Related papers: No phase transition for Gaussian fields with bound…
Following systematically the generalized Hamiltonian approach of Batalin, Fradkin and Tyutin (BFT), we embed the second-class non-abelian SU(2) Higgs model in the unitary gauge into a gauge invariant theory. The strongly involutive…
We consider the fractional $\Phi^3_d$-measure on the $d$-dimensional torus, with Gaussian free field having inverse covariance $(1-\Delta)^\alpha$, and show a phase transition at $d=3\alpha$. More precisely, in a regular regime $d<3\alpha$,…
We give an introductory account of the recently identified gauge invariance of the equilibrium statistical mechanics of classical many-body systems [J. M\"uller et al., Phys. Rev. Lett. Phys. Rev. Lett. 133, 217101 (2024)]. The gauge…
It is proved that in order to keep both the Lagrangian and the motion equation of non-Abelian gauge fields unchanged under the gauge transformation simultaneously, a certain restriction conditions should be established between the gauge…
We consider a class of general spin Hamiltonians of the form $H_s(t)=H_0(t)+H'(t)$ where $H_0(t)$ and $H'(t)$ describe the dipole interaction of the spins with an arbitrary time-dependent magnetic field and the internal interaction of the…
We study the Floquet Hamiltonian: -i omega d/dt + H + V(t) as depending on the parameter omega. We assume that the spectrum of H is discrete, {h_m (m = 1..infinity)}, with h_m of multiplicity M_m. and that V is an Hermitian operator,…
By considering the Einstein vacuum field equations linearized about the Minkowski metric, the evolution equations for the gauge-invariant quantities characterizing the gravitational field are written in a Hamiltonian form by using a…
One proves the equivalence of a Gibbs measure and a Gibbs conformal measure for a dynamical system (G,X) when G is a countably infinite discrete group acting expansively on a compact ultrametric space X. As an application one proves for any…
It is shown that the action for Hamiltonian equations of motion can be brought into invariant symplectic form. In other words, it can be formulated directly in terms of the symplectic structure $\omega$ without any need to choose some…
It is shown that the well-known triviality of the Einstein field equations in two dimensions is not a sufficient condition for the Einstein-Hilbert action to be a total divergence, if the general covariance is to be preserved, that is, a…
The one-dimensional XXZ model (s=1/2, N sites) with uniform long-range interactions among the transverse components of the spins is considered. The Hamiltonian of the model is explicitly given by…
The Gauss law constraint in the Hamiltonian form of the $SU(2)$ gauge theory of gluons is satisfied by any functional of the gauge invariant tensor variable $\phi^{ij} = B^{ia} B^{ja}$. Arguments are given that the tensor $G_{ij} =…
We address the problem of coupling non-Hermitian systems, treated as fundamental rather than effective theories, to the electromagnetic field. In such theories the observables are not the $\bs{x}$ and $\bs{p}$ appearing in the Hamiltonian,…
We investigate the phase transition in the three-dimensional abelian Higgs model for N complex scalar fields, using the gauge-invariant average action \Gamma_{k}. The dependence of \Gamma_{k} on the effective infra-red cut-off k is…
We study a model of spatial random permutations over a discrete set of points. Formally, a permutation $\sigma$ is sampled proportionally to the weight $\exp\{-\alpha \sum_x V(\sigma(x)-x)\},$ where $\alpha>0$ is the temperature and $V$ is…
It is shown that for a given Hermitian Hamiltonian possessing supersymmetry, there is alwayas a non-hermitian Jaynes-Cummings-type Hamiltonian(JCTH) admitting entirely real spectra. The parent supersymmetric Hamiltonian and the…
We consider gradient fields $(\phi_x:x\in \mathbb{Z}^d)$ whose law takes the Gibbs--Boltzmann form $Z^{-1}\exp\{-\sum_{< x,y>}V(\phi_y-\phi_x)\}$, where the sum runs over nearest neighbors. We assume that the potential $V$ admits the…
The $N$-dimensional quantum Hamiltonian $ \hat{H} = -\frac{\hbar^2 {|\mathbf{q} } | }{2(\eta +| {\mathbf{q}} |)} {\mathbf{\nabla}}^2 - \frac{k}{\eta + |{\mathbf{q}} |} $ is shown to be exactly solvable for any real positive value of the…
We show the following symmetry property of a bounded Reinhardt domain $\Omega$ in $\mathbb{C}^{n+1}$: let $M=\partial\Omega$ be the smooth boundary of $\Omega$ and let $h$ be the Second Fundamental Form of $M$; if the coefficient $h(T,T)$…
In this paper we complete the analysis of a statistical mechanics model on Cayley trees of any degree, started in [EsHaRo12,EsRo10,BoEsRo13,JaKuBo14,Bo17]. The potential is of nearest-neighbor type and the local state space is compact but…