arXiv subjects

N. F. Svaiter

Publications and source records attributed to N. F. Svaiter.

At least 91 records · Page 5Linked to original sources

arXiv2004

Finite Size Effects in Thermal Field Theory

We consider a neutral self-interacting massive scalar field defined in a d-dimensional Euclidean space. Assuming thermal equilibrium, we discuss the one-loop perturbative renormalization of this theory in the presence of rigid boundary surfaces (two parallel hyperplanes), which break translational symmetry. In order to identify the singular parts of the one-loop two-point and four-point Schwinger functions, we use a combination of dimensional and zeta-function analytic regularization procedures. The infinities which occur in both the regularized one-loop two-point and four-point Schwinger functions fall into two distinct classes: local divergences that could be renormalized with the introduction of the usual bulk counterterms, and surface divergences that demand countertems concentrated on the boundaries. We present the detailed form of the surface divergences and discuss different strategies that one can assume to solve the problem of the surface divergences. We also briefly mention how to overcome the difficulties generated by infrared divergences in the case of Neumann-Neumann boundary conditions.

hep-th↗

arXiv2004

The Strong-Coupling Expansion and the Ultra-local Approximation in Field Theory

We discuss the strong-coupling expansion in Euclidean field theory. In a formal representation for the Schwinger functional, we treat the off-diagonal terms of the Gaussian factor as a perturbation about the remaining terms of the functional integral. We first study the strong-coupling expansion in the ϕ^4 theory and also quantum electrodynamics. Assuming the ultra-local approximation, we examine the analytic structure of the zero-dimensional generating functions in the complex coupling constants plane. Second, we discuss the ultra-local generating functional in two idealized field theory models. To control the divergences of the strong-coupling perturbative expansion two different steps are used. First, we introduce a lattice structure to give meaning to the ultra-local generating functional. Using an analytic regularization procedure we discuss briefly how it is possible to obtain a renormalized Schwinger functional associated with these scalar models, going beyond the ultra-local approximation. Using the strong-coupling perturbative expansion we show how it is possible to compute the renormalized vacuum energy of a self-interacting scalar field, going beyond the one-loop level.

hep-th↗

arXiv2002

Focusing Vacuum Fluctuations II

The quantization of the scalar and electromagnetic fields in the presence of a parabolic mirror is further developed in the context of a geometric optics approximation. We extend results in a previous paper to more general geometries, and also correct an error in one section of that paper. We calculate the mean squared scalar and electric fields near the focal line of a parabolic cylindrical mirror. These quantities are found to grow as inverse powers of the distance from the focus. We give a combination of analytic and numerical results for the mean squared fields. In particular, we find that the mean squared electric field can be either negative or positive, depending upon the choice of parameters. The case of a negative mean squared electric field corresponds to a repulsive Van der Waals force on an atom near the focus, and to a region of negative energy density. Similarly, a positive value corresponds to an attractive force and a possibility of atom trapping in the vicinity of the focus.

quant-ph↗

arXiv2002

Vacuum Polarization of a Scalar Field in a Rectangular Waveguide

An analysis of the one-loop vacuum fluctuations associated with a scalar field confined in the interior of a infinite waveguide of rectangular cross section is presented. We first consider the massless scalar field defined in a four-dimensional Euclidean space. To identify the infinities of the vacuum fluctuations we use a combination of dimensinal and zeta function analytic regularization procedures. The infinities which occur in the one-loop vacuum fluctuations fall into two distinct classes: ultraviolet divergences that are renormalized by the introduction of bulk counterterms and also surface and edges divergences that demand countertems concentrated on the boundaries. We present the detailed form of the surface and edge divergences. Finally we discuss how to generalize our calculations for a confined massive scalar field defined in a higher dimensional Euclidean space.

hep-th↗

arXiv2002

Effective Lagrangians for Scalar Fields and Finite Size Effects in Field Theory

We discuss the approach of effective field theory on a d-dimensional Euclidean space in a scalar theory with two different mass scales in the presence of flat surfaces. Then considering Dirichlet and Neumann boundary conditions, we implement the renormalization program in the lambda phi^{4} theory in a region bounded by two parallel hyperplanes in the one-loop approximation.

