# An exact QED3+1 effective action

@article{Dunne1997AnEQ, title={An exact QED3+1 effective action}, author={Gerald V. Dunne and Theodore M. Hall}, journal={Physics Letters B}, year={1997}, volume={419}, pages={322-325} }

Abstract We compute the exact QED 3+1 effective action for fermions in the presence of a family of static but spatially inhomogeneous magnetic field profiles. An asymptotic expansion of this exact effective action yields an all-orders derivative expansion, the first terms of which agree with independent derivative expansion computations. These results generalize analogous earlier results by Cangemi et al. in QED 2+1 .

#### 21 Citations

Planar QED in Magnetic or Electric Solitonic Backgrounds

- Physics
- 1997

We review the resolvent technique for computing the effective action in planar QED. For static magnetic backgrounds the effective action yields (minus) the effective energy of the fermions, while for…

QED effective actions in inhomogeneous backgrounds: Summing the derivative expansion

- Physics
- 2000

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…

One-loop effective actions in shape-invariant scalar backgrounds

- Physics
- 2001

Abstract The field-theoretic one-loop effective action in a static scalar background depending nontrivially on a single spatial coordinate is related, in the proper-time formalism, to the trace of…

An addendum to the Heisenberg-Euler effective action beyond one loop

- Physics
- 2016

A bstractWe study the effective interactions of external electromagnetic fields induced by fluctuations of virtual particles in the vacuum of quantum electrodynamics. Our main focus is on these…

Quantum diffusion of magnetic fields in a numerical worldline approach

- Physics
- 2001

Abstract We propose a numerical technique for calculating effective actions of electromagnetic backgrounds based on the worldline formalism. As a conceptually simple example, we consider scalar…

Heisenberg-Euler Effective Lagrangians : Basics and Extensions

- Physics
- 2004

I present a pedagogical review of Heisenberg-Euler effective Lagrangians, beginning with the original work of Heisenberg and Euler, and Weisskopf, for the one loop effective action of quantum…

In-out formalism for the QED effective action in a constant electromagnetic field

- Physics
- 2012

In the in-out formalism, the effective action is given by the vacuum persistence amplitude and is expressed by using Bogoliubov coefficients between the in-vacuum and the out-vacuum. In the second…

Landau Levels in QED in Time-Dependent Magnetic Fields

- Physics
- 2013

The Landau levels of charged fermions in QED make continuous transitions under a homogeneous, time-dependent magnetic field. We analytically formulate the quantum motion as the Cauchy initial value…

Renormalized effective actions in radially symmetric backgrounds: Partial wave cutoff method

- Physics
- 2006

The computation of the one-loop effective action in a radially symmetric background can be reduced to a sum over partial-wave contributions, each of which is the logarithm of an appropriate…

Borel summation of the derivative expansion and effective actions

- Physics
- 1999

We argue that the derivative expansion of the QED effective action is a divergent but Borel summable asymptotic series, for a particular inhomogeneous background magnetic field. A duality…

#### References

SHOWING 1-8 OF 8 REFERENCES

An All-Orders Derivative Expansion

- Physics
- 1996

We evaluate the exact $QED_{2+1}$ effective action for fermions in the presence of a family of static but spatially inhomogeneous magnetic field profiles. This exact result yields an all-orders…

Derivative expansion for the one-loop effective Lagrangian in QED

- Physics
- 1996

The derivative expansion of the one-loop effective Lagrangian in QED4 is considered. The first term in such an expansion is the famous Schwinger result for a constant electromagnetic field. In this…

Derivative expansions in quantum electrodynamics.

- Physics, MedicinePhysical review. D, Particles and fields
- 1989

A new method for calculating the covariant derivative expansions is presented, particularly in Abelian gauge theories, which can be used to find derivative expansions around nonvanishing gauge…

On gauge invariance and vacuum polarization

- Physics
- 1951

This paper is based on the elementary remark that the extraction of gauge invariant results from a formally gauge invariant theory is ensured if one employs methods of solution that involve only…

Effective Energy for QED 2 + 1 with Semilocalized Static Magnetic Field : A Solvable Model ”

- Phys . Rev . D
- 1995

Effective Energy for QED 2 + 1 with Semilocalized Static Magnetic Field : A Solvable Model ”

- Phys . Rev . D
- 1995

Effective Energy for QED 2+1 with Semi-localized Static Magnetic Field: A Solvable Model

- Phys. Rev. D
- 1995

Derivative expansions of fermion determinants: Anomaly-induced vertices, Goldstone-Wilczek currents, and Skyrme terms.

- Physics, MedicinePhysical review. D, Particles and fields
- 1985