Related papers: Closed Path Integrals and Renormalisation in Quant…
We study a quantum system in a Riemannian manifold M on which a Lie group G acts isometrically. The path integral on M is decomposed into a family of path integrals on a quotient space Q=M/G and the reduced path integrals are completely…
A specific class of explicitly time-dependent potentials is studied by means of path integrals. For this purpose a general formalism to treat explicitly time-dependent space-time transformations in path integrals is sketched. An explicit…
We study scaling and renormalization in two dimensional quantum gravity in a covariant framework. After reviewing the definition of a proper path integral measure, we use scaling arguments to rederive the KPZ relations, the fractal…
A method for nonperturbative path integral calculation is proposed. Quantum mechanics as a simplest example of a quantum field theory is considered. All modes are decomposed into hard (with frequencies $\omega^2 >\omega^2_0$) and soft (with…
The path integral by which quantum field theories are defined is a particular solution of a set of functional differential equations arising from the Schwinger action principle. In fact these equations have a multitude of additional…
The thermodynamical formalism is studied for renormalisable maps of the interval and the natural potential $-t \log|Df|$. Multiple and indeed infinitely many phase transitions at positive $t$ can occur for some quadratic maps. All unimodal…
Techniques based on $n$-particle irreducible effective actions can be used to study systems where perturbation theory does not apply. The main advantage, relative to other non-perturbative continuum methods, is that the hierarchy of…
A method is presented which restricts the space of paths entering the path integral of quantum mechanics to subspaces of $C^\alpha$, by only allowing paths which possess at least $\alpha$ derivatives. The method introduces two external…
We put forward the concatenation of Quantum Arnold Transformations as a tool to obtain the wave function of a particle subjected to a harmonic potential which is switched on and off successively. This simulates the capture and release…
Starting from the Dirac equation in external electromagnetic and torsion fields we derive a path integral representation for the corresponding propagator. An effective action, which appears in the representation, is interpreted as a…
We adapt the semiclassical technique, as used in the context of instanton transitions in quantum field theory, to the description of tunneling transmissions at finite energies through potential barriers by complex quantum mechanical…
We analyze by a renormalization method, the dynamics of a particle in a infinite square-well potential driven by an external monochromatic field. This method set up for Hamiltonian systems with two degrees of freedom allows us to analyze…
We implement the concept of Wilson renormalization in the context of simple quantum mechanical systems. The attractive inverse square potential leads to a $\b$ function with a nontrivial ultraviolet stable fixed point and the Hulthen…
We propose to use the complex quantum dynamics of a massive particle in a non-quadratic potential to reconstruct an initial unknown motional quantum state. We theoretically show that the reconstruction can be efficiently done by measuring…
The path integral formulation in quantum mechanics corresponds to the first quantization since it is just to rewrite the quantum mechanical amplitude into many dimensional integrations over discretized coordinates $x_n$. However, the path…
We briefly review a hamiltonian path integral formalism developed earlier by one of us. An important feature of this formalism is that the path integral quantization in arbitrary co-ordinates is set up making use of only classical…
We explore the applicability of the exact renormalization group to the study of tunnelling phenomena. We investigate quantum-mechanical systems whose energy eigenstates are affected significantly by tunnelling through a barrier in the…
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…
In the most general case of the Delta exact operator valued generators constructed of an arbitrary Fermion operator, we present a closed solution for the transformed master action in terms of the original master action in the closed form of…
The path integral representation for a system of N non-relativistic particles on the plane, interacting through a Chern-Simons gauge field, is obtained from the operator formalism. An effective interaction between the particles appears,…