Quantum Field Systems Research Articles

Nonequilibrium quantum fields: Closed-time-path effective action, Wigner function, and Boltzmann equation.

This is the first of a series of papers which describe the functional-integral approach to the study of the statistical and kinetic properties of nonequilibrium quantum fields in flat and curved spacetimes. In this paper we treat a system of self-interacting bosons described by \ensuremath{\lambda}${\ensuremath{\varphi}}^{4}$ scalar fields in flat space. We adopt the closed-time-path (CTP or ``in-in'') functional formalism and use a two-particle irreducible (2PI) representation for the effective action. These formalisms allow for a full account of the dynamics of quantum fields, and put the correlation functions on an equal footing with the mean fields. By assuming a thermal distribution we recover the real-time finite-temperature theory as a special case. By requiring the CTP effective action to be stationary with respect to variations of the correlation functions we obtain an infinite set of coupled equations which is the quantum-field-theoretical generalization of the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy. Truncation of this series leads to dissipative characteristics in the subsystem. In this context we discuss the nature of dissipation in interacting quantum fields.To one-loop order in a perturbative expansion of the CTP effective action, the 2PI formalism yields results equivalent to the leading 1/N expansion for an O(N)-symmetric scalar field. To higher-loop order we introduce a two-time approximation to separate the quantum-field effects of radiative correction and renormalization from the statistical-kinetic effects of collisions and relaxation. In the weak-coupling quasiuniform limit, the system of nonequilibrium quantum fields can subscribe to a kinetic theory description wherein the propagators are represented in terms of relativistic Wigner distribution functions. From a two-loop calculation we derive the Boltzmann equation for the distribution function and the gap equation for the effective mass of the quasiparticles. One can define an entropy function for the quantum gas of quasiparticles which satisfies the H theorem. We also calculate the limits to the validity of the binary collision approximation from a three-loop analysis. The theoretical framework established here can be generalized to nonconstant background fields and for curved spacetimes.

Quantium dynamics of an extended object in Bogolyubov's group variables

Bogolyubov's method of group variables is used to consider the dynamics of a quantum-field Fermi-Bose systems in the neighborhood of a nontrivial classical component in the form of an extended object of the type of a kink. It is shown how the quantum corrections are calculated in the framework of the method. A study is made of the kind dynamics with allowance for the quantum fluctuations that arise when it interacts with the fundamental particles of the fields; the effects due to them and related questions are discussed.

Representation of symmetry group transformation operators in the interaction picture

A representation is obtained for the operators of arbitrary continuous transformations of the symmetry group of an interacting quantum-field system in the form of a time-ordered (anti-ordered) exponential analogous to the Dyson representation. The argument of the exponential is an integral of the density of the interaction Hamiltonian in the Dirac picture over the region determined by the considered symmetry transformation.

Fixed bound atom interacting with a coherent pulse of quantized radiation: Excitation and short-time behavior.

