Related papers: Perturbation Theory with a Variational Basis: the …
Improving perturbation theory via a variational optimization has generally produced in higher orders an embarrassingly large set of solutions, most of them unphysical (complex). We introduce an extension of the optimized perturbation method…
The causal perturbation theory is an axiomatic perturbative theory of the S-matrix. This formalism has as its essence the following axioms: causality, Lorentz invariance and asymptotic conditions. Any other property must be showed via the…
We develop the Hamiltonian theory of axial perturbations around a general time-dependent spherical background spacetime. Using the fact that the linearized constraints are gauge generators, we isolate the physical and unconstrained axial…
Four point correlation functions for many electrons at finite temperature in periodic lattice are analyzed by the perturbation theory with respect to the coupling constant. The correlation functions are characterized as a limit of finite…
Second order corrections to the perturbative ground state wave functional and vacuum energy of a Yang-Mills theory are calculated in the temporal gauge. Using dimensional regularization, the concepts of renormalization and a running…
We discuss the connection between the perturbative and non-perturbative renormalization and related conceptual issues in the few-nucleon sector of the low-energy effective field theory of the strong interactions. General arguments are…
Systems with very long-range interactions (that decay at large distances like $U(r)\sim r^{-l}$ with $l\le d$ where $d$ is the space dimensionality) are difficult to study by conventional statistical mechanics perturbation methods. Examples…
The effective potential is a widely used phenomenological tool to investigate phase transitions occurring in the early Universe at finite temperature. In the standard perturbative treatment the potential becomes complex in some region of…
The boundary-value problem for the perturbation of an electric potential by a homogeneous anisotropic dielectric sphere in vacuum was formulated. The total potential in the exterior region was expanded in series of radial polynomials and…
We develop a scaling theory and a renormalization technique in the context of the modern theory of polarization. The central idea is to use the characteristic function (also known as the polarization amplitude) in place of the free energy…
A new variational perturbation theory is developed based on the $q-$deformed oscillator. It is shown that the new variational perturbation method provides 200 or 10 times better accuracy for the ground state energy of anharmonic oscillator…
Linear cosmological perturbation theory is pivotal to a theoretical understanding of current cosmological experimental data provided e.g. by cosmic microwave anisotropy probes. A key issue in that theory is to extract the gauge invariant…
A new method of approximation scheme with potential application to a general interacting quantum system is presented. The method is non-perturbative, self- consistent, systematically improvable and uniformly applicable for arbitrary…
We present the results of a study of the gauge dependence of spacetime perturbations. In particular, we consider gauge invariance in general, we give a generating formula for gauge transformations to an arbitrary order n, and explicit…
It is shown that the perturbative expansions of the correlation functions of a relativistic quantum field theory at finite temperature are uniquely determined by the equations of motion and standard axiomatic requirements, including the KMS…
"Physical theories of fundamental significance tend to be gauge theories. These are theories in which the physical system being dealt with is described by more variables than there are physically independent degree of freedom. The…
Constraints on cosmological parameters from large-scale structure have traditionally been obtained from two-point statistics. However, non-linear structure formation renders these statistics insufficient in capturing the full information…
Small non-spherical perturbations of a spherically symmetric but time-dependent background spacetime can be used to model situations of astrophysical interest, for example the production of gravitational waves in a supernova explosion. We…
Perturbation theory in geometric theories of gravitation is a gauge theory of symmetric tensors defined on a Lorentzian manifold (the background spacetime). The gauge freedom makes uniqueness problems in perturbation theory particularly…
In this work, a novel mechanism for spontaneous symmetry breaking is presented. This mechanism avoids quadratic divergencies and is thus capable of addressing the hierarchy problem in gauge theories. Using the scale-dependent effective…