相关论文: $\delta$-Function Perturbations and Boundary Probl…
The path integral approach to quantum mechanics provides a method of quantization of dynamical systems directly from the Lagrange formalism. In field theory the method presents some advantages over Hamiltonian quantization. The Lagrange…
Quantum gravitational effects may hold the key to some of the outstanding problems in theoretical physics. In this work we analyze the perturbative quantum effects on the boundary of a gravitational system and Dirichlet boundary condtion…
We study the existence of Feller semigroups arising in the theory of multidimensional diffusion processes. We study bounded perturbations of elliptic operators with boundary conditions containing an integral over the closure of the domain…
Boundary conditions play a crucial role in the path-integral approach to quantum gravity and quantum cosmology, as well as in the current attempts to understand the one-loop semiclassical properties of quantum field theories. Within this…
Boundary effects in quantum mechanics are examined by considering a partition wall inserted at the centre of a harmonic oscillator system. We put an equal number of particles on both sides of the impenetrable wall keeping the system under…
The essence of the path integral method in quantum physics can be expressed in terms of two relations between unitary propagators, describing perturbations of the underlying system. They inherit the causal structure of the theory and its…
We analyze the quantum dynamics of a non-relativistic particle moving in a bounded domain of physical space, when the boundary conditions are rapidly changed. In general, this yields new boundary conditions, via a dynamical composition law…
We use path-integrals to derive a general expression for the semiclassical approximation to the partition function of a one-dimensional quantum-mechanical system. Our expression depends solely on ordinary integrals which involve the…
The formulation of the relativistic spinless path integral on the general affine space is presented. For the one dimensional space, the Duru-Kleinert (DK) method and the $\delta $-function perturbation technique are applied to solve the…
We here put forward a new path-integral over Hilbert space and show that it reproduces quantum mechanics exactly. This approach works by optimizing the generating functional under a variation of the final state; it is hence an example of a…
We develop a non-perturbative method for calculating partition functions of strongly coupled quantum mechanical systems with interactions between subsystems described by a path integral of a dual system. The dual path integral is derived…
The functional integral has many triumphs in elucidating quantum theory. But incorporating charge fractionalization into that formalism remains a challenge.
Two formulations of quantum mechanics, inequivalent in the presence of closed timelike curves, are studied in the context of a soluable system. It illustrates how quantum field nonlinearities lead to a breakdown of unitarity, causality, and…
We introduce the paradigm of destructive many-body interference between quantum trajectories as a means to systematically generate prethermal kinetically constrained dynamics in Floquet systems driven at special frequencies. Depending on…
We study two-dimensional classically integrable field theory with independent boundary condition on each end, and obtain three possible generating functions for integrals of motion when this model is an ultralocal one. Classically…
We investigate the role of external constraints in quantum field theory using the path integral formalism. We begin by reviewing the quantization of constrained systems and extend the analysis to cases where constraints are added to the…
In this work we develop an alternative approach for solution of Quantum Trajectories using the Path Integral method. The state-of-the-art technique in the field is to solve a set of non-linear, coupled partial differential equations (PDEs)…
A path-integral approach for the computation of quantum-mechanical propagators and energy Green's functions is presented. Its effectiveness is demonstrated through its application to singular interactions, with particular emphasis on the…
Fractional-order elliptic problems are investigated in case of inhomogeneous Dirichlet boundary data. The boundary integral form is proposed as a suitable mathematical model. The corresponding theory is completed by sharpening the mapping…
Quantum tunneling in a many-body system is much more non-trivial than that in a one-body system. The most characteristic phenomenon is the mixed tunneling, which has been studied in many fields for decades. For instance, let us consider a…