Proper-time Technique Research Articles

On a structure of the one-loop divergences in 4D harmonic superspace sigma-model

We study the quantum structure of four-dimensional {{mathcal {N}}}=2 superfield sigma-model formulated in harmonic superspace in terms of the omega-hypermultiplet superfield omega . The model is described by harmonic superfield sigma-model metric g_{ab}(omega ) and two potential-like superfields L^{++}_{a}(omega ) and L^{(+4)}(omega ). In bosonic component sector this model describes some hyper-Kähler manifold. The manifestly {{mathcal {N}}}=2 supersymmetric covariant background-quantum splitting is constructed and the superfield proper-time technique is developed to calculate the one-loop effective action. The one-loop divergences of the superfield effective action are found for arbitrary g_{ab}(omega ), L^{++}_{a}(omega ), L^{(+4)}(omega ), where some specific analogy between the algebra of covariant derivatives in the sigma-model and the corresponding algebra in the {{mathcal {N}}}=2 SYM theory is used. The component structure of divergences in the bosonic sector is discussed.

Induced effective action in 6D hypermultiplet theory on a vector/tensor background

We consider the six dimensional hypermultiplet, vector and tensor multiplet models in (1,0) harmonic superspace and discuss the corresponding superfield actions. Manifestly a (1,0) supersymmetric procedure of computing the effective action is developed in the framework of the superfield proper-time technique. The leading low-energy contributions to the effective action is calculated.

Induced low-energy effective action in the 6D, N=(1,0) hypermultiplet theory on the vector multiplet background

We consider the six dimensional N=(1,0) hypermultiplet model coupled to an external field of the Abelian vector multiplet in harmonic superspace approach. Using the superfield proper-time technique we find the divergent part of the effective action and derive the complete finite induced low-energy superfield effective action. This effective action depends on external field and contains in bosonic sector all the powers of the constant Maxwell field strength. The obtained result can be treated as the 6D, N=(1,0) supersymmetric Heisenberg-Euler type effective action.

Some remarks on the use of effective Lagrangians in QED and QCD

We discuss in this paper the usefulness of the effective Lagrangians [Formula: see text] of QED and QCD within the one-loop approximation. Instead of calculating [Formula: see text] via complicated computations with Schwinger’s proper-time technique or Feynman graphs, we prefer to employ the energy–momentum tensor and the leading-log model. The advantage is that we do not have to demand the external electromagnetic or color field to be constant. There are also some critical remarks added which cast doubt on the use of [Formula: see text] with covariant constant fields in explaining the nature of the QCD vacuum.

Leading low-energy effective action in the 6D hypermultiplet theory on a vector/tensor background

We consider a six-dimensional (1,0) hypermultiplet model coupled to an external field of vector/tensor system and study the structure of the low-energy effective action of this model. Manifestly a (1,0) supersymmetric procedure of computing the effective action is developed in the framework of the superfield proper-time technique. The leading low-energy contribution to the effective action is calculated.

Photon splitting in the electromagnetic vacuum

Using a proper time technique, the quadratic response tensor (3-point vertex) in the electromagnetic vacuum is derived from which the scattering amplitudes for photon splitting are obtained for arbitrary fields. In the low frequency limit of the nondispersive vacuum, compact expressions for the scattering amplitudes are obtained whereupon two specific limits are evaluated: one in which both fields are weak and the other in which the electric field is weak and $B\ensuremath{\gg}E.$ In the latter limit, for ${E/E}_{\mathrm{cr}}\ensuremath{\sim}{0.01B/B}_{\mathrm{cr}}$ and $B\ensuremath{\gtrsim}{5B}_{\mathrm{cr}},$ a new splitting mode, absent in the pure magnetic case, has a rate exceeding that of the previously dominant pure magnetic $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\perp}}\ensuremath{\Vert}\ensuremath{\Vert}$ splitting mode. At these stronger electric fields, the process of spontaneous pair production becomes important enough to require consideration. Although it is unlikely that neutron stars with $B\ensuremath{\gg}{B}_{\mathrm{cr}}$ and long periods (magnetars) have parallel electric fields of this strength, their progenitors may have. Other candidates include $\ensuremath{\gamma}$-ray bursters and strange stars. The low frequency results were verified using the Heisenberg-Euler Lagrangian approach.

