The two-loop renormalization of the gauge coupling and the scalar potential for an arbitrary renormalizable field theory

For any renormalize field theory in four dimensions we obtain the two-loop counterterms for the gauge coupling and the scalar potential, using the background-field method. The calculation was performed in two different subtraction schemes: one is the ordinary dimensional regularization, the other is the so-called dimensional reduction scheme. We show that already at the two-loop level differences occur for the scalar coupling-constants. Only dimensional reduction preserves supersymmetry up to this level.     

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.     

Some remarks on zeta function regularization in curved space-times

The question of to what extent zeta function regularization respects the invariances of a quantum field theory in a background gravitational field is investigated. It is shown that zeta function regularization provides a generalization to curved space-time of analytic propagator regularization which is known not to respect gauge invariance. Furthermore, a study of the regularized stress tensor of a conformally invariant scalar field indicates that both conformai and general coordinate invariance are violated.     

Quantum Gravitational Contributions to Gauge Field Theories

We revisit quantum gravitational contributions to quantum gauge field theories in the gauge condition independent Vilkovisky-DeWitt formalism based on the background field method.With the advantage of Landau-DeWitt gauge,we explicitly obtain the gauge condition independent result for the quadratically divergent gravitational corrections to gauge couplings.By employing,in a general way,a scheme-independent regularization method that can preserve both gauge invariance and original divergent behavior of integrals,we show that the resulting gauge coupling is power-law running and asymptotically free.The regularization scheme dependence is clarified by comparing with results obtained by other methods.The loop regularization scheme is found to be applicable for a consistent calculation.     

Diagrammatic methods in phase-space regularization

Using the scalar prototype and gauge theory as the simplest possible examples, diagrammatic methods are developed for the recently proposed phasespace form of continuum regularization. A number of one-loop and all-order applications are given, including general diagrammatic discussions of the no-growth theorem and the uniqueness of the phase-space stochastic calculus. The approach also generates an alternate derivation of the equivalence of the large-β phase-space regularization to the more conventional coordinate-space regularization.     

Gravitational Gauge Interactions of Scalar Field

Quantum gauge theory of gravity is formulated based on gauge principle. Because the Lagrangian has strict local gravitational gauge symmetry, gravitational gauge theory is a perturbatively renormalizable quantum theory. Gravitational gauge interactions of scalar field are studied in this paper. In quantum gauge theory of gravity, scalar field minimal couples to gravitational field through gravitational gauge covariant derivative. Comparing the Lagrangian for scalar field in quantum gauge theory of gravity with the corresponding Lagrangian in quantum fields in curved space-time, the definition for metric in curved space-time in geometry picture of gravity can be obtained, which is expressed by gravitational gauge field. In classical level, the Lagrangian and Hamiltonian approaches are also discussed.     

Nonlocal theory of the electromagnetic and weak interactions with W-boson

The perturbation theory of the electromagnetic and weak interactions is considered in the framework of nonlocal theory. A hypothesis is proposed that the photon and neutrino fields are connected with the charged local fields of the electrons, muons, and W bosons in the nonlocal way.The definite intermediate regularization procedure is introduced that the S matrix is finite, unitary, causal, gauge invariant in perturbation theory when regularization is moved off. The interaction Lagrangian contains no infinite counter terms and the S matrix is finite without any infinite renormalizations.     

Two-loop renormalization group equations in a general quantum field theory: (III). Scalar quartic couplings

The two-loop β-functions for the scalar quartic couplings are computed in a general renormalizable quantum field theory with scalar, $\text{spin}\text{-}\text{1}\text{2}$, and (vector) gauge fields associated with a general gauge group G, using dimensional regularization and modified minimal subtraction (^?MS). A more explicit form is given for the two-loop β-function of the quartic coupling of the Higgs doublet in the minimal QCD electroweak theory based on SU(3) × SU(2) × U(1).     

