相关论文: Path model for quantum loop modules of fundamental…
We propose a path integral formulation for scale invariant quantum field theories. We do it by modifying the functional integration measure in such a way that the partition function is always exactly scale invariant, at the cost of having…
This paper is a review of the works devoted to understanding and reinterpretation of the theory of quantum integrable models solvable by Bethe ansatz in terms of the theory of purely classical soliton equations. Remarkably, studying…
In the context of two illustrative examples from supersymmetric quantum mechanics we show that the semi-classical analysis of the path integral requires complexification of the configuration space and action, and the inclusion of complex…
To date, all proposed quantum algorithms for simulating quantum field theory (QFT) simulate (continuous-time) Hamiltonian lattice QFT as a stepping stone. Two overlooked issues are how large we can take the timestep in these simulations…
We describe an explicit crystal morphism between Nakajima monomials and monomials which give a realization of crystal bases for finite dimensional irreducible modules over the quantized enveloping algebra for Lie algebras of type A and C.…
Any particular classical system and its quantum version are normally viewed as separate formulations that are strictly distinct. Our goal is to overcome the two separate languages and create a smooth and common procedure that provides a…
The path integral of a quantum system with an exact symmetry can be written as a sum of functional integrals each giving the contribution from quantum states with definite symmetry properties. We propose a strategy to compute each of them,…
We introduce semi-infinite Lakshmibai-Seshadri paths by using the semi-infinite Bruhat order (or equivalently, Lusztig's generic Bruhat order) on affine Weyl groups in place of the usual Bruhat order. These paths enable us to give an…
The overcompleteness of the coherent states basis leads to a multiplicity of representations of Feynman's path integral. These different representations, although equivalent quantum mechanically, lead to different semiclassical limits. Two…
Generally speaking, this thesis focuses on the interplay between the representations of Lie groups and probability theory. It subdivides into essentially three parts. In a first rather algebraic part, we construct a path model for geometric…
We construct an integral PBW basis and an integral crystal basis of the quantum affine algebra of type A$_{2}^{(2)}$.
The roles of Lie groups in Feynman's path integrals in non-relativistic quantum mechanics are discussed. Dynamical as well as geometrical symmetries are found useful for path integral quantization. Two examples having the symmetry of a…
Complex (semi-)classical paths, or instantons, form an integral part of our understanding of quantum physics. Whereas real classical paths describe classically allowed transitions in the real-time Feynman path integral, classically…
A quantum measurement model based upon restricted path-integrals allows us to study measurements of generalized position in various one-dimensional systems of phenomenological interest. After a general overview of the method we discuss the…
We study certain aspects of the effective, occasionally called collective, description of complex quantum systems within the framework of the path integral formalism, in which the environment is integrated out. Generalising the standard…
Path integrals are a ubiquitous tool in theoretical physics. However, their use is sometimes hindered by the lack of control on various manipulations -- such as performing a change of the integration path -- one would like to carry out in…
The alternative dynamics of loop quantum cosmology is examined by the path integral formulation. We consider the spatially flat FRW models with a massless scalar field, where the alternative quantization inherit more features from full loop…
In this paper, we consider polyhedral realizations for crystal bases $B(\lambda)$ of irreducible integrable highest weight modules of a quantized enveloping algebra $U_q(\mathfrak{g})$, where $\mathfrak{g}$ is a classical affine Lie algebra…
The modular spaces are a family of polarizations of the Hilbert space that are based on Aharonov's modular variables and carry a rich geometric structure. We construct here, step by step, a Feynman path integral for the quantum harmonic…
We formulate path integrals on any Riemannian manifold which admits the action of a compact Lie group by isometric transformations. We consider a path integral on a Riemannian manifold M on which a Lie group G acts isometrically. Then we…