On The Spectral Zeta Function For The Noncommutative Harmonic Oscillator
نویسندگان
چکیده
منابع مشابه
Special value formula for the spectral zeta function of the non-commutative harmonic oscillator
This series is absolutely convergent in the region Rs > 1, and defines a holomorphic function in s there. We call this function ζQ(s) the spectral zeta function for the non-commutative harmonic oscillator Q, which is introduced and studied by Ichinose and Wakayama [1]. The zeta function ζQ(s) is analytically continued to the whole complex plane as a single-valued meromorphic function which is h...
متن کاملThe Zeta Function Method and the Harmonic Oscillator Propagator
We show how the pre-exponential factor of the Feynman propagator for the harmonic oscillator can be computed by the generalized ζ-function method. Besides, we establish a direct equivalence between this method and Schwinger’s propertime method. ⋆ e-mail: [email protected] † e-mail: [email protected] 1 In a recent paper that appeared in this journal [1] the harmonic oscillator propagator was e...
متن کاملHigher Apéry-like numbers arising from special values of the spectral zeta function for the non-commutative harmonic oscillator
A generalization of the Apéry-like numbers, which is used to describe the special values ζQ(2) and ζQ(3) of the spectral zeta function for the non-commutative harmonic oscillator, are introduced and studied. In fact, we give a recurrence relation for them, which shows a ladder structure among them. Further, we consider the ‘rational part’ of the higher Apéry-like numbers. We discuss several kin...
متن کاملA Variation of Multiple L-values Arising from the Spectral Zeta Function of the Non-commutative Harmonic Oscillator
A variation of multiple L-values, which arises from the description of the special values of the spectral zeta function of the non-commutative harmonic oscillator, is introduced. In some special cases, we show that its generating function can be written in terms of the gamma functions. This result enables us to obtain explicit evaluations of them.
متن کاملNoncommutative Geometry and the Riemann Zeta Function
According to my first teacher Gustave Choquet one does, by openly facing a well known unsolved problem, run the risk of being remembered more by one’s failure than anything else. After reaching a certain age, I realized that waiting “safely” until one reaches the end-point of one’s life is an equally selfdefeating alternative. In this paper I shall first look back at my early work on the classi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Reports on Mathematical Physics
سال: 2007
ISSN: 0034-4877
DOI: 10.1016/s0034-4877(07)80077-2