A model of a coupled atom---quantum-field system is presented, consisting of a time-independent Hamiltonian and a realistic dynamical initial condition. The Hamiltonian describes a fixed bound atom coupled to the complete electromagnetic field. The initial condition is a consistent quantum-mechanical description of an atom in the exact ground state of the coupled atom-field system, on which is superimposed an approaching quasiclassical excitation of the field which will cause the interesting dynamical processes later on. Tools are presented for the manipulation of this model, with emphasis towards series expansions of all relevant quantities suitable for small strength $\ensuremath{\lambda}$ of the atom-field coupling and (potentially) large magnitude $\ensuremath{\alpha}$ of the coherent field excitation, such that the "influence of the coherent excitation on the atom" (i.e., the product $\ensuremath{\lambda}\ensuremath{\alpha}$) remains constant as $\ensuremath{\lambda}$ tends to zero. The following results are obtained, at the lowest nontrivial order in $\ensuremath{\lambda}$, in an approximation suitable for times much shorter than any radiative lifetime of the atom: (a) The change in free-field energy due to the interaction with the atom is exactly compensated at all times by the change in bare-atom energy plus the atom-field coupling energy. This checks the consistency of the proposed scheme. (b) The frequency distribution of this change in free-field energy has a (somewhat unexpected) component, with a smooth spectrum, spreading over the whole width of the spectrum of the exciting pulse, in addition to $\ensuremath{\delta}$ and dispersive singularities centered on the atomic transition frequencies. This frequency distribution is discussed in detail and its features are illustrated by a number of figures, in a simple case, numerically tractable. (c) The heterodyne detection of the radiation emitted by the atom is investigated, with emphasis on the issue of causality and propagation of light. Strict causality is obtained, without further approximation, in a model with an atom-field coupling involving the field at a single point and a detector similarly sensitive to properties of the field at a single point. This result breaks down if one uses nonlocal approximations such as the rotating-wave approximation or a detection observable ${\mathbf{E}}^{\ensuremath{-}}(\mathbf{r})\ifmmode\cdot\else\textperiodcentered\fi{}{\mathbf{E}}^{+}(\mathbf{r})$. Finally, an appendix is devoted to the use, in quantum mechanics, of bases moving with respect to each other.

Discrete vacuum superselection rule in Wightman theory with essentially self-adjoint field operators

The main results of earlier work by the author, Sushko, and Khoruzhii describing the algebraic structure of quantum-field systems with (discrete) vacuum superselection rules are generalized to the large class of Wightman theories with essentially self-adjoint field operators (a very strong restriction was imposed on the theory, namely, that the polynomial Op algebra of the Wightman fields /rho/ belongs to the class II, i.e., /rho/ /sub s'/ =/rho/ /sub w'/). It is also shown that the field Op algebra of a Wightman theory with discrete vaccum superselection rule possesses a class II extension.

Radiation processes in quantum systems with boundary

A study is made of the emission effects in quantum field systems contained in the regions of space with a non-stationary boundary. The back reaction of emission on the boundary is taken into account. The classical equations of motion of a system consisting of a free massless scalar field limited in space by a massive reflecting wall (mirror) are investigated in the two-dimensional case. The system is closed, i.e. external forces are absent. This system is quantised. The effect of the reaction of emission on the trajectory of a mirror is studied. The specific peculiarities of the stimulated emission processes in closed quantum systems with boundary are established and investigated. The results are related to hadronic physics.

Pseudocoherent-state approximation for quantum field systems

By the method of pseudocoherent states (PCS) are derived equations for the first two moments of the scalar fieldU(R) (R={x1,x2,…, xn}). It is shown that forn=1, 2 the regularization of these equations can be done in general form. For the one-dimentional sine-Gordon model the renormalization of the potential in the PCS method is demonstrated to coincide with that obtained earlier by another technique.

Extended Objects in Field Theory with Non‐Abelian Group Symmetry

AbstractThis paper presents a general formalism for the description of topological objects created in quantum field systems with non‐Abelian symmetries. This formalism utilizes relations of differential form and therefore is suitable for the description of the local properties of the topological structure. The presentation of the general considerations is followed by several examples.Even when there is no gauge field, the analysis requires use of a gauge transformation matrix. This coincides with the usual gauge transformation matrix when a gauge field is introduced.

Extended objects in quantum field theory

A general formulation for treatment of extended objects in a quantum field system is presented. It is shown how to construct the solutions of the Heisenberg equation when static extended objects are present. A detailed study of the quantum coordinate is presented. The Hamiltonian for the quantum mechanical object, which comes out of the quantum field theory, is obtained. It is shown that creation of extended objects does not upset the renormalizability.

Non-local conformal anomalies

The vacuum polarization by external gauge fields of conformally invariant quantum field systems is shown to manifest a new, non-local, type of trace anomaly when gauge-invariant dimensional regularisation is used. Examples include neutrino and photon loops in a background metric gravitational field and charged massles fermion loops in background metric and electromagnetic fields.