Large mass invariant asymptotics of the effective action

We study the large mass asymptotics of the Dirac operator with a nondegenerate mass matrix m={diag}(m_1,m_2,m_3) in the presence of scalar and pseudoscalar background fields taking values in the Lie algebra of the U(3) group. The corresponding one-loop effective action is regularized by the Schwinger's proper-time technique. Using a well-known operator identity, we obtain a series representation for the heat kernel which differs from the standard proper-time expansion, if m_1\ne m_2\ne m_3. After integrating over the proper-time we use a new algorithm to resum the series. The invariant coefficients which define the asymptotics of the effective action are calculated up to the fourth order and compared with the related Seeley-DeWitt coefficients for the particular case of a degenerate mass matrix with m_1=m_2=m_3.

Inverse mass expansion of the one-loop effective action

A method is described for the development of the one-loop effective action expansion as an asymptotic series in inverse powers of the fermion mass. The method is based on the Schwinger-DeWitt proper-time technique, which allows for loop particles with non-degenerate masses. The case with SU(2)xSU(2) as the symmetry group is considered. The obtained novel series generalizes the well-known Schwinger-De Witt inverse mass expansion for equal masses, and is chiral invariant at each order. We calculate the asymptotic coefficients up to fifth order and clarify their relationship with the standard Seeley-DeWitt coefficients.

Magnetic photon splitting: TheS-matrix formulation in the Landau representation

Calculations of reaction rates for the third-order QED process of photon splitting in strong magnetic fields traditionally have employed either the effective Lagrangian method or variants of Schwinger's proper-time technique. Recently, Mentzel, Berg and Wunner (1994) presented an alternative derivation via an S-matrix formulation in the Landau representation. Advantages of such a formulation include the ability to compute rates near pair resonances above pair threshold. This paper presents new developments of the Landau representation formalism as applied to photon splitting, providing significant advances beyond the work of Mentzel et al. by summing over the spin quantum numbers of the electron propagators, and analytically integrating over the component of momentum of the intermediate states that is parallel to field. The ensuing tractable expressions for the scattering amplitudes are satisfyingly compact, and of an appearance familiar to S-matrix theory applications. Such developments can facilitate numerical computations of splitting considerably both below and above pair threshold. Specializations to two regimes of interest are obtained, namely the limit of highly supercritical fields and the domain where photon energies are far inferior to that for the threshold of single-photon pair creation. In particular, for the first time the low-frequency amplitudes are simply expressed in terms of the Gamma function, its integral and its derivatives. In addition, the equivalence of the asymptotic forms in these two domains to extant results from effective Lagrangian/proper-time formulations is demonstrated.

Photon splitting in strong magnetic fields:S-matrix calculations

The $S$-matrix approach to the treatment of photon splitting in a magnetized vacuum, with the electron propagators expressed in the Landau representation, is discussed critically. Although the analytic results of Mentzel, Berg and Wunner are confirmed, we propose that their available numerical results may be subject to two previously unidentified sources of error associated with the sum over principal quantum number $n$, leading to spurious contributions to the amplitude, and the extremely slow convergence of the sum for weak fields. It is shown how the sums may be rearranged to avoid the spurious contributions. If the Euler-Maclaurin summation formula is used to evaluate the infinite sums over $n$, the $S$-matrix approach then reproduces results derived by the effective Lagrangian and proper-time techniques in the weak-field, low-frequency limit. This method gives reliable results, for $B\ensuremath{\gtrsim}0.01$ and $\ensuremath{\omega}\ensuremath{\lesssim}0.1,$ that reproduce those obtained by proper-time techniques. The $S$-matrix approach simplifies in the strong-field limit, $B\ensuremath{\gg}1$, where the sum over $n$ converges rapidly. Our results show that the branching ratio for the splittings $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\perp}}\ensuremath{\perp}\ensuremath{\perp}$ and $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\perp}}\ensuremath{\parallel}\ensuremath{\parallel}$ decreases from its known value $\ensuremath{\sim}3.4$ for $B\ensuremath{\ll}1$ towards zero for $B\ensuremath{\gg}1.$ For weak fields the $S$-matrix approach is unnecessarily cumbersome, and future numerical work should be based on the alternative approaches.

