Progress of Theoretical Physics
Vol. 107 No. 1 (2002) pp. 211-230
URL : http://ptp.ipap.jp/link?PTP/107/211/
DOI : 10.1143/PTP.107.211

A New Approach to Scalar Field Theory on Noncommutative Space

Yoshinobu Habara^*

(Received May 1, 2001)

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.

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

References:

1. A. Connes, Noncommutative Geometry (Academic Press, Inc.).
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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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