Intrinsic Loop Regularization and Renormalization in QED

We show how to regularize and renormalize the QED at the one-loop order by means of the intrinsic loop regularization method proposed by the authors. All the results are the same as those derived by means of other regularization methods.     

Intrinsic Loop Regularization and Renormalization in φ4 Field Theory

We find that there exist certain intrinsic relations between the divergent diagrams and the convergent ones at the same loop order in some renormalizable quantum field theories. Whereupon we propose a new method for regularization and renormalization of those divergent diagrams. ,We name it the intrinsic loop regularization. In this paper, we take the renormalized φ⁴ theory up to the second order of the coupling constant as an example to present this method.     

Spin-2 Quantum Gauge Theories and Perturbative Gauge Invariance

In the framework of causal perturbation theory we analyze the gauge structure of a massless self-interacting quantum tensor field. We look at this theory from a pure field theoretical point of view without assuming any geometrical aspect from general relativity. To first order in the perturbation expansion of the S-matrix we derive necessary and sufficient conditions for such a theory to be gauge invariant, by which we mean that the gauge variation of the self-coupling with respect to the gauge charge operator Q is a divergence in the sense of vector analysis. The most general trilinear self-coupling of the graviton field turns out to be the one derived from the Einstein–Hilbert action plus divergences and coboundaries.     

Reparametrization Invariance as Gauge Symmetry

Reparametrization invariance treated as a gaugesymmetry shows some specific peculiarities. We studythese peculiarities both from a general point of viewand by concrete examples. We consider the canonical treatment of reparametrization-invariantsystems in which one fixes the gauge on the classicallevel by means of time-dependent gauge conditions. Insuch an approach one can interpret different gauges as different reference frames. We discuss therelation between different gauges and the problem ofgauge invariance in this case. Finally, we establish ageneral structure of reparametrizations and itsconnection with the zero-Hamiltonian phenomenon.     

Quantum General Invariance and Loop Gravity

A quantum physical projector is proposed for generally covariant theories which are derivable from a Lagrangian. The projector is the quantum analogue of the integral over the generators of finite one-parameter subgroups of the gauge symmetry transformations which are connected to the identity. Gauge variables are retained in this formalism, thus permitting the construction of spacetime area and volume operators in a tentative spacetime loop formulation of quantum general relativity.     

Color Gauge Invariance in Hard Processes

Within the theoretical framework which we apply, a suggested origin for single-spin asymmetries is the presence of gauge links in transverse momentum-dependent distribution functions. Recently we found new gauge-link structures in a number of hard processes. These structures need to be considered in the evolution of parton distribution functions and for establishing factorization.     

Intrinsic Regularization Method in QCD

There exist certain intrinsic relations between the ultraviolet divergent graphs and the convergent ones at the same loop order in renormalizable quantum field theories. Whereupon we may establish a new method, the intrinsic regularization method, to regularize those divergent graphs. In this paper, we apply this method of QCD at the one-loop order. It turns out to be satisfactory: The gauge invariance is preserved manifestly and the results are the same as those derived by means of other regularization methods.     

Intrinsic Regularization Approach to Chiral Anomalies

With the help of the intrinsic regularization method, we present a new method which enables us to calculate the chiral anomalies in a much natural and self-consistent way. By checking Ward iden tities related to various.diagrams involving anomaly, we analyze anomalies in the σ model, in Abelian gauge theory, and in non-Abelian gauge theory as well. Our calculations prove to naively preserve all vector Ward identities and accordingly reproduce the famous ABJ-anomaly with no need of introducing any counterterms.     

On Gauge Invariant Regularization of Fermion Currents

We compare Schwinger and complex powers methods to construct regularized fermion currents. We show that, although both of them are gauge invariant, they are not always yield the same result.     