Numerical evaluation of magnetic photon splitting rates via a proper-time technique

The results of our numerical computation of magnetic photon splitting rates according to the proper-time formulation developed by Stoneham are presented in this paper. Calculations were performed for both the total rate of splitting and the differential distributions for the polarization mode ⊥ → ∥∥ of splitting. Analytic asymptotic limits obtainable from the triple integral expressions of Stoneham's formalism are also presented, and these are reproduced by the full computation of the integrals. The rates produced here agree with numerous previous analyses of photon splitting but fall somewhat below the S-matrix calculation of Wilke and Wunner. The numerical determination of these rates is of great use to current topical models of gamma-ray pulsars and magnetar scenarios for soft gamma repeaters.

Dimensional regularization and the self-energy of a massive quark in a cavity

Self-energies of massive quarks are calculated in the framework of cavity QCD to order αs for the excited modes of a spherical cavity. The calculation, closely related to Schwinger's proper time technique, is based on the ms dimensional regularization scheme in free space.

Proper-time technique in (1, 0) superspace

Abstract The proper-time technique in (1, 0) superspace is developed for analyzing the effective action structure of ghost and matter superfields. The critical parameters for the (p, q) superstrings with and without leftons and rightons are found.

Background-field and Schwinger-DeWitt proper-time algorithm for the low-energy effective-field-theory action.

For a quantum field theory consisting of fields with vastly different mass scales, we develop, within the one-loop approximation, a simple algorithm which allows the construction of the low-energy effective Lagrangian for light particles to any desired order in inverse powers of heavy masses. Nontrivial generalizations of the background-field method and Schwinger-DeWitt proper-time technique are given in connection with finding effective local vertices induced from ``mixed'' loop diagrams, i.e., from one-loop diagrams involving heavy- and light-particle internal lines simultaneously. The factorization theory concerning virtual heavy-particle effects finds a simple realization in our procedure. We illustrate our algorithm in the context of the most general renormalizable four-dimensional scalar field theory in flat space.

Chiral fermion determinants

The one-loop effective action for massive chiral fermions coupled to scalar and vector fields is evaluated in the low energy limit using proper-time techniques. The relationship between the Bardeen anomaly, Pauli-Villars regularisation and Goldstone-Wilczek currents is discussed, and a general form for the abnormal parity effective action, which incorporates the Wess-Zumino term, is derived.

Gradient expansion of the one-loop effective Lagrangian for chiral fermions

Using the proper-time technique we calculate the one-fermion-loop contributions in four and six derivatives to the effective Lagrangian for theSU(2)xSU(2) non-linear σ-model.

One-loop effective potentials in quantum electrodynamics

The author investigates the one-loop effective potential for some typical external fields in electrodynamics, in particular for a constant magnetic field and a laser field. The treatment is based on the corresponding Green function as explicit functional of the prescribed field. Schwinger's source- and proper-time techniques are used throughout.

Low-Energy Theorem forγ→3π

A low-energy theorem relating $\ensuremath{\gamma}\ensuremath{\rightarrow}3\ensuremath{\pi}$ to ${\ensuremath{\pi}}^{0}\ensuremath{\rightarrow}2\ensuremath{\gamma}$ is derived by using anomalous Ward identities and by using Schwinger's proper-time technique. We discuss the theoretical significance of this low-energy theorem. In particular, the theorem is meaningful only if the partially conserved axial-vector current anomaly is in fact responsible for the decay ${\ensuremath{\pi}}^{0}\ensuremath{\rightarrow}2\ensuremath{\gamma}$.