hep-th↗

arXiv2001

Constructing Bidimensional Scalar Field Theory Models From Zero Mode Fluctuations

In this paper we review how to reconstruct scalar field theories in two dimensional spacetime starting from solvable Schrodinger equations. Three different Schrodinger potentials are analyzed. We obtained two new models starting from the Morse and Scarf II hyperbolic potentials, {\it i.e}, the $U(ϕ)=ϕ^2\ln^2(ϕ^2)$ model and $U(ϕ)=ϕ^2\cos^2(\ln(ϕ^2))$ model respectively.

hep-th↗

arXiv2001

Quantum Properties of Solitons in $U(ϕ)=ϕ^2\ln^2(ϕ^2)$ and $U(ϕ)=ϕ^2\cos^2(ϕ^2)$ Models

Recently we constructed two new $(1+1)$-dimensional scalar field theory models that posses solitonic solutions. They are the $U(ϕ)=ϕ^2\ln^2(ϕ^2)$ and the $U(ϕ)=ϕ^2\cos^2(ϕ^2)$ models . The first quantum corrections for these models are given by exactly solvable Schrodinger equations. In this paper we first examine the quantum meaning of the solitonic solutions and study the scattering of the mesons by the quantum soliton at order $\hbar$. Finally we give a finite expression for the soliton masses of both models and evaluate such expression approximately in the case of the second model.

hep-th↗

arXiv2001

Vacuum Stress Tensor of a Scalar Field in a Rectangular Waveguide

Using the heat kernel method and the analytic continuation of the zeta function, we calculate the canonical and improved vacuum stress tensors, ${T_{μν}(\vec{x})}$ and ${Θ_{μν}(\vec{x})}$, associated with a massless scalar field confined in the interior of an infinitely long rectangular waveguide. The local depence of the renormalized energy for two special configurations when the total energy is positive and negative are presented using ${T_{00}(\vec{x})}$ and ${Θ_{00}(\vec{x})}$. From the stress tensors we obtain the local Casimir forces in all walls by introducing a particular external configuration. It is shown that this external configuration cannot give account of the edge divergences of the local forces. The local form of the forces is obtained for three special configurations.

hep-th↗

arXiv2001

The Effective Potential for Composite Operator in the Scalar Model at Finite Temperature

We discuss the $ϕ^4$ and $ϕ^6$ theory defined in a flat $D$-dimensional space-time. We assume that the system is in equilibrium with a thermal bath at temperature $β^{-1}$. To obtain non-perturbative result, the $ 1/N $ expansion is used. The method of the composite operator (CJT) for summing a large set of Feynman graphs, is developed for the finite temperature system. The ressumed effective potential and the analysis of the D=3 and D=4 cases are given.

hep-th↗

arXiv2000

Radiatively Induced Lorentz and CPT Violation in QED at Finite Temperature

In this paper we evaluate the induced Lorentz and CPT violating Chern-Simons term in the QED action at finite temperature. We do this using the method of derivative expansion of fermion determinants. Also, we use the imaginary-time formalism to calculate the temperature dependence of the Chern-Simons term

hep-th↗

arXiv2000

A Rotating Vacuum and the Quantum Mach's Principle

In this work we consider a quantum analog of Newton's bucket experiment in a flat spacetime: we take an Unruh-DeWitt detector in interaction with a real massless scalar field. We calculate the detector's excitation rate when it is uniformly rotating around some fixed point and the field is prepared in the Minkowski vacuum and also when the detector is inertial and the field is in the Trocheries-Takeno vacuum state. These results are compared and the relations with a quantum analog of Mach's principle are discussed.

