相关论文: Bosons Live in Symplectic Coset Spaces
Let $(M, \omega)$ be a connected compact symplectic manifold equipped with a Hamiltonian SU(2) or SO(3) action. We prove that, as fundamental group of topological spaces, $\pi_1(M)=\pi_1(M_{red})$, where $M_{red}$ is the symplectic quotient…
A microscopic model of the Brout-Englert-Higgs (BEH) mechanism is proposed. Massless fermions and antifermions do not belong to the Fock space with definite particle-number distribution, but belong to a non-Fock space with indefinite one.…
A long-standing problem with the many-body approximations for interacting condensed bosons has been the dichotomy between the ``conserving'' and ``gapless'' approximations, which either obey the conservations laws or satisfy the…
We show that space-time evolution of one-dimensional fermionic systems is described by nonlinear equations of soliton theory. We identify a space-time dependence of a matrix element of fermionic systems related to the {\it Orthogonality…
The enveloping algebra,$D_{n}$,of fermions is extended on the lattice to include the discrete space invariance.This extended algebra,denoted X, has the space symmetry as a factor : $X/D_{n}$ = space group.
We study a 2+1 dimensional theory of bosons and fermions with an omega ~ k^2 dispersion relation. The most general interactions consistent with specific symmetries impart fractional statistics to the fermions. Unlike examples involving…
We investigate the existence of homotopy comoment maps (comoments) for high-dimensional spheres seen as multisymplectic manifolds. Especially, we solve the existence problem for compact effective group actions on spheres and provide…
We investigate the shape of the spectrum and the spectral fluctuations of the $k$-body Embedded Gaussian Ensemble for Bosons in the dense limit, where the number of Bosons $m \to \infty$ while both $k$, the rank of the interaction, and $l$,…
We study the large-time behaviour of a sample $\mathcal{S}$ consisting of an ensemble of fermionic walkers on a graph interacting with a structured infinite reservoir of fermions $\mathcal{E}$ through an exchange of particles in preferred…
The notion of higher-order topological phases can have interesting generalizations to systems with subsystem symmetries that exhibit fractonic dynamics for charged excitations. In this work, we systematically study the higher-order…
The construction and classification of crystalline symmetry protected topological (SPT) phases in interacting bosonic and fermionic systems have been intensively studied in the past few years. Crystalline SPT phases are not only of…
A geometric description of the first Poisson cohomology groups is given in the semilocal context, around (possibly singular) symplectic leaves. This result is based on the splitting theorems for infinitesimal automorphisms of coupling…
In the first-quantized description of bosonic systems permutation cycles formed by the particles play a fundamental role. In the ideal Bose gas Bose-Enstein condensation (BEC) is signaled by the appearance of infinite cycles. When the…
The mechanism underlying any bosonisation or fermionisation is exposed.It is shown that any local theory of fermions on a lattice in any spatial dimension greater than one is equivalent to a local theory of Ising spins coupled to a $Z_{2}$…
We propose a generalization of the supersymmetric representation of spins with symplectic symmetry, generalizing the rotation group of the spin from SU(2) to SP(N). As a test application of this new representation, we consider two toy…
One of the major differences between fermions and bosons is that fermionic states have a maximum occupation number of one, whereas the occupation number for bosonic states is in principle unlimited. For bosons that are made up of fermions,…
Three-dimensional topological insulators can be described by an effective field theory involving two `hydrodynamic' Abelian gauge fields. The action contains a bulk topological BF term and a surface term, called loop model. This describes…
The set of equivalence classes of cobounded actions of a group on different hyperbolic metric spaces carries a natural partial order. The resulting poset thus gives rise to a notion of the "best" hyperbolic action of a group as the largest…
The symmetric group on a set acts transitively on its subsets of a given size. We define homomorphisms between the corresponding permutation modules, defined over a field of characteristic two, which generalize the boundary maps from…
We investigate continuous transitive actions of semitopological groups on spaces, as well as separately continuous transitive actions of topological groups.