Comptes Rendus
no. 8
Mathematical Physics
A formal computation of the splitting for the Klein–Gordon operator

Presented by: Jean-Michel Bony

Emmanuelle Servat1
1 The Fields Institute, 222 College Street, Toronto, Ontario, M5T 3J1, Canada
Comptes Rendus. Mathématique, Volume 338 (2004) no. 8, pp. 657-660.

We study the semi-classical Klein–Gordon operator in the one dimensional case, for a double-well potential. We obtain a formal computation of the splitting in cases that were not yet studied.

On étudie l'opérateur de Klein–Gordon dans le cas de la dimension un, pour un potentiel présentant un double puits symétrique. On obtient une expression formelle du splitting dans des cas qui n'étaient pas envisagés auparavant.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2004.02.005

Emmanuelle Servat 1

1 The Fields Institute, 222 College Street, Toronto, Ontario, M5T 3J1, Canada 
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Emmanuelle Servat. A formal computation of the splitting for the Klein–Gordon operator. Comptes Rendus. Mathématique, Volume 338 (2004) no. 8, pp. 657-660. doi : 10.1016/j.crma.2004.02.005. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.02.005/

[1] M. Dimassi; J. Sjöstrand Spectral Asymptotics in the Semi-Classical Limit, London Math. Soc. Lecture Note Ser., vol. 268, Cambridge University Press, Cambridge, 1999

[2] B. Helffer; B. Parisse Comparaison entre la décroissance de fonctions propres pour les opérateurs de Dirac et de Klein–Gordon. Application à l'effet tunnel, Ann. Inst. H. Poincaré, Volume 60 (1994), pp. 147-187

[3] B. Helffer; J. Sjöstrand Multiple wells in the semi-classical limit I, Comm. Partial Differential Equations, Volume 9 (1984), pp. 337-408

[4] M. Reed; B. Simon Methods of Modern Mathematical Physics I–IV, Academic Press, New York, 1975

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