyharmonic maps. We show the existence of a conservation law for these systems by using a small perturbation of Uhlenbeck's…

These lectures study two correspondences between gauge theories and integrable many-body systems. The first arises from infinite-dimensional Hamiltonian reduction and relates gauge-theoretic dynamics directly to Calogero--Moser-type systems…

The relation between SU(2) Yang-Mills mechanics, originated from the 4-dimensional SU(2) Yang-Mills theory under the supposition of spatial homogeneity of the gauge fields, and the Euler-Calogero-Moser model is discussed in the framework of…

A constraint correlation dynamics up to 4-point Green functions is proposed for SU(N) gauge theories which reduces the N-body quantum field problem to the two-body level. The resulting set of nonlinear coupled equations fulfills all…

The connection between symmetries and conservation laws as made by Noether's theorem is extended to the context of causal variational principles and causal fermion systems. Different notions of continuous symmetries are introduced. It is…

We discuss the behavior of two non-supersymmetric chiral SU(N) gauge theories, involving fermions in the symmetric and antisymmetric two-index tensor representations respectively. In addition to global anomaly matching, we employ a recently…

In this paper we will present Lagrangian and Hamiltonian $k$-symplectic formalisms, we will recall the notions of symmetry and conservation law and we will define the notion of pseudosymmetry as a natural extension of symmetry. Using…

We explicitly construct a supersymmetric $so(n)$ spin-Calogero model with an arbitrary even number $\cal N$ of supersymmetries. It features $\frac{1}{2}{\cal N}n(n{+}1)$ rather than ${\cal N}n$ fermionic coordinates and a very simple…

We explore aspects of the phase structure of SU(2) and SU(3) lattice gauge theories at strong coupling with many flavours $N_f$ of Wilson fermions in the fundamental representation. The pseudoscalar meson mass as a function of hopping…

We study N=2 supersymmetric U(1) gauge theory in the noncommutative harmonic superspace with nonanticommutative fermionic coordinates. We examine the gauge transformation which preserves the Wess-Zumino gauge by harmonic expansions of…

Noether's Theorem yields conservation laws for a Lagrangian with a variational symmetry group. The explicit formulae for the laws are well known and the symmetry group is known to act on the linear space generated by the conservation laws.…

We first review the construction of the supersymmetric extension of the (quantum) Calogero-Moser-Sutherland (CMS) models. We stress the remarkable fact that this extension is completely captured by the insertion of a fermionic exchange…

We study dynanics of $SU(N-4)$ gauge theories with fermions in rank-2 symmetric tensor and $N$ anti-fundamental representations, by perturbing supersymmetric theories with anomaly-mediated supersymmetry breaking. We find the $SU(N)\times…

A phenomenon of classical quantization is discussed. This is revealed in the class of pseudoclassical gauge systems with nonlinear nilpotent constraints containing some free parameters. Variation of parameters does not change local (gauge)…

After a proper definition of the dimerization order parameter for a spin-$S$ system, I show that this order parameter in the $SU(n)$ ($n=2S+1$) antiferromagnetic chains (or equivalently the $SU(2)$ spin-$S$ chains with Hamiltonians which…

We present basics of the gauged superfield approach to constructing N-superconformal multi-particle Calogero-type systems developed in arXiv:0812.4276, arXiv:0905.4951 and arXiv:0912.3508. This approach is illustrated by the multi-particle…