Renormalization of Quantum Field Theory in Curved Space-Time and Renormalization Group Equations

The structure of quantum field theory renormalization in curved space-time is investigated. The equations allowing us to investigate the behaviour of vacuum energy and vertex functions in the limit of small distances in the external gravitational field are established. The behaviour of effective charges corresponding to the parameters of nonminimal coupling of the matter with the gravitational field is studied and the conditions under which asymptotically free theories become asymptotically conformally invariant are found. The examples of asymptotically conformally invariant theories are given. On the basis of a direct solution of renormalization group equations the effective potential in the external gravitational field and the effective action in the gravity with the high derivatives are obtained. The expression for the cosmological constant in terms of R²-gravity Lagrangian parameters is given which does not contradict the observable data. Renormalization and renormalization group equations for the theory in curved space-time with torsion are investigated.     

Rarita-Schwinger Quantum Free Field via Deformation Quantization

Rarita-Schwinger (RS) quantum free field is reexamined in the context of deformation quantization (DQ). It is interesting to consider this alternative for the specific case of the spin 3/2 field because DQ avoids the problem of dealing from the beginning with the extra degrees of freedom which appears in the conventional canonical quantization. It is found out that the subsidiary condition does not introduce any change either in the Wigner function or in other aspects of the Weyl-Wigner-Groenewold-Moyal formalism, such as: the Stratonovich-Weyl quantizer and normal ordering, in relation to de Dirac field case. The RS propagator is also calculated within this framework.     

Static Conformally Flat Spherically Symmetric Space-Time in Einstein-Cartan Theory of Gravitation

The exact solution of Einstein-Cartan field equations for static, conformally flat spherically symmetric space-time is derived and it is proved to be Petrov-type D.     

On Static Asymptotically Flat Solutions of Fourth Order Gravitational Field Equations

It is shown that each non-flat regular static asymptotically flat solution of the gravitational field equation following from the Lagrangian has in a certain sense positive energy. Further, for a set of parameters including the BACH -EINSTEIN theory some results concerning the full nonlinear behaviour of the solutions of the field equation will be given.     

Relative Quantum Field Theory

We highlight the general notion of a relative quantum field theory, which occurs in several contexts. One is in gauge theory based on a compact Lie algebra, rather than a compact Lie group. This is relevant to the maximal superconformal theory in six dimensions.     

PT-Symmetric Quantum Field Theory

In the context of the PT-symmetric version of quantum electrodynamics, it is argued that the C-operator introduced in order to define a unitary inner product has nothing to do with charge conjugation.     

Shuffling Quantum Field Theory

We discuss shuffle identities between Feynman graphs using the Hopf algebra structure of perturbative quantum field theory. For concrete exposition, we discuss vertex function in massless Yukawa theory.     

Braided Quantum Field Theory

We develop a general framework for quantum field theory on noncommutative spaces, i.e., spaces with quantum group symmetry. We use the path integral approach to obtain expressions for n-point functions. Perturbation theory leads us to generalised Feynman diagrams which are braided, i.e., they have non-trivial over- and under-crossings. We demonstrate the power of our approach by applying it to φ⁴-theory on the quantum 2-sphere. We find that the basic divergent diagram of the theory is regularised. Received: 3 July 1999 / Accepted: 10 November 2000     

非对易时空中的量子场论及其唯象学

首先介绍非对易时空量子场论的基本思想, 并简短地回顾直线对撞机上的唯象学研究. 然后, 较详细地讨论通过e⁺e^－碰撞的中性Higgs粒子对产生来探测非对易信号, 及如何利用洛仑兹对称性破坏从标准模型背景中分离出信号. 最后, 简要地提及构造现实模型方面的近期进展.     

Null Surfaces and Their Singularities in Three-Dimensional Minkowski Space-Time

In this work we integrate the null geodesic equations in three-dimensional Minkowski space-time in order to obtain the light-cone cut function; that is, the function that describes the intersection, C_x ^a, of the light cone from each space-time point, _x ^a, with future null infinity I ⁺. Furthermore, using this result, we locate the singularities of the null surface obtained as the envelope of the past light cones from points on a deformed light-cone cut of I ⁺.     

The Quantum R-Matrix via Canonical Quantization in the Liouville Theory

Starting from the classical Liouville theory, we study its quantum theory through canonical quantization. We find that if the Poisson bracket relations between two vectors are,dominated by the classical r-matrix in the classical case, their quantum analogue is replaced by the exchange relations dominated by the quantum R-matrix. The quantum group structure in the quantum LiouviUe theory is studied and the central charge of the quantum Liouville theory is also obtained.     

Source Methods in Quantum Field Theory

Schwinger's source theory is used to present a pedagogical review of various methods and models in quantum field theory. In the interest of simplicity we start out with a charged scalar model. Later on we also incorporate more complicated concepts in order to treat quantum electrodynamics, effective Lagrangians and model approximations.     

Anomalies in PT-Symmetric Quantum Field Theory

It is shown that a version of PT-symmetric electrodynamics based on an axial-vector current coupling massless fermions to the photon possesses anomalies and so is rendered nonrenormalizable. An alternative theory is proposed based on the conventional vector current constructed from massive Dirac fields, but in which the PT transformation properties of electromagnetic fields are reversed. Such a theory seems to possess many attractive features.     

Group Contraction in Quantum Field Theory

Group contraction plays a relevant rôle in spontaneously broken symmetry theories. Its physical meaning in connection with Bose condensation and the origin of macroscopic quantum systems is discussed.     

Particle Correlation in Quantum Field Theory

The paper deals with studies of the angular correlation of two mono-energetic particles produced in several fundamental processes in quantum field theory. The angular correlation is defined as the average (expectation value) of the cosine of the angle between the momenta of the two outgoing particles. A positive correlation indicates, in a statistical sense, that the particles tend to travel in the same directions (as in beam formation) while a negative one indicates that they tend to travel in opposing directions. The angular correlations for photons and electrons produced by sources, and in quantum eletrodynamics, to lowest order, γγ produced in e⁺e⁻ collision (annihilation), e⁺e⁻ pair production in γγ collision, and finally e⁺e⁻ pair production by a Nambu string are studied in detail.     

Quantum Field Theory and Dense Measurement

We show, using quantum field theory (QFT), that performing a large number of identical repetitions of the same measurement does not only preserve the initial state of the wave function (the Zeno effect), but also produces additional physicaleffects. We first discuss the Zeno effect in the framework of QFT, that is, as a quantum field phenomenon. We then derive it from QFT for the general case in which the initial and final states are different. We use perturbation theory and Feynman diagrams and refer to the measurement act as an external constraint upon the system that corresponds to the perturbative diagram that denotes this constraint. The basic physical entities dealt with in this work are not the conventional once-perfomed physical processes, but their n times repetition where n tends to infinity. We show that the presence of these repetitions entails the presence of additional excited state energies, and the absence of them entails the absence of these excited energies.