The possibility of the non-perturbative an-harmonic correction to Mehler's formula for propagator of the harmonic oscillator
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2013
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| _version_ | 1866910411124637696 |
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| author | Boháčik, J. Prešnajder, P. Augustín, P. |
| author_facet | Boháčik, J. Prešnajder, P. Augustín, P. |
| contents | We find the possibility of the non-perturbative an-harmonic correction to Mehler's formula for propagator of the harmonic oscillator. We evaluate the conditional Wiener measure functional integral with a term of the fourth order in the exponent by an alternative method as in the conventional perturbative approach. In contrast to the conventional perturbation theory, we expand into power series the term linear in the integration variable in the exponent. We discuss the case, when the starting point of the propagator is zero. We present the results in analytical form for positive and negative frequency. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1306_1694 |
| institution | arXiv |
| publishDate | 2013 |
| record_format | arxiv |
| spellingShingle | The possibility of the non-perturbative an-harmonic correction to Mehler's formula for propagator of the harmonic oscillator Boháčik, J. Prešnajder, P. Augustín, P. Mathematical Physics High Energy Physics - Theory Quantum Physics We find the possibility of the non-perturbative an-harmonic correction to Mehler's formula for propagator of the harmonic oscillator. We evaluate the conditional Wiener measure functional integral with a term of the fourth order in the exponent by an alternative method as in the conventional perturbative approach. In contrast to the conventional perturbation theory, we expand into power series the term linear in the integration variable in the exponent. We discuss the case, when the starting point of the propagator is zero. We present the results in analytical form for positive and negative frequency. |
| title | The possibility of the non-perturbative an-harmonic correction to Mehler's formula for propagator of the harmonic oscillator |
| topic | Mathematical Physics High Energy Physics - Theory Quantum Physics |
| url | https://arxiv.org/abs/1306.1694 |