Related papers: Perturbation theory in covariant canonical quantiz…
Perturbation theory (PT) might be one of the most powerful and fruitful tools for both physicists and chemists, which has led to a wide variety of applications. Over the past decades, advances in quantum computing provide opportunities for…
The unsatisfactory status of the search for a consistent and predictive quantization of gravity is taken as motivation to study the question whether geometrical laws could be more fundamental than quantization procedures. In such an…
Canonical quantization has taught us great things. A common example is that of the harmonic oscillator, which is like swinging a ball on a string back and forth. However, the half-harmonic oscillator blocks the ball at the bottom and then…
In this paper, we show how to use canonical perturbation theory for dissipative dynamical systems capable of showing limit cycle oscillations. Thus, our work surmounts the hitherto perceived barrier for canonical perturbation theory that it…
In strongly coupled field theories, perturbation theory cannot be employed to study the low-energy spectrum. Thus, non-perturbative techniques are required. We employ the variational method, a rigorous, non-perturbative approach which…
Guided by idealized but soluble nonrenormalizable models, a nontraditional proposal for the quantization of covariant scalar field theories is advanced, which achieves a term-by-term, divergence-free perturbation analysis of interacting…
We investigate the sensitivity of quantum systems that are chaotic in a classical limit, to small perturbations of their equations of motion. This sensitivity, originally studied in the context of defining quantum chaos, is relevant to…
Standard derivations of ``time-independent perturbation theory'' of quantum mechanics cannot be applied to the general case where potentials are energy dependent or where the inverse free Green function is a non-linear function of energy.…
A new perturbation theory is proposed for studying finite-size effects near critical point of the $\phi^4$ model with a one-component order parameter. The new approach is based on the techniques of generating functional and functional…
In this paper, I present a mapping between representation of some quantum phenomena in one dimension and behavior of a classical time-dependent harmonic oscillator. For the first time, it is demonstrated that quantum tunneling can be…
In hep-th/0411028 a new manifestly covariant canonical quantization method was developed. The idea is to quantize in the phase space of arbitrary histories first, and impose dynamics as first-class constraints afterwards. The Hamiltonian is…
In order to better understand a complex theory like quantum mechanics, it is sometimes useful to take a step back and create alternative theories, with more intuitive foundations, and examine which features of quantum mechanics can be…
Conventional weak-coupling perturbation theory suffers from problems that arise from resonant coupling of successive orders in the perturbation series. Multiple-scale perturbation theory avoids such problems by implicitly performing an…
In the presence of interactions the frequency of a simple harmonic oscillator deviates from the noninteracting one. Various methods can be used to compute the changes to the frequency perturbatively. Some of them resemble the methods used…
In this paper we propose a perturbative method for the reconstruction of the covariance matrix of a multinormal distribution, under the assumption that the only available information amounts to the covariance matrix of a spherically…
Effective field theory provides a perturbative framework to study the evolution of cosmological large-scale structure. We investigate the underpinnings of this approach, and suggest new ways to compute correlation functions of cosmological…
We present an approach to cosmological perturbations based on a covariant perturbative expansion between two worldlines in the real inhomogeneous universe. As an application, at an arbitrary order we define an exact scalar quantity which…
In the framework of perturbation theory the reality of the perturbed eigenvalues of a class of $\PT$symmetric Hamiltonians is proved using stability techniques. We apply this method to $\PT$symmetric unperturbed Hamiltonians perturbed by…
Classical objects have been excluded as subjects of the observed quantum properties, and the related problem of quantum objects nature has been suspended since the early days of Quantum Theory. Recent experiments show that the problem could…
Review of the most basic issues appearing in the most conservative approaches to quantum theory of gravity is given. The most part of the review is devoted to issues of perturbative quantization based on functional integral technique.…