LETTER: Gauge Invariance of Complex General Relativity

In this paper it is implemented how to make compatible the boundary conditions and the gauge fixing conditions for complex general relativity written in terms of Ashtekar variables using the approach of Ref. [1]. Moreover, it is found that at first order in the gauge parameters, the Hamiltonian action is (on shell) fully gauge-invariant under the gauge symmetry generated by the first class constraints in the case when spacetime has the topology % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWefv3ySLgznf% gDOfdaryqr1ngBPrginfgDObYtUvgaiuaacqWFZestcqWFaCFpcqGH% 9aqpcaWGsbGaey41aq7exLMBbXgBd9gzLbvyNv2CaeXbbjxAHXgiv5% wAJ9gzLbsttbacgaGaa43Odaaa!52EB!\[\mathcal{M} = R \times \Sigma \] = R × and has no boundary. Thus, the statement that the constraints linear in the momenta do not contribute to the boundary terms is right, but only in the case when has no boundary.     

Electromagnetic Gauge Invariance of Bound State Annihilation Amplitudes

Gauge invariance of the electromagnetic vertex of bound state annihilation matrix elements is demonstrated by using Ward identities and Dyson equations. This problem is also discussed when potential assumption of the B-S kernel and the approximation of neglecting photon lines hung on closed fermion loop are considered. Under these two approximations, the simplified matrix element expression is given, which preserves the gauge invariance. The reliability of using zero point wave function approximation in cc, bb system is also discussed.     

Gauge Invariance of Sedeonic Equations for Massive and Massless Fields

In the present paper we discuss the gauge invariance of generalized second-order and first-order wave equations for massive and massless fields based on sedeonic space-time operators and sedeonic wave functions.     

Electrodynamics of Superconductors as a Consequence of Local Gauge Invariance

The electromagnetic properties of superconductors are studied in the framework of a quantum gauge-invariant theory. The formulation is developed in the generalized pair approximation which preserves the Ward-Takahashi identities. The macroscopic equations which regulate current and electromagnetic fields are derived by means of the boson transformation method. Comparison with previous works is reported.     

Gauge Invariance of Banks-Peskin differential forms (flat background)

We discuss some aspects of the gauge invariance of Banks-Peskin differential forms on a flat background.     

Localization via Automorphisms of the CARs: Local Gauge Invariance

The classical matter fields are sections of a vector bundle E with base manifold M, and the space L ²(E) of square integrable matter fields w.r.t. a locally Lebesgue measure on M, has an important module action of C_b^￥(M){C_b^\infty(M)} on it. This module action defines restriction maps and encodes the local structure of the classical fields. For the quantum context, we show that this module action defines an automorphism group on the algebra of the canonical anticommutation relations, CAR(L ²(E)), with which we can perform the analogous localization. That is, the net structure of the CAR(L ²(E)) w.r.t. appropriate subsets of M can be obtained simply from the invariance algebras of appropriate subgroups. We also identify the quantum analogues of restriction maps, and as a corollary, we prove a well–known “folk theorem,” that the CAR(L ²(E)) contains only trivial gauge invariant observables w.r.t. a local gauge group acting on E.     

Further Study on U(1) Gauge Invariance Restoration

To further investigate the applicability of the projection scheme for eliminating the unphysical divergence s/m_e² due to U(1) gauge invariance violation, we study the process e^- + W⁺ → e^- + t + b which possesses advantages of simplicity and clearness. Our study indicates that the projection scheme can indeed eliminate the unphysical divergence s/m_e² caused by the U(1) gauge invariance violation and the scheme can be applied to very high energy region.     

Principal Loop Bundles: Toward Nonassociative Gauge Theories

We introduce a nonassociative gauge field theory with nonassociative symmetries. The approach is based on the nonassociative generalization of principal bundles theory.     

Gauge Invariance of a Time-Dependent Harmonic Oscillator in Magnetic Dipole Approximation

A manifestly gauge-invariant formulation of non-relativistic quantum mechanics is applied to the case of time-dependent harmonic oscillator in the magnetic dipole approximation. A general equation for obtaining gauge-invariant transition probability amplitudes is derived.