Worldline instantons, vacuum pair production and Gutzwiller's trace formula

Journal of Physics A: Mathematical and Theoretical

Volumn 41, Issue 16, 2008, Pages

  Dunne, Gerald V ^a,b  

^a UNIVERSITY OF CONNECTICUT   (United States)

^b INSTITUT FÜR THEORETISCHE PHYSIK   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 42949161568     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/41/16/164041     Document Type: Conference Paper

References (40)

1. Heisenberg W and Euler H 1936 Consequences of Dirac's theory of positrons Z. Phys. 98 714 (Engl. Transl.) (Preprint physics/0605038)
2. Dunne G V 2004 Heisenberg-Euler effective Lagrangians: basics and extensions (Ian Kogan Memorial Collection) From Fields to Strings: Circumnavigating Theoretical Physics vol 1 ed M Shifman et al pp 445-522 (Preprint hep-th/0406216)
3. Ringwald A 2003 Fundamental physics at an x-ray free electron laser Proc. Erice Workshop on Electromagnetic Probes of Fundamental Physics ed W Marciano and S White (Singapore: World Scientific) (Preprint hep-ph/0112254)
4. Schwinger J 1951 On gauge invariance and vacuum polarization Phys. Rev. 82 664
5. Keldysh L V 1965 Ionization in the field of a strong electromagnetic wave Sov. Phys.-JETP 20 1307
6. Narozhnyi N B and Nikishov A I 1970 The simplest processes in a pair-producing field Yad. Fiz. 11 1072
7. Narozhnyi N B and Nikishov A I 1970 The simplest processes in a pair-producing field Sov. J. Nucl. Phys. 11 596 (Engl. Transl.)
8. Brézin E and Itzykson C 1970 Pair production in vacuum by an alternating field Phys. Rev. D 2 1191
9. Popov V S 1972 Pair production in a variable external field (quasiclassical approximation) Sov. Phys.-JETP 34 709
10. Popov V S and Marinov M S 1972 Pair production in a variable and homogeneous electric field as an oscillator problem Sov. Phys.-JETP 35 659
11. Kim S P and Page D N 2002 Schwinger pair production via instantons in a strong electric field Phys. Rev. D 65 105002 (Preprint hep-th/0005078)
12. Kim S P and Page D N 2006 Schwinger pair production in electric and magnetic fields Phys. Rev. D 73 065020 (Preprint hep-th/0301132)
13. Dunne G V and Schubert C 2005 Worldline instantons and pair production in inhomogeneous fields Phys. Rev. D 72 105004 (Preprint hep-th/0507174)
14. Dunne G V, Wang Q-h, Gies H and Schubert C 2006 Worldline instantons: II. The fluctuation prefactor Phys. Rev. D 73 065028 (Preprint hep-th/0602176)
15. Dunne G V and Wang Q-h 2006 Multidimensional worldline instantons Phys. Rev. D 74 065015 (Preprint hep-th/0608020)
16. Gutzwiller M C 1971 Periodic orbits and classical quantization conditions J. Math. Phys. 12 343
17. Littlejohn R G 1990 Semiclassical structure of trace formulas J. Math. Phys. 31 2952
18. Cvitanović P et al Chaos: Classical and Quantum http://chaosbook.org/
19. Muratore-Ginanneschi P 2003 Path integration over closed loops and Gutzwiller's trace formula Phys. Rep. 383 299 (Preprint nlin.cd/0210047)
20. Dietrich D D and Dunne G V 2007 Gutzwiller's trace formula and vacuum pair production J. Phys. A: Math. Theor. 40 F825-30 (Preprint 0706.4006)
21. Feynman R P 1950 Mathematical formulation of the quantum theory of electromagnetic interaction Phys. Rev. 80 440
22. Feynman R P 1951 An operator calculus having applications in quantum electrodynamics Phys. Rev. 84 108
23. Halpern M B, Jevicki A and Senjanovic P 1977 Field theories in terms of particle-string variables: spin, internal symmetry and arbitrary dimension Phys. Rev. D 16 2476
24. Halpern M B and Siegel W 1977 The particle limit of field theory: a new strong coupling expansion Phys. Rev. D 16 2486
25. For an extensive review, see Schubert C 2001 Perturbative quantum field theory in the string-inspired formalism Phys. Rep. 355 73 (Preprint hep-th/0101036)
26. Gies H and Langfeld K 2001 Quantum diffusion of magnetic fields in a numerical worldline approach Nucl. Phys. B 613 353 (Preprint hep-ph/0102185)
27. Gies H and Langfeld K 2002 Loops and loop clouds: a numerical approach to the worldline formalism in QED Int. J. Mod. Phys. A 17 966 (Preprint hep-ph/0112198)
28. Gies H, Langfeld K and Moyaerts L 2003 Casimir effect on the worldline J. High Energy Phys. JHEP06(2003)018 (Preprint hep-th/0303264)
29. Gies H and Klingmüller K 2006 Casimir effect for curved geometries: PFA validity limits Phys. Rev. Lett. 96 220401 (Preprint quant-ph/0601094)
30. Gies H and Klingmüller K 2005 Pair production in inhomogeneous fields Phys. Rev. D 72 065001 (Preprint hep-ph/0505099)
31. Affleck I K, Alvarez O and Manton N S 1982 Pair production at strong coupling in weak external fields Nucl. Phys. B 197 509
32. Gies H and Klingmüller K 2005 Pair production in inhomogeneous fields Phys. Rev. D 72 065001 (Preprint hep-ph/0505099)
33. Gelfand I M and Yaglom A M 1960 Integration in functional spaces and its applications in quantum physics J. Math. Phys. 1 48
34. Levit S and Smilansky U 1977 A theorem on infinite products of eigenvalues of Sturm-Liouville type Proc. Am. Math. Soc. 65 299
35. Kirsten K and McKane A J 2004 Functional determinants for general Sturm-Liouville problems J. Phys. A: Math. Gen. 37 4649 (Preprint math-ph/0403050)
36. Kleinert H 2004 Path Integrals in Quantum Mechanics, Statistics, Polymer Physics and Financial Markets (Singapore: World Scientific)
37. Nambu Y 1968 Quantum electrodynamics in nonlinear gauge Prog. Theor. Phys. Suppl. 190 (we are indebted to Ö Sarioǧlu and B Tekin for this reference)
38. Wong S K 1970 Field and particle equations for the classical Yang-Mills field and particles with isotopic spin Nuovo Cimento A 65 689
39. Iancu E, Leonidov A and McLerran L D 2001 Nonlinear gluon evolution in the color glass condensate: I Nucl. Phys. A 692 583 (Preprint hep-ph/0011241)
40. Jalilian-Marian J, Jeon S and Venugopalan R 2001 Wong's equations and the small x effective action in QCD Phys. Rev. D 63 036004 (Preprint hep-ph/0003070)