相关论文: Q-Deformed Path Integral

We show that the unitary evolution of a harmonic oscillator coupled to a two-level system can be undone by a suitable manipulation of the two-level system -- more specifically: by a quasi-instantaneous phase change. This enables us to…

We consider classical and quantum mechanics related to an additional noncommutativity, symmetric in position and momentum coordinates. We show that such mechanical system can be transformed to the corresponding one which allows employment…

These lectures are intended for graduate students who want to acquire a working knowledge of path integral methods in a wide variety of fields in physics. In general the presentation is elementary and path integrals are developed in the…

We construct the integrals of motion for several models of the quantum damped oscillators in nonrelativistic quantum mechanics in a framework of a general approach to the time-dependent Schroedinger equation with variable quadratic…

We discuss path integrals for quantum mechanics with a potential which is a perturbation of the upside-down oscillator. We express the path integral (in the real time) by the Wiener measure. We obtain the Feynman integral for perturbations…

We derive combinatorial formulae for the modified Macdonald polynomial $H_{\lambda}(x;q,t)$ using coloured paths on a square lattice with quasi-cylindrical boundary conditions. The derivation is based on an integrable model associated to…

When the $q$-deformed creation and annihilation operators are used in a second quantization procedure, the algebra satisfied by basis vectors (orthogonal complete set) should be also deformed such as a field operator remains invariant under…

We report on the status of the string-inspired world line path integral formalism, a recently developed powerful tool for the reorganisation of standard perturbative amplitudes in quantum field theory. The method is outlined and the present…

Fractional calculus and q-deformed Lie algebras are closely related. Both concepts expand the scope of standard Lie algebras to describe generalized symmetries. A new class of fractional q-deformed Lie algebras is proposed, which for the…

We study finite-dimensional integrals in a way that elucidates the mathematical meaning behind the formal manipulations of path integrals occurring in quantum field theory. This involves a proper understanding of how Wick's theorem allows…

Representations of the quantum q-oscillator algebra are studied with particular attention to local Hamiltonian representations of the Schroedinger type. In contrast to the standard harmonic oscillators such systems exhibit a continuous…

Relation between Bopp-Kubo formulation and Weyl-Wigner-Moyal symbol calculus, and non-commutative geometry interpretation of the phase space representation of quantum mechanics are studied. Harmonic oscillator in phase space via creation…

Extension of Feynman's path integral to quantum mechanics of noncommuting spatial coordinates is considered. The corresponding formalism for noncommutative classical dynamics related to quadratic Lagrangians (Hamiltonians) is formulated.…

Introduction Path Integrals - Introduction - Propagator - Free Particle - Path Integral Representation of Quantum Mechanics - Particle on a Ring - Particle in a Box - Driven Harmonic Oscillator - Semiclassical Approximation - Imaginary Time…

A path-integral representation for the kernel of the evolution operator of general Hamiltonian systems is reviewed. We study the models with bosonic and fermionic degrees of freedom. A general scheme for introducing boundary conditions in…

In quantum mechanics, one can express the evolution operator and other quantities in terms of functional integrals. The main goal of this paper is to prove corresponding results in the geometric approach to quantum theory. We apply these…

A geometrical approach to quantum computation is presented, where a non-abelian connection is introduced in order to rewrite the evolution operator of an energy degenerate system as a holonomic unitary. For a simple geometrical model we…

A natural mapping of paths in a curved space onto the paths in the corresponding (tangent) flat space may be used to reduce the curved-space-time path integral to the flat-space-time path integral. The dynamics of the particle in a curved…

We outline a strategy to compute deeply inelastic scattering structure functions using a hybrid quantum computer. Our approach takes advantage of the representation of the fermion determinant in the QCD path integral as a quantum mechanical…

We analyze two simple models derived from a quantum-mechanical particle on an elliptical path. The first Hamiltonian operator is non-Hermitian but equivalent to an Hermitian operator. It appears to exhibit the same two-fold degeneracy as…