Gravitational Gauge Interactions of Scalar Field

Quantum gauge theory of gravity is formulated based on gauge principle. Because the Lagrangian hasstrict local gravitational gauge symmetry, gravitational gauge theory is a perturbatively renormalizable quantum theory.Gravitational gauge interactions of scalar field are studied in this paper. In quantum gauge theory of gravity, scalar fieldminimal couples to gravitational field through gravitational gauge covariant derivative. Comparing the Lagrangian forscalar field in quantum gauge theory of gravity with the corresponding Lagrangian in quantum fields in curved space-time, the definition for metric in curved space-time in geometry picture of gravity can be obtained, which is expressedby gravitational gauge field. In classical level, the Lagrangian and Hamiltonian approaches are also discussed.     

Ward identities and chiral anomalies in stochastic quantization

We derive the Ward identities (WI) for vector and axial currents in stochastic quantization at any given fictitious time t. This is achieved through a functional integral representation of the fermionic Langevin equations. The currents for this effective field theory differ in general from the naive ones; if stochastic regularization is used they are both conserved. We establish the connection between those WI and the field theory ones. The physical source of chiral anomalies is identified: these result from the quantum fluctuations in the fictitious time evolution of the system. In this context, both a traditional regularization method (Pauli-Villars) and stochastic regularization are considered.     

Nonlocal stochastic model for the free scalar field theory

The free scalar field is investigated within the framework of the Davidson stochastic model and of the hypothesis on space-time stochasticity. It is shown that the resulting Markov field obtained by averaging in this space-time is equivalent to a nonlocal Euclidean Markov field with the times scaled by a common factor which depends on the diffusion parameter. Our result generalizes Guerra and Ruggiero's procedure of stochastic quantization of scalar fields. On the basis of the assumption about unobservability of in quantum field theory, the Efimov nonlocal theory is obtained from Euclidean Markov field with form factors of the class of entire analytical functions.     

On the invariant regularization of the standard model

We show that the gauge invariant regularization of the Standard Model proposed by Frolov and Slavnov describes a nonlocal theory with quite simple Lagrangian.     

Implicit regularization beyond one-loop order: gauge field theories

We extend a constrained version of implicit regularization (CIR) beyond one-loop order for gauge field theories. In this framework, the ultraviolet content of the model is displayed in terms of momentum loop integrals order by order in perturbation theory for any Feynman diagram, while the Ward–Slavnov–Taylor identities are controlled by finite surface terms. To illustrate, we apply CIR to massless abelian gauge field theories (scalar and spinorial QED) to two-loop order and calculate the two-loop beta-function of spinorial QED. PACS  11.10.Gh; 11.15.Bt; 11.15.-q     

Aspects of the derivative coupling model in four dimensions

A concise discussion of a $3+1$ -dimensional derivative coupling model, in which a massive Dirac field couples to the four-gradient of a massless scalar field, is given in order to elucidate the role of different concepts in quantum field theory like the regularization of quantum fields as operator-valued distributions, correlation distributions, locality, causality, and field operator gauge transformations.     

Nonlocal Scalar Electrodynamics from Chern-Simons Theory

The theory of a complex scalar interacting with a pure Chern-Simons gauge field is quantized canonically. Dynamical and nondynarnical variables are separated in a gaugeindependent way. In the physical subspace of the full Hilbert space, this theory reduces to a pure scalar theory with nonlocal interaction. Several scattering processes are studied and the cross sections are calculated.     

Stochastic quantization of gauge theories

The equivalence between a scalar quantum field theory in D dimensions and its classical counterpart in D + 2 dimensions which is coupled to an external random source with Gaussian correlations was observed by previous authors. This stochastic quantization is extended to gauge theories. The proof exploits the supersymmetry formalism suggested by Parisi and Sourlas.     

Intrinsic Loop Regularization and Gauge Invariance

A regularization method named the intrinsic loop regularization is proposed by WANG and GUO. Here, we apply it to the quantum electrodynamics, we find this method can remain gauge invariance very well.     

Renormalization of an abelian gauge theory in stochastic quantization

The renormalization of an abelian gauge field coupled to a complex scalar field is disccused in the stochastic quantization method. The supper space formulation of the stochastic quantization method is used to derived the Ward Takahashi identities assocoated with supersymmetry. These Ward Takahashi identities together with previously derived Ward Takahshi identities associated with gauge invariance are shown to be sufficient to fix all the renormalization constant in temrs of scaling of the fields and of the parameters appearing in the stochastic theory.