On the spectrum of particles created in a Robertson-Walker universe

Created particle spectra are calculated in Robertson-Walker universes with scale factora∝t ^α(0 <α≦ 1) anda∝e ^t, and discussed with a special emphasis on their dependence upon the initial and final times at which a WKB-like positive frequency condition should be imposed. It is shown that the obtained spectra are very sensitive to these times if the WKB approximation for the field equation is not valid in their neighborhood. It is also shown that the total number density of created particles remains finite if the final time is set to be finite.     

The energy-momentum spectrum in the Yukawa2 quantum field theory

We prove that the Yukawa₂ quantum field theory with periodic boundary conditions satisfies the spectral condition, i.e., the joint spectrum of the energy operatorH and the momentum operatorP is contained in the forward cone. In addition, the -bound is obtained.     

On the spectrum of internal symmetries in the algebraic quantum field theory

It is shown that the point spectrum of internal symmetries is always symmetric. It is a group provided the intersection of all local subalgebras is trivial.     

Local properties of equilibrium states and the particle spectrum in quantum field theory

It is shown that in a quantum field theory describing free, scalar particles with masses m _i , i there exist locally normal equilibrium states with finite energy density for all temperature >0 if and only if . This result lends support to the conjecture that the nuclearity criterion proposed by Buchholz and Wichmann is sensitive to the thermodynamical properties of field-theoretic models.     

Particle creation,classicality and related issues in quantum field theory: II. Examples from field theory

We adopt the general formalism, which was developed in Paper I to analyze the evolution of a quantized time-dependent oscillator, to address several questions in the context of quantum field theory in time dependent external backgrounds. In particular, we study the question of emergence of classicality in terms of the phase space evolution and its relation to particle production, and clarify some conceptual issues. We consider a quantized scalar field evolving in a constant electric field and in FRW spacetimes which illustrate the two extreme cases of late time adiabatic and highly non-adiabatic evolution. Using the time-dependent generalizations of various quantities like particle number density, effective Lagrangian etc. introduced in Paper I, we contrast the evolution in these two limits bringing out key differences between the Schwinger effect and evolution in the de Sitter background. Further, our examples suggest that the notion of classicality is multifaceted and any one single criterion may not have universal applicability. For example, the peaking of the phase space Wigner distribution on the classical trajectory alone does not imply transition to classical behavior. An analysis of the behavior of the classicality parameter, which was introduced in Paper I, leads to the conclusion that strong particle production is necessary for the quantum state to become highly correlated in phase space at late times.     

Modeling the quantum evolution of the universe through classical matter

It is well known that the canonical quantization of the Friedmann–Lemaître–Robertson–Walker (FLRW) filled with a perfect fluid leads to nonsingular universes which, for later times, behave as their classical counterpart. This means that the expectation value of the scale factor $\left<a\right>(t)$ never vanishes and, as $t\rightarrow \infty $ , we recover the classical expression for the scale factor. In this paper, we show that such universes can be reproduced by classical cosmology given that the universe is filled with an exotic matter. In the case of a perfect fluid, we find an implicit equation of state (EoS). We then show that this single fluid with an implict EoS is equivalent to two non-interacting fluids, one of them representing stiff matter with negative energy density. In the case of two non-interacting scalar fields, one of them of the phantom type, we find their potential energy. In both cases we find that quantum mechanics changes completely the configuration of matter for small values of time, by adding a fluid or a scalar field with negative energy density. As time passes, the density of negative energy decreases and we recover the ordinary content of the classical universe. The more the initial wave function of the universe is concentrated around the classical big bang singularity, the more it is necessary to add negative energy, since this type of energy will be responsible for the removal of the classical singularity.     

