相关论文: Structure of nonlinear gauge transformations

Electromagnetism contains an infinite dimensional symmetry group of large gauge transformations. This gives rise to an infinite number of conserved quantities called "soft charges" via Noether's theorem. When charged particles scatter, the…

Given $\mathbf{n}=(n_{1},\ldots,n_{r})\in\mathbb{N}^r$, let $\Gamma_{\mathbf{n}}$ be a group presentable as $$\left\langle \gamma_{1},\ldots,\gamma_{r}\:|\:\gamma_{1}^{n_{1}}=\gamma_{2}^{n_{2}}=\cdots=\gamma_{r}^{n_{r}}\right\rangle. $$ If…

Let (G, X) be a transformation group where the group $G$ does not necessarily act freely on the space X. We investigate the extent to which the action of G may fail to be proper. Stability subgroups are used to define new notions of…

We present a general scheme for the nonlinear gauge realizations of spacetime groups on coset spaces of the groups considered. In order to show the relevance of the method for the rigorous treatment of the translations in gravitational…

We consider several integrable systems from a standpoint of the SL(2,R) invariant gauge theory. In the Drinfeld-Sokorov gauge, we get a one parameter family of nonlinear equations from zero curvature conditions. For each value of the…

We propose a technique called dimensional descent to show that Wigner's little group for massless particles, which acts as a generator of gauge transformation for usual Maxwell theory, has an identical role even for topologically massive…

We analyze several non-Hermitian Hamiltonians with antiunitary symmetry from the point of view of their point-group symmetry. It enables us to predict the degeneracy of the energy levels and to reduce the dimension of the matrices necessary…

Chords in musical harmony can be viewed as objects having shapes (major/minor/etc.) attached to base sets (pitch class sets). The base set and the shape set are usually given the structure of a group, more particularly a cyclic group. In a…

The assignment of local observables in the vacuum sector, fulfilling the standard axioms of local quantum theory, is known to determine uniquely a compact group G of gauge transformations of the first kind together with a central involutive…

Spin networks are natural generalization of Wilson loops functionals. They have been extensively studied in the case where the gauge group is compact and it has been shown that they naturally form a basis of gauge invariant observables.…

The problem of an electron gas interacting via exchanging transverse gauge bosons is studied using the renormalization group method. The long wavelength behavior of the gauge field is shown to be in the Gaussian universality class with a…

In this paper we continue our investigation of the global categorical symmetries that arise when gauging finite higher groups and their higher subgroups with discrete torsion. The motivation is to provide a common perspective on the…

We consider the construction of gauge theories of gravity that are invariant under local conformal transformations. We first clarify the geometric nature of global conformal transformations, in both their infinitesimal and finite forms, and…

This paper investigates the statistical properties of non-linear transformations (NLT) of random variables, in order to establish useful tools for estimation and information theory. Specifically, the paper focuses on linear regression…

Gauging a discrete 0-form symmetry of a QFT is a procedure that changes the global form of the gauge group but not its perturbative dynamics. In this work, we study the Seiberg-Witten solution of theories resulting from the gauging of…

We describe symmetry structure of a general singular theory (theory with constraints in the Hamiltonian formulation), and, in particular, we relate the structure of gauge transformations with the constraint structure. We show that any…

Evolution of power spectrum is studied for non-Gaussian models of structure formation. We generalize the dark-matter-approach to these models and find that the evolved spectrum at weakly nonlinear regime is mainly determined by a simple…

We introduce non-linear $\sigma$-models in the framework of noncommutative geometry with special emphasis on models defined on the noncommutative torus. We choose as target spaces the two point space and the circle and illustrate some…

We investigate the semigroup structure of bosonic Gaussian quantum channels. Particular focus lies on the sets of channels which are divisible, idempotent or Markovian (in the sense of either belonging to one-parameter semigroups or being…

Meta-elliptical copulas are often proposed to model dependence between the components of a random vector. They are specified by a correlation matrix and a map $g$, called density generator. While the latter correlation matrix can easily be…