相关论文: Constrained Fock spaces as Virasoro modules
The reduction of Hamiltonian systems aims to build smaller reduced models, valid over a certain range of time and parameters, in order to reduce computing time. By maintaining the Hamiltonian structure in the reduced model, certain…
Quantum hamiltonian reduction is a fundamental tool of conformal field theory and vertex algebra representation theory. It has traditionally been applied to study highest-weight modules. On the other hand, inverse quantum hamiltonian…
We develop a partial Hamiltonian framework to obtain reductions and closed-form solutions via first integrals of current value Hamiltonian systems of ordinary differential equations (ODEs). The approach is algorithmic and applies to many…
It is well known that the normaized characters of integrable highest weight modules of given level over an affine Lie algebra $\hat{\frak{g}}$ span an $SL_2(\mathbf{Z})$-invariant space. This result extends to admissible…
We introduce fibrewise compactifications in both the setting of locally compact Hausdorff spaces and continuous maps, and the parallel setting of $C^*$-algebras and nondegenerate multiplier-valued $*$-homomorphisms. In both situations, we…
We investigate refined algebraic quantisation within a family of classically equivalent constrained Hamiltonian systems that are related to each other by rescaling a momentum-type constraint. The quantum constraint is implemented by a…
The dynamical systems invariant under gauge transformations with higher order time derivatives of the gauge parameter are considered from the Hamiltonian point of view. We investigate the consequences of the basic requirements that the…
In this paper we discuss variational constrained mechanics (vakonomic mechanics) on Lie affgebroids. We obtain the dynamical equations and the aff-Poisson bracket associated with a vakonomic system on a Lie affgebroid ${\mathcal A}$. We…
By using the variational minimizing method with a special constraint and the direct variational minimizing method without constraint, we study second order Hamiltonian systems with a singular potential $V\in C^2(R^n\backslash O,R)$ and…
We propose the new quantization of homogenous cosmological models. Four fundamental methods are applied to the cosmological model and efficiently jointed. The Dirac method for constrained systems is used, then the Fock space is built and…
We will pick up the concepts of partial and complete observables introduced by Rovelli in order to construct Dirac observables in gauge systems. We will generalize these ideas to an arbitrary number of gauge degrees of freedom. Different…
The relationship between the Dirac and reduced phase space quantizations is investigated for spin models belonging to the class of Hamiltonian systems having no gauge conditions. It is traced out that the two quantization methods may give…
The Hubbard model has often been studied with exact diagonalization (ED). This impurity solver is fundamentally limited by the exponential scaling of the Fock space. To address this problem, we introduce Monte Carlo diagonalization. Using a…
This is an introduction to the author's recent work on constrained systems. Firstly, a generalization of the Marsden-Weinstein reduction procedure in symplectic geometry is presented - this is a reformulation of ideas of Mikami-Weinstein…
We aim to characterise boundedness of commutators $[b,T]$ of singular integrals $T$. Boundedness is studied between weighted Lebesgue spaces $L^p(X)$ and $L^q(X)$, $p\leq q$, when the underlying space $X$ is a space of homogeneous type.…
Dirac formalism of Hamiltonian constraint systems is studied for the noncommutative Abelian Proca field. It is shown that the system of constraints are of second class in agreement with the fact that the Proca field is not guage invariant.…
The way of finding all the constraints in the Hamiltonian formulation of singular (in particular, gauge) theories is called the Dirac procedure. The constraints are naturally classified according to the correspondig stages of this…
We prove results concerning the behavior of Hodge ideals under restriction to hypersurfaces or fibers of morphisms, and addition. The main tool is the description of restriction functors for mixed Hodge modules by means of the…
The method of construction of Fock space realizations of Lie algebras is generalized for nonlinear algebras. We consider as an example the nonlinear algebra of constraints which describe the totally symmetric fields with higher spins in the…
The (constrained) minimization of a ratio of set functions is a problem frequently occurring in clustering and community detection. As these optimization problems are typically NP-hard, one uses convex or spectral relaxations in practice.…