The Higher Derivative Expansion of the Effective Action by the String Inspired Method, II

Fliegner, D.; Haberl, P.; Schmidt, Michael G.; Schubert, Christian

doi:10.1006/aphy.1997.5778

Cited by 87 publications

(111 citation statements)

References 61 publications

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“…In [31] they present the functional trace of the first six heat kernel coefficients for this case in flat spacetime, reduced to a so-called minimal basis. It should be possible to compare their result to the sixth heat kernel coefficient as presented here, after taking its trace and integrating it.…”

Section: Discussionmentioning

confidence: 99%

Index-free heat kernel coefficients

Ven¹

1998

Class. Quantum Grav.

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Using index-free notation, we present the diagonal values a j (x, x) of the first five heat kernel coefficients a j (x, x ′ ) associated with a general Laplace-type operator on a compact Riemannian space without boundary. The fifth coefficient a 5 (x, x) appears here for the first time. For the special case of a flat space, but with a gauge connection, the sixth coefficient is given too. Also provided are the leading terms for any coefficient, both in ascending and descending powers of the Yang-Mills and Riemann curvatures, to the same order as required for the fourth coefficient. These results are obtained by directly solving the relevant recursion relations, working in Fock-Schwinger gauge and Riemann normal coordinates. Our procedure is thus noncovariant, but we show that for any coefficient the 'gauged' respectively 'curved' version is found from the corresponding 'non-gauged' respectively 'flat' coefficient by making some simple covariant substitutions. These substitutions being understood, the coefficients retain their 'flat' form and size. In this sense the fifth and sixth coefficient have only 26 and 75 terms respectively, allowing us to write them down. Using index-free notation also clarifies the general structure of the heat kernel coefficients. In particular, in flat space we find that from the fifth coefficient onward, certain scalars are absent. This may be relevant for the anomalies of quantum field theories in ten or more dimensions.

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Section: Discussionmentioning

confidence: 99%

Index-free heat kernel coefficients

Ven¹

1998

Class. Quantum Grav.

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“…In reference [23] they are given up to O 8 ; with the new world-line method they can easily be calculated to even higher order. For n > d/2 the t-integral gives Γ(n − d/2).…”

Section: The Heat Kernel Expansionmentioning

confidence: 99%

Perturbative contributions to the electroweak interface tension

Kripfganz

Laser

Schmidt

1997

Zeitschrift f�r Physik C Particles and Fields

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The main perturbative contribution to the free energy of an electroweak interface is due to the effective potential and the tree level kinetic term. The derivative corrections are investigated with one-loop perturbation theory. The action is treated in derivative, in heat kernel, and in a multi local expansion. The massive contributions turn out to be well described by the Z-factor. The massless mode, plagued by infrared problems, is numerically less important. Its perturbatively reliable part can by calculated in derivative expansion as well. A self consistent way to include the Z-factor in the formula for the interface tension is presented.

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“…This is what we set out to find, and we see that it arose through the divergence of the derivative expansion. I stress that this exponential correction is not accessible from low orders of the derivative expansion, such as those studied in [8][9][10]. But the situation is even more interesting than this result (17) suggests.…”

mentioning

confidence: 85%

“…For a general inhomogeneous background field we need some sort of approximation to determine the effective action. One such approximation is the derivative expansion [7][8][9][10], in which one assumes that F µν is "slowly varying", so that one can make the following formal expansion…”

mentioning

confidence: 99%

“…First, the derivative expansion is not actually a series. This is because as one goes to higher orders, there is a rapid proliferation of new terms that do not have a counterpart at previous orders [8][9][10]. Second, it is extremely difficult to calculate any of these terms at very high order, so we could not expect anyway to observe any asymptotic behaviour of the expansion coefficients.…”

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confidence: 99%

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QED effective actions in inhomogeneous backgrounds: Summing the derivative expansion

Dunne¹

2001

AIP Conference Proceedings

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Abstract. The QED effective action encodes nonlinear interactions due to quantum vacuum polarization effects. While much is known for the special case of electrons in a constant electromagnetic field (the Euler-Heisenberg case), much less is known for inhomogeneous backgrounds. Such backgrounds are more relevant to experimental situations. One way to treat inhomogeneous backgrounds is the "derivative expansion", in which one formally expands around the soluble constant-field case. In this talk I use some recent exactly soluble inhomogeneous backgrounds to perform precision tests on the derivative expansion, to learn in what sense it converges or diverges. A closely related question is to find the exponential correction to Schwinger's pair-production formula for a constant electric field, when the electric background is inhomogeneous.This talk is concerned with the one-loop QED effective action [1,2]:Here D µ = ∂ µ + ieA µ is the covariant derivative, and so S[A] is a functional of the classical background field A µ (x). The effective action is the generating functional for one-fermion-loop Green's functions, which describe the nonlinear QED effects to this order. Ideally, one would like to know S[A] for any field A µ (x), but this is not feasible. However, for the special case where the field strength tensor, F µν = ∂ µ A ν − ∂ ν A µ , is uniform, the effective action can be evaluated in closed form [3][4][5]:Here the first term is the familiar classical Maxwell action, while the next term gives the leading quantum correction, which is quartic in the field strengths. The fine structure constant α = e 2 4π in these units. All higher terms in the expansion (2) are known explicitly [3][4][5]. It can also be shown that when the background field is a constant electric field of strength E, the effective action has an exponentially small imaginary part

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The Higher Derivative Expansion of the Effective Action by the String Inspired Method, II

Cited by 87 publications

References 61 publications

Index-free heat kernel coefficients

Index-free heat kernel coefficients

Perturbative contributions to the electroweak interface tension

QED effective actions in inhomogeneous backgrounds: Summing the derivative expansion

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