# Fast way to compute functional determinants of radially symmetric partial differential operators in general dimensions

@article{Hur2008FastWT, title={Fast way to compute functional determinants of radially symmetric partial differential operators in general dimensions}, author={Jin Hur and Hyunsoo Min}, journal={Physical Review D}, year={2008}, volume={77}, pages={125033} }

Recently the partial-wave cutoff method was developed as a new calculational scheme for a functional determinant of quantum field theory in radial backgrounds. For the contribution given by an infinite sum of large partial waves, we derive explicitly radial-WKB series in the angular momentum cutoff for d=2, 3, 4, and 5 (d is the space-time dimension), which has uniform validity irrespectively of any specific values assumed for other parameters. Utilizing this series, precision evaluation of the…

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## References

SHOWING 1-10 OF 24 REFERENCES

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

- Physics, Mathematics
- 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…

### Functional determinants for radial operators

- Physics
- 2006

We derive simple new expressions, in various dimensions, for the functional determinant of a radially separable partial differential operator, thereby generalizing the one-dimensional result of…

### Calculation of QCD instanton determinant with arbitrary mass

- Physics
- 2005

The precise quark mass dependence of the one-loop effective action in an instanton background has recently been computed [Phys. Rev. Lett. 94, 072001 (2005).]. The result interpolates smoothly…

### Precise quark-mass dependence of the instanton determinant.

- PhysicsPhysical review letters
- 2005

The fermion determinant in an instanton background for a quark field of arbitrary mass is determined exactly using an efficient numerical method to evaluate the determinant of a partial-wave radial…

### Renormalized effective actions in radially symmetric backgrounds: Exact calculations versus approximation methods

- Physics
- 2008

Our previously developed calculational method (the partial-wave cutoff method) is employed to evaluate explicitly scalar one-loop effective actions in a class of radially symmetric background gauge…

### Beyond the thin-wall approximation : Precise numerical computation of prefactors in false vacuum decay

- Physics
- 2005

We present a general numerical method for computing precisely the false vacuum decay rate, including the prefactor due to quantum fluctuations about the classical bounce solution, in a…

### Instanton determinant with arbitrary quark mass: WKB phase-shift method and derivative expansion

- Physics
- 2004

### One loop corrections to the metastable vacuum decay

- Physics
- 2004

We evaluate the one-loop prefactor in the false vacuum decay rate in a theory of a self-interacting scalar field in $3+1$ dimensions. We use a numerical method, established some time ago, which is…

### Functional determinants and geometry

- Mathematics
- 1987

SummaryIn this paper we study the zeta-function determinant in the context of elliptic boundary value problems. Our main technique is to relate the determinant of an operator, or a ratio of…

### Massive field contributions to the QCD vacuum tunneling amplitude

- Physics
- 2000

For the one-loop contribution to the QCD vacuum tunneling amplitude by quarks of generic mass value, we make use of a calculational scheme exploiting a large mass expansion together with a small mass…