On the mass spectrum of the 2+1 gauge-Higgs lattice quantum field theory

We investigate the mass spectrum of a 2+1 lattice gauge-Higgs quantum field theory with Wilson action A _P+A _H, whereA _P(A _H) is the gauge (gauge-Higgs) interaction. We determine the complete spectrum exactly for all , >0 by an explicit diagonalization of the gauge invariant transfer matrix in the approximation that the interaction terms in the spatial directions are omitted; all gauge invariant eigenfunctions are generated directly. For fixed momentum the energy spectrum is pure point and disjoint simple planar loops and strings are energy eigenfunctions. However, depending on the gauge group and Higgs representations, there are bound state energy eigenfunctions not of this form. The approximate model has a rich particle spectrum with level crossings and we expect that it provides an intuitive picture of the number and location of bound states and resonances in the full model for small , >0. We determine the mass spectrum, obtaining convergent expansions for the first two groups of masses above the vacuum, for small , and confirm our expectations.Research partially supported by CNPq, Brasil     

Zitterbewegung in quantum field theory

Traditionally, the zitterbewegung （ZB） of the Dirac electron has just been studied at the level of quantum mechanics. Seeing the fact that an old interest in ZB has recently been rekindled by the investigations on spintronic, graphene, and superconducting systems, etc., this paper presents a quantum-field-theory investigation on ZB and obtains the conclusion that, the ZB of an electron arises from the influence of virtual electron-positron pairs （or vacuum fluctuations） on the electron.     

Duality in quantum field theory

We postulate a convergent version of operator product expansions on the vacuum and explore some of their consequences. They lead to structures much reminiscent of dual resonance models.     

Connection between the spectrum condition and the Lorentz invariance of the Yukawa2 quantum field theory

We prove, under assumptions, the Lorentz invariance of some quantum field theories. In the separate paper we show that our assumptions are fulfilled in the (renormalized) Yukawa₂ quantum field theory with the periodic boundary conditions.     

Induced spin interactions in the early universe from discrete time quantum theory

By considering a system of spinning particles in an external magnetic field we demonstrate that the system develops non-local spin interactions due to discrete time quantum effects. Such interactions can lead to a domain like structure in the early universe possibly serving as generic seeds to large scale structure.     

Particle behavior in aesthetic field theory

We review the principles of aesthetic field theory and the latest results obtained from computer studies of the equations.     

Particle behavior in aesthetic field theory

We discuss the structure of a particle system obtained in “aesthetic” field theory and study the evolution of this system in time. We find the particle system to have more structure than particles found by other authors investigating particlelike behavior in nonlinear field theories. Our particle system has a maximum center in proximity to a minimum center. Thus, we can interpret our system as being constructed of two bodies. We find that the maximum center and the minimum center move in straight lines, to computer accuracy. Thus, we have not found any nontrivial force laws. This suggests that the situation with respect to basic principles be kept fluid. So far as we know, we are the first investigators to study the trajectories of a two-body system which arises as a consequence of nonlinear field equations.     

Entropy and correlators in quantum field theory

It is well known that loss of information about a system, for some observer, leads to an increase in entropy as perceived by this observer. We use this to propose an alternative approach to decoherence in quantum field theory in which the machinery of renormalisation can systematically be implemented: neglecting observationally inaccessible correlators will give rise to an increase in entropy of the system. As an example we calculate the entropy of a general Gaussian state and, assuming the observer's ability to probe this information experimentally, we also calculate the correction to the Gaussian entropy for two specific non-Gaussian states.     

Numerical calculations in quantum field theory

The relevance of numerical calculations for quantum field theories in general, and in particular for quantum chromodynamics, is illustrated. The evaluation of the force between static quark and antiquark is presented in some detail as exemplification.     

Particle asymmetries in the early universe

The total lepton asymmetry l=∑_fl_f in our universe is only poorly constrained by theories and experiments. It might be orders of magnitudes larger than the observed baryon asymmetry b?O(10⁻¹⁰), |l|/b≤O(10⁹). We found that the dynamics of the cosmic QCD transition changes for large asymmetries. Predictions for asymmetries in a single flavour l_f allow even larger values. We find that asymmetries of l_f≤O(1) in single or two flavours may change the relic abundance of WIMPs. However, large lepton and large individual lepton flavour asymmetries influence significantly the dynamics of the early universe between the electroweak phase transition and the onset of neutrino oscillations.