gr-qc↗

arXiv2000

The Rotating Detector and Vacuum Fluctuations

In this work we compare the quantization of a massless scalar field in an inertial frame with the quantization in a rotating frame. We used the Trocheries-Takeno mapping to relate measurements in the inertial and the rotating frames. An exact solution of the Klein-Gordon equation in the rotating coordinate system is found and the Bogolubov transformation between the inertial and rotating modes is calculated, showing that the rotating observer defines a vacuum state different from the Minkowski one. We also obtain the response function of an Unruh-De Witt detector coupled with the scalar field travelling in a uniformly rotating world-line. The response function is obtained for two different situations: when the quantum field is prepared in the usual Minkowski vacuum state and when it is prepared in the Trocheries-Takeno vacuum state. We also consider the case of an inertial detector interacting with the field in the rotating vacuum.

hep-th↗

arXiv2000

Focusing Vacuum Fluctuations

The focusing of the vacuum modes of a quantized field by a parabolic mirror is investigated. We use a geometric optics approximation to calculate the energy density and mean squared field averages for scalar and electromagnetic fields near the focus. We find that these quantities grow as an inverse power of the distance to the focus. There is an attractive Casimir-Polder force on an atom which will draw it into the focus. Some estimates of the magnitude of the effects of this focusing indicate that it may be observable.

quant-ph↗

arXiv1999

The Composite Operator (CJT) Formalism in the $(λϕ^4+ηϕ^{6})_{D=3}$ Model at Finite Temperature

We discuss three-dimensional $ λϕ^4+ηϕ^6 $ theory in the context of the 1/N expansion at finite temperature. We use the method of the composite operator (CJT) for summing a large sets of Feynman graphs. We analyse the behavior of the thermal square mass and the thermal coupling constant in the low and high temperature limit. The existent of the tricritical point at some temperature is found using this non-pertubative method.

hep-th↗

arXiv1999

Finite Size Effects in the Anisotropic λ/4!(ϕ^4_1 + ϕ^4_2)_d Model

We consider the $\fracλ{4!}(ϕ^{4}_{1}+ϕ^{4}_{2})$ model on a d-dimensional Euclidean space, where all but one of the coordinates are unbounded. Translation invariance along the bounded coordinate, z, which lies in the interval [0,L], is broken because of the boundary conditions (BC's) chosen for the hyperplanes z=0 and z=L. Two different possibilities for these BC's boundary conditions are considered: DD and NN, where D denotes Dirichlet and N Newmann, respectively. The renormalization procedure up to one-loop order is applied, obtaining two main results. The first is the fact that the renormalization program requires the introduction of counterterms which are surface interactions. The second one is that the tadpole graphs for DD and NN have the same z dependent part in modulus but with opposite signs. We investigate the relevance of this fact to the elimination of surface divergences.

hep-th↗

arXiv1999

A Non-perturbative Solution of the Zero-Dimensional lambda phi^4 Field Theory

We have done a study of the zero-dimensional $λϕ^{4}$ model. Firstly, we exhibit the partition function as a simple exact expression in terms of the Macdonald's function for $Re(λ)>0$. Secondly, an analytic continuation of the partition function for $Re(λ)<0$ is performed, and we obtain an expression defined in the complex coupling constant plane $λ$, for $|arg λ|<π$. Consequently, the partition function understood as an analytic continuation is defined for all values of $λ$, except for a branch cut along the real negative $λ$ axis. We also evaluate the partition function on perturbative grounds, using the Borel summation technique and we found that in the common domain of validity for $Re(λ)>0$, it coincides precisely with the exact expression.

hep-th↗

arXiv1999

From spinning to non-spinning cosmic string spacetimes

We analyse the properties of a fluid generating a spinning cosmic string spacetime with flat limiting cases corresponding to a constant angular momentum in the infinite past and static configuration in the infinite future. The spontaneous loss of angular momentum of a spinning cosmic string due to particle emission is discussed. The rate of particle production between the spinning and non-spinning cosmic string spacetimes is calculated.

gr-qc↗

arXiv1999

Casimir Energy of Massless Fermions in the Slab-bag

The zero-point energy of a massless fermion field in the interior of two parallel plates in a D-dimensional space-time at zero temperature is calculated. In order to regularize the model, a mix between dimensional and zeta-function regularization procedure is used and it is found that the regularized zero-point energy density is finite for any number of space-time dimensions. We present a general expression for the Casimir energy for the fermionic field in such a situation.

hep-th↗