New measures for nonrenormalizable quantum field theory

Generic interactions characteristic of so-called nonrenormalizable scalar and spinor quantum field theories are interpreted as discontinuous perturbations in the sense that the theory does not return to the unperturbed theory as the interaction coupling vanishes. To proceed beyond this interpretation specific alternatives to conventional quantization schemes are developed. Solution of a highly idealized (independent-value), nonrenormalizable scalar field theory automatically entails a formally scale-invariant measure (rather than the conventional translation-invariant measure) in a functional integral formulation, and the success of this measure suggests its use more generally. Such a measure can be motivated (by augmented field theory) on heuristic grounds as taking into account the partial hardcore nature of the interaction responsible for its behavior as a discontinuous perturbation. This modification leads generally to what we call scale-covariant quantization, which can be formulated in terms of unconventional functional differential equations, coupled Green's function equations and operator field equations. Use of affine fields establishes equivalence of these various approaches and enables analogous coupled Green's function equations for models with fermions to be most easily obtained. The basic concepts of this program are illustrated with elementary wave-mechanical examples.     

Heat kernel expansion in the covariant perturbation theory

Working within the framework of the covariant perturbation theory, we obtain the coincidence limit of the heat kernel of an elliptic second order differential operator that is applicable to a large class of quantum field theories. The basis of tensor invariants of the curvatures of a gravity and gauge field background, to the second order, is derived, and the form factors acting on them are obtained in two integral representations. The results are verified by the functional trace operation, by the short proper time (Schwinger–DeWitt) expansions, as well as by the computation of the Green function for the two-dimensional scalar field model.     

Perturbative symplectic field theory and Wigner function

We study relativistic quantum field theories in phase space, based on representations of the Poincaré group, using the Moyal product. We develop a perturbative theory for quantizing fields, with functional methods in phase space. The two-point function is related to relativistic Wigner functions for bosons and fermions. As an example we analyze the complex scalar field with quartic self-interaction.     

On the Light-Cone Expansion in Gauge Field Theories (QED)

The techniques for the derivation of light-cone expansions in scalar field theories are generalized to nonscalar, especially gauge field theories. For this reason the smallness of the remainder is proved in an arbitrary renormalizable theory provided an infrared regularization is present. Then we apply the formalism to derive a light-cone expansion for the product of two scalar currents in Quantum Electrodynamics in leading order. Thereby the gauge-invariance of the underlying theory is used from the very beginning by the application of the known solutions of the Ward identities. As a result of that, one obtains two gauge-invariant light cone operators, and the corresponding coefficient functions are independent one from another.     

EXACT SOLUTIONS OF CLASSICAL SCALAR FIELD EQUATIONS

We give a class of exact solutions of quartic scalar field theories. These solutions prove to be interesting as are characterized by the production of mass contributions arising from the nonlinear terms while maintaining a wave-like behavior. So, a quartic massless equation has a nonlinear wave solution with a dispersion relation of a massive wave and a quartic scalar theory gets its mass term renormalized in the dispersion relation through a term depending on the coupling and an integration constant. When spontaneous breaking of symmetry is considered, such wave-like solutions show how a mass term with the wrong sign and the nonlinearity give rise to a proper dispersion relation. These latter solutions do not change the sign maintaining the property of the selected value of the equilibrium state. Then, we use these solutions to obtain a quantum field theory for the case of a quartic massless field. We get the propagator from a first-order correction showing that is consistent in the limit of a very large coupling. The spectrum of a massless quartic scalar field theory is then provided. From this we can conclude that, for an infinite countable number of exact classical solutions, there exist an infinite number of equivalent quantum field theories that are trivial in the limit of the coupling going to infinity.     

Quantization of chiral gauge theories in two-dimensions

It is shown that both abelian and non abelian chiral gauge theories in two dimensions can be made gauge invariant at the quantum level by adding a scalar field. In the bosonized form of the theory, the scalar field appears in a gauged Wess-Zumino action. The current algebra of the extended abelian theory is shown to be free of anomalous terms.     

Cosmological perturbations and quantum fields in curved space

We identify the quantum theory of cosmological perturbations with the quantum field theory in curved spacetime with emphasis on its field concept. We materialize this idea by using a coherent state as a quantum analogue of a nontrivial classical field configuration. We present analytic results in a de Sitter universe for the massless and massive minimal free scalar fields. Some new features on the spectrum of perturbations are obtained for the massive case. We also show how such quantum field theories can be derived from quantum gravity using the semiclassical approximation. A physical degree of freedom is picked up from three scalar perturbations in the quantum gravity scalar system and its Schrödinger equation is derived. Peculiar features of quantum fields at imaginary time and its possible implications on boundary conditions for the wave function of the universe are also discussed.     

On the orthonormalization of generalized free Fermi-field-functionals

Dynamics of quantum field theory can be formulated by functional equations. To develop a complete functional quantum theory the physical information has to be given by functional operations only. In order to calculate the global physical observables in the functional map a functional scalar product has to be defined. This has been done in preceding papers by Stumpf. It is shown that the free Fermi fields are orthonormalized with this scalar product.     

