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Prog. Theor. Phys. Vol. 107 No. 1 (2002) pp. 211-230

A New Approach to Scalar Field Theory on Noncommutative Space

Yoshinobu Habara^*

Yukawa Institute for Theoretical Physics, Kyoto University,
Kyoto 606-8502, Japan

(Received May 1, 2001)

Abstract:

A new approach to constructing a noncommutative scalar field theory is presented. We give non-trivial commutation relations not only between \hatx_i and \hatp_j but also between \hatx_i and \hatx_j and between \hatp_i and \hatp_j. We also give a new representation of \hatx_i and \hatp_i. We carry out both first and second quantization explicitly. The second quantization is performed in both the operator formalism and the functional integral formalism.

URL : http://ptp.ipap.jp/link?PTP/107/211/
DOI : 10.1143/PTP.107.211

^*E-mail: habara@yukawa.kyoto-u.ac.jp

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References:

1. A. Connes, Noncommutative Geometry (Academic Press, Inc.).
2. A. Connes, M. R. Douglas and A. Schwarz, hep-th/9711162[e-print arXiv].
3. G. Landi, hep-th/9701078[e-print arXiv].
4. T. Banks, W. Fischler, S. H. Shenker and L. Susskind, hep-th/9610043[e-print arXiv].
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7. S. Minwalla, M. Van Raamsdonk and N. Seiberg, hep-th/9912072[e-print arXiv].
8. Jean Zinn-Justin, Quantum Field Theory and Critical Phenomena (Oxford Science Publications).

Citing Article(s) :

1. Progress of Theoretical Physics Vol. 109 No. 3 (2003) pp. 465-481 :

   Supersymmetric Field Theories on Noncommutative Spaces

   Yoshinobu Habara

2. Progress of Theoretical Physics Vol. 116 No. 4 (2006) pp. 771-781 :

   Gauge Theory and a Dirac Operator on a Noncommutative Space

   Yoshinobu Habara

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