Trace anomaly of the stress-energy tensor for massless vector particles propagating in a general background metric

We reanalyze the problem of regularization of the stress-energy tensor for massless vector particles propagating in a general background metric, using covariant point separation techniques applied to the Hadamard elementary solution. We correct an error, pointed out by Wald, in the earlier formulation of Adler, Lieberman, and Ng, and find a stress-energy tensor trace anomaly agreeing with that found by other regularization methods.     

Pion production by neutral currents in neutrino-nucleon collisions

It is argued that the apparent arbitrariness of the “anomaly” in Fujikawa's approach should be placed into the context of the regularization of the theory not just the regularization of the anomaly. When the theory is regularized at the level of the action the consistent anomaly arises. The converse also holds, namely that if the anomaly is not consistent then the regulator employed does not, by itself, regulate the theory at the level of the action. The criterion that the regularization presription be given at the outset is advocated, and a discussion of results of various two-dimensional models given.     

Dispersive derivation of the trace anomaly

We present a simple derivation of the one-loop trace anomaly in spinor QED through dispersion relations, avoiding completely any ultraviolet regularization. The anomaly can be expressed as a convergent sum rule for the imaginary part of a relevant formfactor. In the massless limit, the imaginary part produces a delta-function singularity at zero external momentum squared. Such a treatment reveals an “infrared face” of the trace anomaly, in striking similarity with the well-known case of the axial anomaly.     

Calculation of the color axial anomaly on the basis of the gauge-invariant spatial point-splitting regularization

The nonsinglet axial anomaly is calculated by employing Schwinger’s point-splitting regularization of the interaction between fermions and a non-Abelian gauge field. This method makes it possible to obtain a covariant expression for the anomaly directly from the effective action for the gauge field. Previously, the anomaly under study was calculated by many other methods. However, all calculations based on the point-splitting regularization (from the pioneering study of Bardeen in 1969) involve a number of intermediate steps and subtractions of specially chosen polynomials in the field.     

Path-integral formulation of conformal anomalies

We present a path-integral formulation of conformal anomalies and point out an intimate interplay of the local Poincaré anomaly and the dilatational anomaly. A key observation in our approach is that the algorithm of the path-integral formulation has natural foundation within the zeta-function regularization scheme. This observation shows us how to treat nonlinear systems as well as higher-order anomalies and suggests a way to understand the Adler-Bardeen theorem for chiral anomalies within the path-integral approach.     

Anomalies in supergravity

There has been much interest recently in the problem of anomalies in field theory. This is a consequence of recent work on the regularization of stress tensors, and of renewed interest in the axial vector anomaly. In this paper, I shall present a derivation of both the trace anomaly and the axial vector anomaly for the spin-$\text{3}\text{2}$ Majorana field using a zeta function regularization procedure. This result is also of interest in supergravity and extended supergravity.     

Gauge Anomaly in 'Arbitrary Even Dimensions from Stochastic Quantization

The stochastic quantization method is applied to evaluate gauge anomaly in arbitrary even dimensions. Stochastic regularization plays a distinct role in our method. The. anomaly structure of the anomalous model is studied.     

A REGULARIZATION SCHEME FOR OBTAINING BARDEEN ANOMALY

A new regularization operator, (e^{-Ø_L(X)Ø_R(X)/M2}+e^{-Ø_R(X)Ø_L(X)/M2})|_M→∞’ is proposed to calculate the variation of the fermion path-in-tegral measure under a chiral transformation, and the normal anomaly, i.e.Bardeen anomaly, is obtained .in this paper. Moreover, the non-Abelian anomaly of the cosec pure gauge fields is calcula-ted by means of this regularization operator.The corresponding results in Minkowski space can readily be obtained in the principal value integral.     

One loop vacuum polarization in a locally de Sitter background

We compute the one loop vacuum polarization from massless, minimally coupled scalar QED in a locally de Sitter background. Gauge invariance is maintained through the use of dimensional regularization, whereas conformal invariance is explicitly broken by the scalar kinetic term as well as through the conformal anomaly. A fully renormalized result is obtained. The one loop corrections to the linearized, effective field equations do not vanish when evaluated on-shell. In fact the on-shell one loop correction depends quadratically on the inflationary scale factor, similar to a photon mass. The contribution from the conformal anomaly is insignificant by comparison.     

On the Peierls transition in exactly soluble models

We propose two simplified models in order to discuss the origin of the Peierls transition in one-dimensional systems. For the finite-mode model we show that the thermodynamic properties are described correctly by the most general mean field approximation. But the discussion of the zero-bandwidth model suggests that this result is probably due to the fact of taking into account only a finite number of phonon modes even in the thermodynamic limit.     

Zeta function regularization, anomaly and complex mass term

If zeta function regularization is used and a complex mass term considered for fermions, the phase does not appear in the fermion determinant. This is not a drawback of the regularization, which can recognize the phase through source terms, as demonstrated by the anomaly equation which is explicitly derived here for a complex mass term.     

Renormalized energy-momentum tensor of λ Φ<Superscript>4</Superscript> theory in curved space-time

Divergenceless expression for the energy-momentum tensor of scalar field is obtained using the momentum cut-off regularization technique. We consider a scalar field with quartic self-coupling in a spatially flat (3+1)-dimensional Robertson-Walker space-time, having arbitrary mass and coupled to gravity. As special cases, energy-momentum tensor for conformal and minimal coupling are also obtained. The energy-momentum tensor is observed to exhibit trace anomaly in curved space-time     

Exact calculation of the Fermion determinant in chiral QCD2 reflecting the full regularization dependence

The fermion determinant of non-abelian anomalous gauge theory in two space-time dimensions is computed using the path-integral approach. The regularization dependence of the fermion determinant is worked out. Apart from a regularization dependentA ² term, the fermion determinant contains a Wess-Zumino-Witten anomaly functional.     

手征QCD2模型的有效拉氏量和质量生成

利用路径积分方法,研究了(1+1)维带γ₅耦合的规范理论。通过进行一非阿贝耳手征变量变换和选择更一般的正规化算子,精确解出了费密子行列式,证明了理论中可以存在玻色子的质量生成机制。除了一质量项外,得到的解也包含有一规范化的Wess-Zumino-Witten反常作用量泛函和一些别的非定域项。 关键词：     

Point‐splitting Regularization of Composite Operators and Anomalies

The point‐splitting regularization technique for composite operators is discussed in connection with anomaly calculation. We present a pedagogical and self‐contained review of the topic with an emphasis on the technical details. We also develop simple algebraic tools to handle the path ordered exponential insertions used within the covariant and non‐covariant version of the point‐splitting method. The method is then applied to the calculation of the chiral, vector, trace, translation and Lorentz anomalies within diverse versions of the point‐splitting regularization and a connection between the results is described. As an alternative to the standard approach we use the idea of deformed point‐split transformation and corresponding Ward‐Takahashi identities rather than an application of the equation of motion, which seems to reduce the complexity of the calculations.     

Gauged Goldstone boson effective action from direct integration of bardeen anomaly

We derive the effective action which describes the anomalous Goldstone boson interactions in the presence of external flavour SU(N)_L×SU(N)_R gauge fields, by a direct integration of the Bardeen anomaly. Through comparison with other results, we are able to elucidate the relationship between anomalies based on different regularization schemes. We also give a compact representation of the anomalous part of the fermionic determinant allowing for a simpler rederivation of our results.