Scalar-tetrad theories of gravity

A general theory of gravitation is constructed using a tetrad and a scalar field. The resulting theory, called a scalar-tetrad theory, does not contain Einstein's or the Brans-Dicke theories as special cases. However, there is a range of scalar-tetrad theories with the same post-Newtonian limit as Einstein's theory. Two particular models are interesting because of their simplicity.     

Gravitational Frames and Scalar Field Dynamics

Scalar fields describe interesting phenomena such as Higgs bosons, dark matter and dark energy, and are found to be quite common in physical theories. These fields are susceptible to gravitational forces so that being massless is not enough to remain conformal invariant. They should also be connected directly to the scalar curvature. Because of this characteristics, we investigated the structure and interactions of scalar fields under the conformal transformations. We show how to reduce the quadratic quantum contributions in the single scalar field theory. In the multi-scalar field theories, we analyzed interactions in certain limits. We suggest a new method for stabilizing Higgs bosons.

     

Field Diffeomorphisms and the Algebraic Structure of Perturbative Expansions

We consider field diffeomorphisms in the context of real scalar field theories. Starting from free field theories we apply non-linear field diffeomorphisms to the fields and study the perturbative expansion for the transformed theories. We find that tree-level amplitudes for the transformed fields must satisfy BCFW type recursion relations for the S-matrix to remain trivial. For the massless field theory these relations continue to hold in loop computations. In the massive field theory the situation is more subtle. A necessary condition for the Feynman rules to respect the maximal ideal and co-ideal defined by the core Hopf algebra of the transformed theory is that upon renormalization all massive tadpole integrals (defined as all integrals independent of the kinematics of external momenta) are mapped to zero.     

用于光盘分析的标量衍射理论综述

标量衍射理论是最早用于分析光盘读出光场的理论,它用标量函数描述光场,计算和理解读出过程比较简单。在只读光盘(CD及其兼容类)发展的过程中,它一直扮演着基础理论的角色。综述和比较了1970年以来的一些标量衍射理论,重点讨论了光盘信息符的模型及标量衍射分析方法等。对各种方法的优缺点作了评述,对如何定量描述标量衍射理论在分析高密度光盘方面的局限性问题提出了建议。     

Superspace,dimensional reduction,and stochastic quantization

The equivalence between a 6-dimensional stochastic classical scalar field theory and the corresponding 4-dimensional quantum field theory has been shown to stem from a hidden supersymmetry of the former. This has led to a formulation of quantum field theory in a superspace of 6 commuting and 2 anticommuting dimensions. We study gauge and spinor field theories defined on this superspace, showing that the dimensional reduction is a consequence of the geometry of the superspace, and that the stochastic formalism for gauge theories is a natural consequence of the structure of the superspace theory. This allows us to extend the stochastic formalism to include spinors.     

Heavy fermions in gauge theories: (I). Analysis of a general spinor loop

A general one-loop spinor diagram is analyzed in the coordinate space with an arbitrary number of external scalar, pseudoscalar, vector and axial vector legs. We identify chiral anomalies, and an unambiguous definition of a renormalized spinor loop amplitude in gauge theories is given by studying its symmetry properties. We then study the case when some of fermions carry very large masses compared to external momentum scales. Using a new calculational technique based on Schwinger's proper-time method, we provide the explicit forms of dominant effective local vertices induced by virtual heavy fermions in general spontaneously broken gauge theories. In the sequel to the present paper, these results will be applied to various interesting field theory models.     

A quantitative approach to low-energy quantum chromodynamics

A general method for solving the low-energy spectrum of an infrared unstable field theory is presented. The method involves a strong coupling expansion of the lattice approximation to the theory. Ultimately the results must be continued to zero-coupling constant in accord with the asymptotic freedom of such theories. The method is applied to the pure gauge field (glueball) part of quantum chromodynamics. The spectrum of lowest-lying states consists of a scalar and tensor which are almost degenerate and an axial vector with mass ≈1.6 times the scalar mass.The same procedure applied to the Abelian gauge theory yields unstable results which may indicate the presence of a phase transition.     

CRAVITATION AND SPINOR GAUGE FIELD

Basing on the Lorentz covariance and SO (4, 2) symmetry of Dirac theory, anobvious covariant theory of spinor gauge field is obtained by expanding the Lorentztransformation to general coordinate tranformation and making the SO (4, 2) to belocalized. We have proved that, by the gauge independence, the symmetrygroup is reduced to the localized rotation of Lorentz group in Riemann space automa-tically. So our theory is the natural generalization of Dirac theory in curved space.We have also proved that, the spinor gauge field can not appear in flat space, thenthe existence of spinor gauge field is closely related to the curvature. The differencesbetween our theory and Utiyama and Kibble theories are also discussed, and it is poin-ted out that the so-called scalar property of Dirac wave function in general relativity isa misunderstanding caused by the unobvious covariance of those theories, even inthose theories We can not distinguish what is the genuine gauge. field and what is theeffect of the structure of space. In obvious covariant theory this paradox disappears.